It’s hard to think when someone Hadamards your brain

“Unperformed measurements have no results.” —Asher Peres


With two looming paper deadlines, two rambunctious kids, an undergrad class, program committee work, faculty recruiting, and an imminent trip to Capitol Hill to answer congressional staffers’ questions about quantum computing (and for good measure, to give talks at UMD and Johns Hopkins), the only sensible thing to do is to spend my time writing a blog post.

So: a bunch of people asked for my reaction to the new Nature Communications paper by Daniela Frauchiger and Renato Renner, provocatively titled “Quantum theory cannot consistently describe the use of itself.”  Here’s the abstract:

Quantum theory provides an extremely accurate description of fundamental processes in physics.  It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally.  Here, we propose a Gedankenexperiment to investigate the question whether quantum theory can, in principle, have universal validity.  The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory.  Analysing the experiment under this presumption, we find that one agent, upon observing a particular measurement outcome, must conclude that another agent has predicted the opposite outcome with certainty.  The agents’ conclusions, although all derived within quantum theory, are thus inconsistent.  This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.

I first encountered Frauchiger and Renner’s argument back in July, when Renner (who I’ve known for years, and who has many beautiful results in quantum information) presented it at a summer school in Boulder, CO where I was also lecturing.  I was sufficiently interested (or annoyed?) that I pulled an all-nighter working through the argument, then discussed it at lunch with Renner as well as John Preskill.  I enjoyed figuring out exactly where I get off Frauchiger and Renner’s train—since I do get off their train.  While I found their paper thought-provoking, I reject the contention that there’s any new problem with QM’s logical consistency: for reasons I’ll explain, I think there’s only the same quantum weirdness that (to put it mildly) we’ve known about for quite some time.

In more detail, the paper makes a big deal about how the new argument rests on just three assumptions (briefly, QM works, measurements have definite outcomes, and the “transitivity of knowledge”); and how if you reject the argument, then you must reject at least one of the three assumptions; and how different interpretations (Copenhagen, Many-Worlds, Bohmian mechanics, etc.) make different choices about what to reject.

But I reject an assumption that Frauchiger and Renner never formalize.  That assumption is, basically: “it makes sense to chain together statements that involve superposed agents measuring each other’s brains in different incompatible bases, as if the statements still referred to a world where these measurements weren’t being done.”  I say: in QM, even statements that look “certain” in isolation might really mean something like “if measurement X is performed, then Y will certainly be a property of the outcome.”  The trouble arises when we have multiple such statements, involving different measurements X1, X2, …, and (let’s say) performing X1 destroys the original situation in which we were talking about performing X2.

But I’m getting ahead of myself.  The first thing to understand about Frauchiger and Renner’s argument is that, as they acknowledge, it’s not entirely new.  As Preskill helped me realize, the argument can be understood as simply the “Wigner’s-friendification” of Hardy’s Paradox.  In other words, the new paradox is exactly what you get if you take Hardy’s paradox from 1992, and promote its entangled qubits to the status of conscious observers who are in superpositions over thinking different thoughts.  Having talked to Renner about it, I don’t think he fully endorses the preceding statement.  But since I fully endorse it, let me explain the two ingredients that I think are getting combined here—starting with Hardy’s paradox, which I confess I didn’t know (despite knowing Lucien Hardy himself!) before the Frauchiger-Renner paper forced me to learn it.

Hardy’s paradox involves the two-qubit entangled state

$$\left|\psi\right\rangle = \frac{\left|00\right\rangle + \left|01\right\rangle + \left|10\right\rangle}{\sqrt{3}}.$$

And it involves two agents, Alice and Bob, who measure the left and right qubits respectively, both in the {|+〉,|-〉} basis.  Using the Born rule, we can straightforwardly calculate the probability that Alice and Bob both see the outcome |-〉 as 1/12.

So what’s the paradox?  Well, let me now “prove” to you that Alice and Bob can never both get |-〉.  Looking at |ψ〉, we see that conditioned on Alice’s qubit being in the state |0〉, Bob’s qubit is in the state |+〉, so Bob can never see |-〉.  And conversely, conditioned on Bob’s qubit being in the state |0〉, Alice’s qubit is in the state |+〉, so Alice can never see |-〉.  OK, but since |ψ〉 has no |11〉 component, at least one of the two qubits must be in the state |0〉, so therefore at least one of Alice and Bob must see |+〉!

When it’s spelled out so plainly, the error is apparent.  Namely, what do we even mean by a phrase like “conditioned on Bob’s qubit being in the state |0〉,” unless Bob actually measured his qubit in the {|0〉,|1〉} basis?  But if Bob measured his qubit in the {|0〉,|1〉} basis, then we’d be talking about a different, counterfactual experiment.  In the actual experiment, Bob measures his qubit only in the {|+〉,|-〉} basis, and Alice does likewise.  As Asher Peres put it, “unperformed measurements have no results.”

Anyway, as I said, if you strip away the words and look only at the actual setup, it seems to me that Frauchiger and Renner’s contribution is basically to combine Hardy’s paradox with the earlier Wigner’s friend paradox.  They thereby create something that doesn’t involve counterfactuals quite as obviously as Hardy’s paradox does, and so requires a new discussion.

But to back up: what is Wigner’s friend?  Well, it’s basically just Schrödinger’s cat, except that now it’s no longer a cat being maintained in coherent superposition but a person, and we’re emphatic in demanding that this person be treated as a quantum-mechanical observer.  Thus, suppose Wigner entangles his friend with a qubit, like so:

$$ \left|\psi\right\rangle = \frac{\left|0\right\rangle \left|FriendSeeing0\right\rangle + \left|1\right\rangle \left|FriendSeeing1\right\rangle}{\sqrt{2}}. $$

From the friend’s perspective, the qubit has been measured and has collapsed to either |0〉 or |1〉.  From Wigner’s perspective, no such thing has happened—there’s only been unitary evolution—and in principle, Wigner could even confirm that by measuring |ψ〉 in a basis that included |ψ〉 as one of the basis vectors.  But how can they both be right?

Many-Worlders will yawn at this question, since for them, of course “the collapse of the wavefunction” is just an illusion created by the branching worlds, and with sufficiently advanced technology, one observer might experience the illusion even while a nearby observer doesn’t.  Ironically, the neo-Copenhagenists / Quantum Bayesians / whatever they now call themselves, though they consider themselves diametrically opposed to the Many-Worlders (and vice versa), will also yawn at the question, since their whole philosophy is about how physics is observer-relative and it’s sinful even to think about an objective, God-given “quantum state of the universe.”  If, on the other hand, you believed both that

  1. collapse is an objective physical event, and
  2. human mental states can be superposed just like anything else in the physical universe,

then Wigner’s thought experiment probably should rock your world.

OK, but how do we Wigner’s-friendify Hardy’s paradox?  Simple: in the state

$$\left|\psi\right\rangle = \frac{\left|00\right\rangle + \left|01\right\rangle + \left|10\right\rangle}{\sqrt{3}},$$

we “promote” Alice’s and Bob’s entangled qubits to two conscious observers, call them Charlie and Diane respectively, who can think two different thoughts that we represent by the states |0〉 and |1〉.  Using far-future technology, Charlie and Diane have been not merely placed into coherent superpositions over mental states but also entangled with each other.

Then, as before, Alice will measure Charlie’s brain in the {|+〉,|-〉} basis, and Bob will measure Diane’s brain in the {|+〉,|-〉} basis.  Since the whole setup is mathematically identical to that of Hardy’s paradox, the probability that Alice and Bob both get the outcome |-〉 is again 1/12.

Ah, but now we can reason as follows:

  1. Whenever Alice gets the outcome |-〉, she knows that Diane must be in the |1〉 state (since, if Diane were in the |0〉 state, then Alice would’ve certainly seen |+〉).
  2. Whenever Diane is in the |1〉 state, she knows that Charlie must be in the |0〉 state (since there’s no |11〉 component).
  3. Whenever Charlie is in the |0〉 state, she knows that Diane is in the |+〉 state, and hence Bob can’t possibly see the outcome |-〉 when he measures Diane’s brain in the {|+〉,|-〉} basis.

So to summarize, Alice knows that Diane knows that Charlie knows that Bob can’t possibly see the outcome |-〉.  By the “transitivity of knowledge,” this implies that Alice herself knows that Bob can’t possibly see |-〉.  And yet, as we pointed out before, quantum mechanics predicts that Bob can see |-〉, even when Alice has also seen |-〉.  And Alice and Bob could even do the experiment, and compare notes, and see that their “certain knowledge” was false.  Ergo, “quantum theory can’t consistently describe its own use”!

You might wonder: compared to Hardy’s original paradox, what have we gained by waving a magic wand over our two entangled qubits, and calling them “conscious observers”?  Frauchiger and Renner’s central claim is that, by this gambit, they’ve gotten rid of the illegal counterfactual reasoning that we needed to reach a contradiction in our analysis of Hardy’s paradox.  After all, they say, none of the steps in their argument involve any measurements that aren’t actually performed!  But clearly, even if no one literally measures Charlie in the {|0〉,|1〉} basis, he’s still there, thinking either the thought corresponding to |0〉 or the thought corresponding to |1〉.  And likewise Diane.  Just as much as Alice and Bob, Charlie and Diane both exist even if no one measures them, and they can reason about what they know and what they know that others know.  So then we’re free to chain together the “certainties” of Alice, Bob, Charlie, and Diane in order to produce our contradiction.

As I already indicated, I reject this line of reasoning.  Specifically, I get off the train at what I called step 3 above.  Why?  Because the inference from Charlie being in the |0〉 state to Bob seeing the outcome |+〉 holds for the original state |ψ〉, but in my view it ceases to hold once we know that Alice is going to measure Charlie in the {|+〉,|-〉} basis, which would involve a drastic unitary transformation (specifically, a “Hadamard”) on the quantum state of Charlie’s brain.  I.e., I don’t accept that we can take knowledge inferences that would hold in a hypothetical world where |ψ〉 remained unmeasured, with a particular “branching structure” (as a Many-Worlder might put it), and extend them to the situation where Alice performs a rather violent measurement on |ψ〉 that changes the branching structure by scrambling Charlie’s brain.

In quantum mechanics, measure or measure not: there is no if you hadn’t measured.


Unrelated Announcement: My awesome former PhD student Michael Forbes, who’s now on the faculty at the University of Illinois Urbana-Champaign, asked me to advertise that the UIUC CS department is hiring this year in all areas, emphatically including quantum computing. And, well, I guess my desire to do Michael a solid outweighed my fear of being tried for treason by my own department’s recruiting committee…


Another Unrelated Announcement: As of Sept. 25, 2018, it is the official editorial stance of Shtetl-Optimized that the Riemann Hypothesis and the abc conjecture both remain open problems.

294 Responses to “It’s hard to think when someone Hadamards your brain”

  1. Quantum theory - Nature Paper 18 Sept | Page 2 | Physics Forums Says:

    […] is a recent comment by Scott Aaronson on Frauchiger's and Renner's paper: https://www.scottaaronson.com/blog/?p=3975   Lord Jestocost, Sep 25, 2018 at 4:09 […]

  2. Usman Nizami Says:

    Sir how can great mathematician like Michael Atiyah come up with false proof of Riemann hypothesis? He is making mistakes in recent years. Is that because of his age. Dpse no one do a good math in old age? What do you think? Atiyah has said “Solve the Riemann hypothesis and you become famous. If you are famous already, you become infamous, ”

    And what is problem with Inter-universal Teichmüller theory. Shinichi Mochizuki is serious mathematician. How one should handle such complicated work.

  3. Usman Nizami Says:

    So Michael Atiyah’s proof of Riemann hypothesis is wrong.

  4. Peter Says:

    Wow, they really went out of their way to rehash a pretty basic reformulation of psychologism, I guess this time with quantum mechanics. Maybe I’ve just had to read and reread too much Frege over the years but the second I saw “it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory” in the abstract I knew exactly what the rest of the paper was going to be arguing for.

    I think that your technical arguments against their conclusion are sound and do a great job of showing part of what the issue is. I would love to see them engage with the philosophy on this topic and defend why they think quantum mechanics opens the door to psychologism, rather than implying it ambiently and just focusing on a technical physical argument.

  5. Jay Says:

    So clear, thanks!

    Unrelated question about entropy, computation and neural nets.

    Because of adiabetic computing we could theorically perform a computation as long as we want for free. Because of Landauer’s principle we know that measuring the result (and preparing the computation) must always incur at some entropy cost.

    Now, non linearities are considered a key ingredient for deep learning (actually for any neural net, deep or shallow). However, because of the former lines it seems that deep learning could theorically rely on linear transforms only, and delays the true non linearities until we want to measure the resulting net. Are they known caveats? For example, one could imagine that measuring the error gradient might require either a true non linearity (and some entropy cost) or keeping track of all the examples (at no entropy cost but at the cost of increasing computation length or memory requirement). Do you know the answer or where you would start looking for an answer?

  6. Scott Says:

    Peter #4: But this is actually not a question that can be resolved with verbal philosophy. The reason their paper was published in Nature is that they give a technical argument for why the axioms of QM, together with certain reasonable-looking auxiliary postulates, lead to a contradiction. That demands a response that meets their argument on the battlefield, for example by identifying an error, rejecting one of the postulates, or (as I think I did) identifying and rejecting an additional unstated postulate.

  7. David Says:

    Peter #4

    “just focusing on a technical physical argument”

    Well, they are physicists, not philosophers.

  8. DarMM Says:

    Scott,

    My reading of the paper:

    Bob (I think I have the F,F’,W,W’ to Alice,Bob,Charlie,Diane Map right! :)) when reasoning using the initial state would conclude he and Alice will get (okay,okay) 1/12 of the time. However when reasoning about Charlie’s reasoning (concerning Diane) he would conclude this is impossible.

    The bulk of the paper concerns Bob “transferring” Charlie’s conclusion to himself, via a special case of the Born Rule (P(E) = 1) and the assumption of consistent reasoning between agents.

    However your point is that one of the steps in the transference involves hearing about an Alice measurement. However an Alice measurement is the exact scenario that would invalidate Charlie’s initial reasoning and thus Bob should discard Charlie’s original reasoning about Diane.

    Is this remotely correct?

  9. Scott Says:

    DarMM #7: Yes, that sounds right to me.

  10. DarMM Says:

    Scott #8: Thanks, kind of you to answer.

  11. John K Clark Says:

    The inability of the mathematical community to figure out if the proofs of the ABC conjecture and the Riemann hypothesis are valid makes me wonder if that could have implications for another unsolved problem, is P= NP? If they are not equal then you’d expect it would be fundamentally easier to check a proof than find a proof, but then why are world class mathematicians unable to check them? If I have a valid proof of the ABC conjecture but it would take you as much brain power to understand it as it would for you to find a proof of it on your own have I accomplished anything of value, would there be any point in you reading it?

    John K Clark

  12. Daniel Says:

    This seems like yet another example of someone trying to pound a round peg (quantum mechanics) into a square hole (classical measurement theory) and getting confused. The contradiction is with the antiquated assumptions of the authors, not with quantum mechanics.

  13. Scott Says:

    John #10: No, it’s much more prosaic than that. According to Erica Klarreich’s excellent Quanta article, Scholze identified the issues with Corollary 3.12 of Mochizuki’s paper not long after the paper came out, but held off on going public because he hoped someone else would do it, and it sounds like the same may have been true for other experts. As for Atiyah’s claimed half-page proof of RH, it looks like people were pointing out serious issues with it within hours.

  14. Neel Krishnaswami Says:

    Hi Scott, can you explain to me what people are trying to achieve with “quantum interpretations”? (This sounds more hostile than I mean it — I’m actually genuinely confused.)

    To my understanding, undergrad QM consists of basically four claims:

    1. States of an experimental system are described by elements of a Hilbert space.
    2. Observables are self-adjoint operators of that Hilbert space.
    3. The time evolution of an experimental system is described by the Schrodinger equation.
    4. Observing an experimental system is described by Born’s law.

    The repetition of “experimental system” here means that we are talking about controlled experiments: a system which is isolated from the rest of the universe, with the sole interaction being the process of observation. (This ideal is hard to achieve in practice, but experimental physicists and engineers are getting ever better at it.)

    Since (a) Born’s law has a statistical, probabilistic character unlike the other three parts of QM, and (b) observation is a primitive concept of quantum mechanics, it is reasonable to wonder if it can be derived. That is, can we model both an observer and an experiment as a larger, interacting quantum system, and then derive the Born rule for the observer from an analysis of the joint system? (Basically, this is what I understand the measurement problem to be.)

    This seems like a really great, natural question to me. If we can, that’s great news! We now know where Born’s law comes from, in the same way that statistical mechanics explains where thermodynamics comes from. If we can’t, that’s even better, because it means that there must be some deep physics we have overlooked, which make Born’s law work out!

    But, it seems like to answer that question, we have to do the work: someone has to come up with a physically reasonable model of a coupled system consisting of an experiment and observer, and then actually solve the equations. Only then can the model be compared with the empirical fact of Born’s rule.

    Quantum interpretations (like MWI) mostly seem like an assertion that if you wave your hands enough, you don’t need to do this work, a claim I find deeply dubious. But plenty of smart people — people who have thought much more about QM than me! — seem to think that there is something serious going on with these interpretations. So there must be something I’m missing.

  15. Peter Says:

    Scott #5, David #6

    I feel as though both of you missed my point.

    “I would love to see them engage with the philosophy on this topic and defend why they think quantum mechanics opens the door to psychologism, rather than implying it ambiently and just focusing on a technical physical argument.”

    I said I would love *to see* them do this. As in, it would make me happy if they did this. So saying, “well they wrote a technical paper” isn’t a counter to what I said. I didn’t say they should be reprimanded and banished from academia for doing what they did, I said I would love it if they had engaged one of the glaring issues in their argument instead of only presenting a technical argument. I am not going to say that every physics paper requires half of it to be about philosophy, it doesn’t in the slightest. But why is me saying “I wish they had engaged in the philosophical issues here” in regards to a paper that makes claims about questions at the very heart of the grey area between physics and philosophy, reductionism and it’s ilk, refutable by pointing out that they aren’t philosophers?

    Secondly, Scott your second example of what should be done is exactly what I’m saying should be done. On of their postulates is that “contrary to philosophical consensus, this revivification of psychologism is valid.” That is a presupposition they used in their argument, it is not a conclusion that is drawn from their other presuppositions. Me bringing this up is exactly what you described as, “identifying and rejecting an additional unstated postulate.” So I agree completely that we should engage them on their own battlefield. But their battlefield is a grey area and part of their assumptions involve opening the door to a almost universally dismissed school of thought and as I said, I would have loved if they engaged that part of their argument.

    Refuting psychologism isn’t about verbal philosophy. The rejection of a reduction of physical laws to psychological entities and then drawing conclusions about the nature of those laws given various postulates about those psychological entities isn’t just a matter of toying with language. Dismissing someone drawing universal physical and metaphysical conclusions based off of the internal psychological states of agents isn’t just ‘dismissing their language games as pseudo-problems.’

  16. Scott Says:

    Neel #14: Yes, what people are trying to accomplish with “interpretations” is basically just to understand how unitary evolution and measurement can coexist in the same universe, and to put it crudely, how the universe knows when to apply one rule and when the other. On the spectrum of possible positions, MWI is the extreme that answers this question by holding that only unitary evolution has any fundamental ontological status; “measurement” is just an approximate concept that observers use to describe their experience of not knowing which branch of the wavefunction they’re going to find themselves in (i.e., indexical uncertainty). You don’t have to like it — many people don’t! — but it’s certainly a natural point in possibility space; if Hugh Everett hadn’t proposed it then someone else would have.

  17. Joe Says:

    Scott, when are you speaking at JHU? I can’t find any information about the talk online.

  18. Kevin Van Horn Says:

    Forgive my ignorance, but how are the {|0>, |1>} and {|+>, |->} bases related? You mentioned the Hadamard transformation; is that what relates them?

  19. Scott Says:

    Kevin #18: Yes.

  20. Aula Says:

    Scott #13: It seems to me that Atiyah’s claimed proof of RH is in some ways a rerun of Deolalikar’s claimed proof that P!=NP. In each case, the claimed proof both has/had obvious elementary errors (Atiyah appears to have forgotten some basic facts about complex analysis) and is/was trying to prove too much (there are functions that don’t satisfy an analogue of RH but have all those properties of the Riemann zeta function that Atiyah uses), so it’s no wonder that people started to pick apart both attempts almost immediately.

  21. Craig Gidney Says:

    > *in my view it ceases to hold once we know that Alice is going to measure Charlie in the {|+〉,|-〉} basis*

    I would describe this slightly differently. Consider how you would actually go about implementing a measurement in the {|0 BobSawAndThoughtAbout0〉+ |1 BobSawAndThoughtAbout1〉, |0 BobSawAndThoughtAbout0〉- |1 BobSawAndThoughtAbout1〉} basis. I would do it as follows:

    Step 1: Uncompute those pesky “BobSawAndThoughtAbout” qubits. As in literally reverse time for Bob, so he unthinks his thoughts.
    Step 2: The relevant information is now factored into a single qubit. Perform a {|+〉,|-〉} basis measurement on that qubit.
    Step 3: Recompute the “BobSawAndThoughtAbout” qubits.

    The reason that the measurement is a problem is because it forces us to uncompute Bob thinking about his initially-valid conclusion, then recompute him thinking the same things but the conclusions are no longer valid (because the initial qubits are no longer in the |00〉+|10〉+|01〉state).

    In order for Bob’s thoughts to actually be correct, he has to think something like “If this is before the uncomputation and recomputation, and I saw 0, then Alice is definitely in the + state. But if this is after the recomputation, I don’t know what Alice’s state is.”.

  22. Craig Gidney Says:

    Hm, actually, I think this “recompute with different thoughts” paradox has a classical analogue.

    1. Alice and Bob are loaded into separate reversible classical computers.
    2. We flip a coin to generate a random bit, then give Alice and Bob each a copy of that bit.
    3. Suppose w.l.o.g. that the random bit is 0.
    4. We run the computer for a bit. Alice thinks “My bit is 0, therefore Bob’s bit is 0.”. This conclusion is valid.
    5. We uncompute Bob back to the initial state, flip the bit we gave him, and recompute.
    6. Bob’s bit must be in state 1. But using “transitivity of knowledge” it must be in state 0 because Alice validly concluded that his bit was in state 0. Paradox.

    Obviously the mistake here is assuming that Alice’s conclusions about Bob’s state after step 3 must also apply to Bob’s state after step 5. It’s much easier to see the problem here than in the quantum case because the perturbation of Bob is directly described (we flip his bit), instead of hiding behind an anti-commuting measurement.

  23. Scott Says:

    Joe #17: Info for my JHU talk is here. It’s on Thursday at 10:30am.

  24. Edward Measure Says:

    Re Atiyah and the RH: Many years ago, two semi-famous physicists (SFP) were listening to Eddington, then an old man, expound one of the highly questionable theories of his old age. SFP1 to SFP2: “Is that going to happen to us?” SFP2: “Don’t worry – a genius like Eddington may go nuts, but guys like you just get dumber and dumber.”

  25. Harry Johnston Says:

    Neel #14:

    That is, can we model both an observer and an experiment as a larger, interacting quantum system, and then derive the Born rule for the observer from an analysis of the joint system?

    I believe so, sort of. But if I understand correctly, when you ask the question, “what is the probability that I will observe that the other observer got result X” you have to use the Born rule to answer it.

    That’s not a trivial result. It means that it doesn’t matter when you apply the Born rule – you can apply it to the original measurement, or to your observation of the other observer, and you’ll always get the same answer, and that’s important. But it doesn’t really count as an independent derivation of the Born rule.

    Obviously, the “actually solve the equations” bit doesn’t explicitly model a conscious observer, or even a real-world measuring device, but a simplified model of one. I believe one way you might model a measuring device is by allowing the state of the system being measured to interact with a thermodynamic reservoir, which introduces decoherence. You can sum over the microstates of the reservoir to turn the pure quantum state into a density matrix, and that gives you your classical probabilities – but you’re implicitly using the Born rule when you do that.

    I’m told that Everett actually did the necessary math way back in 1957.

    [Epistemic status: mostly guesswork. I haven’t personally read the relevant articles, and I don’t know whether Everett used the approach I suggest above or something different.]

  26. ppnl Says:

    Scott #16

    ” Yes, what people are trying to accomplish with “interpretations” is basically just to understand how unitary evolution and measurement can coexist in the same universe, and to put it crudely, how the universe knows when to apply one rule and when the other.”

    Why doesn’t decoherence answer this in a simple and obvious way?

    You put a system in a box that isolates it and unitary evolution applies. If you allow a tiny interaction with the outside then the Born rule applies in a tiny way. You allow strong thermodynamic interactions and the Born rule is applied many many times in tiny increments and the system looks classical.

    There is no unitary or Born rule. There is just the amount of quantum information leaking out. The Born rule is an expression of the lack of information and so by definition must be random.

  27. Andrei Says:

    Scott,

    My take on these thought experiments involving “isolated” systems is that they are not possible, even in practice.

    There is no way you can build a box so that an outside observer cannot find out, without opening it, if there is a dead cat or alive cat inside. One can for example measure the electric, magnetic, gravitational fields produced by the particles that make up the cat. These fields are of unlimited range and cannot be completely blocked by any box, whatever the material this box is made of.

    In other words, all observers, no matter where they are have access to the same amount of information about the system under consideration, so all those paradoxes disappear.

    What do you think about this?

    Thank you,

    Andrei

  28. mjgeddes Says:

    Both metaphysics and foundations of mathematics need to be clarified to understand quantum mechanics and crack the Riemann hypothesis.

    Coming back to the ‘3 Worlds’ of Penrose (Physics, Mathematics and Cognition) , my current view is that 2 of them *are* fundamental (Physics and Mathematics) and 1 is *not* fundamental- Cognition is emergent and composed of the other two primitives, having no reality over and above the other two.

    Budding philosophers of meta-physics that are realists about physical reality and abstract objects often want to unify mathematics and physics somehow, and the first ideas that leap to mind are that ‘all is math’ (modern platonism) or ‘all is information’ (‘it from qubit’). But this is precisely where all the confusion starts! The ‘it from qubit’ and Tegmark multiverse ideas try to have the physical world emerging from a foundation of information/math, but it just doesn’t make sense. This had me so confused for a long long time. The fault is with the ideas! These ideas have really confused everyone and lead them seriously astray!

    Rejecting ‘it from qubit’ and Tegmark multiverse, I settled on the only other sensible possibility : physical and mathematical existence are mostly separate. I came to the conclusion that *both* physical and mathematical existence are co-foundations of reality, but neither is primary. One doesn’t ’emerge’ from the other. Whilst there may be some over-lap, most mathematical (abstract) objects *aren’t* physically realized. There just isn’t a single foundation of reality – there are *two* foundations.

    So what is the nature of ‘information in this picture’? I think it’s where physical and mathematical existence *do* over-lap. Computation is the portion of mathematics that *is* physically realized. But *not* everything physical is computation. The ‘it from qubit’ project errs in the claim that ‘everything is computation/information’. I think the mistake is to stretch the definition of ‘computation’ to the point of it being meaningless. My new view is that only goal-directed systems that form symbolic representations of reality qualify as ‘computation’ – computers, brains and minds. The *mind* is made of information. Computers and brains too. But most of physical reality is not. So, in this picture, Cognition is synonymous with information (the portion of math that is physically realized).

    This clarification of metaphysics should hopefully lead to a clarification of quantum mechanics and quantum computing.

    As to mathematics, perhaps it has a ‘dual-foundation’ as well. The main candidate for the foundation of math is ‘set theory’, but it appears to me that ‘arithmetic/number theory’ qualifies as a genuine rival. According to wikipedia, it appears that most of classical mathematics can be derived from second-order arithmetic, and sets aren’t needed. Just as mathematical/physical existence could form a dual-foundation of reality in metaphysics, what if sets/numbers form a dual-foundation for mathematics? Perhaps mathematics just doesn’t have a single foundation either.

    The Riemann hypothesis can be approached purely from number theory and sets dispensed with. John Baez in a recent tweet mentioned a hypothetical ‘F1’ (finite field with one element), which looks very intriguing – if such a thing existed it would completely revise abstract algebra (by dispensing with the need for sets), and lead to a solution to RH.

  29. fred Says:

    Scott, when you write

    “In quantum mechanics, measure or measure not: there is no if you hadn’t measured.”

    How is that different from the first claim of superdeterminism that there’s really no such thing as counterfactuals, ever?

  30. fred Says:

    Scott, what do you make of the claim in the paper that

    “We conclude by suggesting a modified variant of the experiment, which may be technologically feasible. The idea is to substitute agents F¯¯¯ and F by computers.”

    Does it mean there’s really a chance that this entire setup could be done practically?

  31. fred Says:

    Andrei #27

    “My take on these thought experiments involving “isolated” systems is that they are not possible, even in practice.
    [..]These fields are of unlimited range and cannot be completely blocked by any box, whatever the material this box is made of.”

    Black holes!

  32. Scott Says:

    fred #29: The two things have nothing to do with each other. To violate the Bell inequality doesn’t actually require any counterfacual reasoning, involving “if I had measured this state in this basis” (even though I didn’t). All it requires is repeating the Bell experiment many times, while randomly varying the measurement bases. To deny the possibility of doing that requires denying that it’s ever possible to make any random choices at all, which is much much crazier than anything we’re talking about here.

  33. Scott Says:

    fred #30: Yes, you could even do the experiment today, not with conscious beings in superposition but at least with qubits (i.e., the original Hardy’s Paradox). But even if you were able to do the experiment with conscious beings, it would still tell you nothing whatsoever that you didn’t already know. All you’d find is that the measurement outcomes are exactly the ones predicted by quantum mechanics — so in particular, that the “impossible” outcome occurs with probability 1/12. But that would still leave the task of identifying the fallacious assumption in the argument for why that outcome was “impossible.”

  34. Amir Says:

    Scott #33:You sound like a mathematician – assuming that once we have a consistent theory, experimental results will agree with it. I’m sure physicists would insist on actually doing the experiment, for instance to disprove spontaneous collapse theories.

  35. Andrei Says:

    fred #31:

    I am not sure if you intended it as a joke, but from the point of view of an external observer the cat will never pass the event horrizon, so it will never be inside the “box”.

    It is also questionable if black holes do have an interior where one can make experiments.

  36. Harry Johnston Says:

    @Andrei #27, as far as I’m aware the purpose of the box in the Schrödinger’s cat thought experiment is just to make it clear that the experimenter is not looking directly at the cat during the experiment. It isn’t necessary for the observer to have no way to tell whether the cat is dead or alive, so long as they don’t actually go ahead and make the necessary measurements.

    In other words, it isn’t access to the information that counts, it’s the information you actually choose to collect. Do you have some reason to believe differently?

  37. Andrei Says:

    Scott #33:

    “To violate the Bell inequality doesn’t actually require any counterfacual reasoning, involving “if I had measured this state in this basis” (even though I didn’t). All it requires is repeating the Bell experiment many times, while randomly varying the measurement bases. To deny the possibility of doing that requires denying that it’s ever possible to make any random choices at all, which is much much crazier than anything we’re talking about here.”

    I think that you may find superdeterminism more acceptable if you agree with the following steps:

    Step 1: When thinking about classical physics forget about Newtonian billiard balls that travel in straight lines and only interact by direct collisions. Think about field theories like general relativity or classical electromagnetism. Such theories have built-in the type of contextuality required to understand QM.

    Step 2: A Bell/EPR experiment, just like any other experiment, is nothing but a particular case of charged particles interacting with other charged particles. The particle source, the detectors, the human experimenters or whatever you may use are made of such charged particles (electrons and quarks). According to classical electromagnetism these particles are continuously influencing each other’s motion as the result of their associated electric and magnetic fields. Such influence never stops because of the unlimited range of those fields.

    Step 3: the hidden variable (say the polarization of the entangled photons) is expected to depend on the electric and magnetic fields acting at the location of the particle source. So, if you agree on Step 2 you would accept that the hidden variable does depend on the detectors’ settings, which is all superdeterminism is about.

  38. Harry Johnston Says:

    Scott #33, while I’m personally reasonably confident that yes, you would get the result predicted by QM, aren’t Frauchiger & Renner claiming otherwise? (I haven’t read the entire paper, but the abstract says “This indicates that quantum theory cannot be extrapolated to complex systems, at least not in a straightforward manner.”)

    … of course, I guess they’re talking about their version of the experiment, where the entangled states are agents, not the experiment that we can actually perform right now.

  39. Scott Says:

    Amir #34: No, it would be batshit insane to believe that “once we have a consistent theory, experimental results will agree with it”—since there are many consistent theories that disagree with each other (as any ‘mathematician’ surely understands…!).

    But we’re not talking here about some arbitrary theory that happens to be consistent—we’re talking about quantum mechanics, about which any proposed experimental test has to be evaluated for novelty in light of a century of previous tests (every single one of which QM has passed).

    Googling it just now, there’s indeed a whole literature on experimental tests of Hardy’s paradox, reporting exactly the results (Pr=1/12, in the example in my post) that QM predicts. So, would an experimental test of Frauchiger-Renner need to check what happened if we replaced the qubits by conscious observers? If so, how would we know when they were conscious? Or would it be enough to replace the qubits by AI’s? If so, then why couldn’t a qubit already count as an “AI” for our purposes—extremely rudimentary, of course, but recording the relevant information and therefore good enough to test the prediction? But if so, then the experiments on Hardy’s paradox have already tested Frauchiger-Renner, and shown that the results are just the ones predicted by QM.

  40. Scott Says:

    Andrei #37: No, superdeterminism is still crazy. Of course humans and their detectors are made of the same charged and uncharged particles as everything else. But science has only ever worked because it’s possible to isolate some things in the universe from other things—not perfectly, but well enough. And this is completely uncontroversial in cases other than the Bell inequality, which shows that the superdeterminists aren’t consistent about their own theory. E.g., a political poll of 1000 households reveals 48% support for a certain candidate, plus or minus 5%. Why isn’t anyone free to believe that the real number is actually 1%, or 99%, because the pollster’s auto-dialer is also made of subatomic particles governed by physics, so maybe it was predetermined since the Big Bang that the dialer would overwhelmingly pick the numbers of the candidate’s supporters (or opponents)? I’ll tell you why: because, absent some positive reason to believe it and some account of how it happened, that would be stupid!

    Yet with the Bell inequality, and only with the Bell inequality, we’re asked to believe that a cosmic conspiracy exactly like the above one is in force—and, the craziest part of all, this conspiracy does not lead to faster-than-light communication, or any of the other world-changing effects that it could just as easily lead to and that we might expect, but only to the precise results that QM already predicted for us without any need for such a conspiracy, like winning the CHSH game 85% of the time (and not 86%). Occam’s Razor yearns to slice.

  41. Scott Says:

    Harry Johnston #38: OK, point taken. But if one has any experience with experiments in the foundations of QM, one knows full well what’s going to happen next. Namely: some experimental group will do a slightly souped-up test of Hardy’s Paradox, of course getting just the results that QM predicts, and will then market it in Science or Nature as “the first experimental probe of the logical contradiction at the heart of QM … who could’ve imagined that the ‘impossible’ outcome would occur with probability 1/12?” And then the science journalists will wet themselves with excitement. It’s all nearly as predictable as QM itself! 🙂

  42. Andrei Says:

    Scott: #40

    “science has only ever worked because it’s possible to isolate some things in the universe from other things—not perfectly, but well enough.”

    There are two main reasons why it is possible to treat a subsystem (say the Solar system) of a large system (our galaxy) in isolation.

    1. Physics is local. The state of a subsystem is completely described by a specification of positions and velocities of particles and the field magnitudes. But of course, this does not imply that the subsystem is independent from the large system because the local fields are themselves a function of position/momenta of all particles in the whole system.

    2. If there is a large distance between the subsystem and the rest of the particles one can ignore, to some extent the fields produced by them. However, it is important to notice that this approximation only works if you are only interested in the relative motions of the particles inside the subsystem. For example you can ignore the galactic field if you want to calculate the trajectory of the Earth around the Sun. But if you are interested in the relative motion of the Earth and some planet in another region of the galaxy you need to know the galactic field. Assuming that the two distant planets move independently would lead to false predictions as there is no good reason why they should orbit the galactic center.

    In a Bell test we are in a similar situation as two distant planets in a galaxy. We are not interested in the internal evolution of each detector and of the particle source but in their relative evolution. We are interested in the correlations of distant measurements. So, in this case, ignoring the mutual EM interactions leads to wrong predictions.

    ” it’s possible to isolate some things in the universe from other things—not perfectly, but well enough. And this is completely uncontroversial in cases other than the Bell inequality, which shows that the superdeterminists aren’t consistent about their own theory.”

    The choice one makes does depend a lot on the available options. There is no need to appeal to superdeterminism in the case of the political poll because we can explain those results within the limits of accepted physics. There is nothing surprising about them. On the contrary, Bell’s theorem gives us only dificult options, like:

    1. non-realism

    If you agree with non-realism will you be consistent enough to apply this non-realist view to the political poll?

    2. non-locality

    If you agree with non-locality will you be consistent enough to apply this non-local view to the political poll?

    Another answer to your argument is the following:

    The purpose of any interpretation of QM is to recover QM’s predictions. So, unless you think there is a conflict between QM and the political poll there is no reason to expect a superdeterminist to have a different take on it as opposed to a Bohmian or QBist.

  43. John Sidles Says:

    Scott remarks  “If one has any experience with experiments in the foundations of QM, one knows full well what’s going to happen next …

    This sentence has many possible completions, of which the following completion is suggested as consonant with the traditional excellences of Shtetl Optimized discourse:

    …  scientists will employ ingenious new theoretical insights, and ingenious new experimental techniques, to add more decimal places to measurements of the fine structure constant α

    This particular continuation is motivated by the extraordinary success of ongoing efforts to measure α within ever-smaller error bounds. The theoretical, experimental, and social reasons for this α-success brightly illuminate (for me anyway) two recent quantum computing preprints, namely, “How many qubits are needed for quantum computational supremacy?” (arXiv:1805.05224v2, mainly out of MIT/CalTech) and “Fluctuations of energy-relaxation times in superconducting qubits” (arXiv:1809.01043v1, mainly by the Google/Martinis group).

    In brief, the two chief technical paths to higher-precision measurements of α directly parallel the two chief technical paths to demonstrating quantum supremacy. The first path emphasizes coherent quantum dynamics, as exemplified by “g-2″/”geonium” experiments (e.g., arXiv:0801.1134), and by low-noise qubit arrays (e.g., arXiv:1709.06678v1). The second path emphasizes error-corrected/topologically-protected quantum dynamics, as exemplified by quantum metrology triangles (QMTs, e.g., arXiv:1204.6500), and by proposals for scalable quantum error correction (e.g., arXiv:1801.00862).

    In a nutshell, better appreciation of the realities of α-measurement techniques are helpful in evolving better-informed views regarding the scalable viability of the extended Church-Turing Thesis, versus the scalable feasibility of Quantum Supremacy demonstrations.
    ——
    PS: Michael Atiyah’s recently proposed α-theory inexplicably considers none of these subtly interlocking quantum electrodynamical issues … which is one more overarching reason to agree with the Shtetl Optimized editorial policy, that Atiyah’s theory probably is not right.

  44. Ted Says:

    Scott’s argument at the end of the main post (emphasizing the importance of distinguishing between human experimenter’s thoughts in situations in which certain experiments are or are not performed) reminds me a lot of Guy Blaylock’s article “The EPR paradox, Bell’s inequality, and the question of locality” (Am. J. Phys. 78, 111 (2009), arXiv:0902.3827). Blaylock argues that the real takeaway of Bell’s theorem isn’t the failure of local realism in quantum mechanics, as is often claimed, but actually the failure of counterfactual definiteness – e.g. he claims that Many-Worlds completely respects local realism. (To clarify, he defines “causality” to mean “no FTL communication” and “locality” as the stronger requirement “no establishment of spacelike correlations, whether or not they can be used for communication”. In this terminology, all interpretations of QM are causal, but not all are local – e.g. Many-Worlds is but Copenhagen isn’t.)

  45. ppnl Says:

    Harry Johnston @36

    ” … as far as I’m aware the purpose of the box in the Schrödinger’s cat thought experiment is just to make it clear that the experimenter is not looking directly at the cat… ”

    No that’s just wrong. The whole point of Schrödinger’s cat is to try to isolate when a measurement is made. Say you put the cat in a box and watch it by closed circuit TV. Well you are watching so the wave collapses right? OK try again but you do not look at the TV but only record it so that you can watch it later. Wave collapse? Ok what if you chop up the cd containing the recording? Well you could in principle reassemble the cd. So let’s try burning it. In a deep quantum sense the information is still out and so in theory the quantum wave must collapse. Think black hole information paradox where not even feeding the disk to a black hole destroys the information.

    Now think of all the other ways information could leak out of the box. Do you smell decomp? How about the sound of the cat’s heart beating? What is that scratching noise? What about body heat radiated that you cannot see but affects the air around the box?

    No, the whole thing makes no sense unless you are talking about total isolation in the box.

    The difficulty of making quantum computers is exactly the difficulty of building Schrödinger’s cat type boxes around every logic gate in a computer. And then allowing the boxes to interact with each other without interacting with the rest of the world.

    If it were just about not directly looking quantum computers would be easy.

  46. AM Says:

    Scott,
    Just by looking at Mochizuki’s web page: http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html

    1) Scholze and Stix: “We, the authors of this note, came to the conclusion that there is no proof”.
    Well, don’t expect to see something like: “Let’s assume Mochizuki’s Corollary 3.12 holds true, then by the above argument XYZ it leads to a contradiction.” In fact, in their write-up you won’t find even a single theorem/lemma by the authors!

    2) Nevertheless, Mochizuki does a good job addressing (in a VERY accessible way!) their imprecise arguments.

    Scott, you always present yourself as a careful and polite thinker, but it seems unfair to judge a mathematical breakthrough based on a popular science article.
    In Ivan Fesenko’s words: “[It] almost entirely consists of ignorant opinions of a small group of closely related people who have been active in negatively talking about IUT publicly but have their research track record in the subject area empty and are not known to have applied serious efforts to study even anabelian geometry.”

    Thanks. Alex

  47. Lorenzo Maccone Says:

    Hi Scott, thanks for you blog post which is really nice! The connection to Hardy’s paradox is nontrivial but explains very neatly the argument. Thanks! (Please keep up your blog)

  48. Renato Renner Says:

    Hi Scott

    There are currently many who are blogging about our result, so I started to use my little quantum random number generator on my desk: outcome “0” means I don’t react to it, outcome “1” means I write a reply. For your blog the outcome was “1”!

    Now, we are already in a situation that involves superposed agents, namely me who wrote this reply and you who are reading it. (I am assuming that you do not believe in objective wavefunction collapses and hence accept assumption Q of our paper.) You would now probably say that this does not prevent us from reasoning as usual, but that we would be getting in trouble if our brains were subject to measurements in the Hadamard basis. So far I would definitively agree. And I would certainly subscribe the claim: “It is hard (if not impossible) to think after someone has Hadamarded your brain.”

    But this brings me to the core of my reply. Note the small difference between my claim and your title. While I agree that it is hard to think *after* someone has Hadamarded your brain, I do not see any reason to deny that we can think *before* the Hadamarding.

    Talking more technically, the reason why, as you noted, I do not endorse your scenario (the “Wigner’s friendification of Hardy’s paradox” or maybe the “Hardyfication of Wigner’s paradox”) is that it neglects a key element: Your simplified argument completely ignores the timing. But, clearly, it makes a difference whether I think before or after my brain is Hadamarded. In our argument, we were therefore careful to ensure that, whenever one agent talks about the conclusions drawn by another agent, he does so *before* any Hadamarding.

    This should be apparent from Table 3 of our paper, which essentially summarises our entire argument. Take, for example, the reasoning by agent \bar{W}. He reasons around time 0:23 about the conclusions drawn at time 0:14 by agent F. The key fact to notice here is that both relevant agents, i.e., F and \bar{W}, are in a similar situation as we are (hopefully) now when reading this text. While, from an outside viewpoint, they may be in a superposition state, no Hadamard has been applied to them.

    The only way I can hence make sense of your claim that we are using an additional implicit assumption in our argument (the chaining of statements) is that you are questioning the step that, in Table 3, corresponds to going from the third column to the fourth (the “further implied statement”). Did I get this right? (All the other steps are explicitly covered by our three assumptions, Q, C, and S.)

    Before concluding, and since you mentioned this several times in your blog, let me stress that “consciousness” does not play any role in our argument. The agents may as well be computers, which are programmed with rules corresponding to our assumptions Q, C, and S, and which they use for their reasoning (summarised in Table 3). So, when we talk about “agents”, we just mean “users” of quantum theory. After all, the question we are asking is: “Can quantum theory be used to consistently describe users of the same theory?” This question has little to do with consciousness (which is why we tried to avoid this term).

  49. Harry Johnston Says:

    @ppnl #45, I’m not entirely sure whether we’re disagreeing about the physics or just the philosophy around it. But see the Quantum Eraser Experiment.

  50. DarMM Says:

    I was just thinking about this a bit more.

    If \bar{F} gets tails, then he knows (given the state he prepares) that the L lab will evolve into the fail state. Thus W will measure fail definitely.

    If agent F measures z=+1/2, F can conclude that \bar{F} knows r=tails.

    Already here I’m a bit confused.

    F himself would think that since he sees z=+1/2 he and his lab are not in a determined state in the fail,okay basis. From that he would think W could get either fail or okay.

    However since z=+1/2 => r=tails, he could reason that \bar{F} is certain W will get the fail result. However he would know that \bar{F}’s conclusions about his lab result from \bar{F} reasoning about him using a superposed state.

    Is there not already a contradiction at this point between F and \bar{F}’s reasoning. F would reach one conclusion about W based purely on his own z=+1/2 result and a different one when reasoning via \bar{F}’s superposed treatment of his lab.

    Or (more likely) am I missing something?

  51. Scott Says:

    Harry Johnston: ppnl is 100% correct. The purpose of the box, in the Schrödinger’s cat experiment, is to isolate the cat from the entire rest of the universe, not merely from some particular observer. Any interaction with the environment could have the effect of entangling the cat with the environment, and thereby changing the local state of the cat from a pure state (i.e., a superposition) to a mixed state (i.e., either dead OR alive), which is a completely different situation.

  52. fred Says:

    Scott #40

    “science has only ever worked because it’s possible to isolate some things in the universe from other things—not perfectly, but well enough.”

    Well, I guess it also depends on what we mean by “works”.

    In the case of gravitational mechanics, isolation is difficult.
    Even in the simple case of the three body problem, there’s no closed solution, and predictions become hard because numerical instabilities (chaos).

    Another example is accounting for the effect of an electron on itself.

  53. fred Says:

    I have a dumb question for anyone’s who understand black holes and the holographic principle.

    Assuming a black holes forms from a collapsing star, is all the material of the star crossing its own even horizon has the collapse progresses?
    What about the very first few particles (or clumps of such particles) where the collapse initiates? Aren’t they always inside the black hole? But if so, how would their information ever end up encoded on the BH surface?

  54. fred Says:

    Btw, those sorts of difficulties related with the “everything is connected to everything else” (like chicken and egg issues between fields and particles) or “an infinite amount of effects need to be accounted for” (like when summing all the possible paths in Feynman QED)… make me really question the general claim that the universe is so “elegantly” mathematical.

    Either there’s some clever type of mathematics we’ve not discovered yet or the physical universe basically has infinite resources (aka magic)… or we need to understand better what’s going on a the Planck’s level.

  55. sf Says:

    Dear Scott,
    Grazie mille for this extremely clear, intuitive explanation. On the one hand you make perfectly clear what was not kosher with the paradox, but, on the other, one has to worry whether we have enough defences to be able to catch other potential traps on the fly, before we fall into them. It often seems one has to get to the absurd punch line each time, before backtracking and spotting the flaw.

    It seems to me that if one wants to formalize the Born rule a bit, one of the rules would have to say that you can apply it by repeating an experiment and counting outcomes, but there’s no messing around with the internals of the experiment during repetitions. The ‘measurement’ involves the input set-up or preparation of a quantum state, just as much as it involves the meter reading at the output. The references to ‘knowing’ what Alice et al know are trying to get around this Bohr type censorship of “messing around with the internals”. The only admissible ‘knowledge’ should be in reference to states where everything in the system has collapsed. If this doesn’t change anything about our view of QM, it could provide for some subtleties about what ‘knowledge’ can mean in a QM world. In fact, maybe ‘knowledge’ should be grounded in notions of prediction, and repeated experiments.

    One issue I wonder about; is it worth trying to formalize QM ‘measurement’ in terms of a Turing machine which does the ‘measurement’ and counts outputs in a series of trials? ie the ‘measurement process’ should consist of more than just a one shot experiment; something more like an ensemble (over time). Is it necessary or useful to have the series of repetitions defined, as part of the context for Born’s rule? I guess this is trying to make the notion of probability more operational/empirical.

    Turing like ‘states’ are somehow conceptually very different from QM states; they are is in some sense designed, with a way to control them, and so that they recur ‘as desired’.

    If this doesn’t relate directly to consciousness, it can illustrate how notions like ‘access’ and grounding aka embodiment, have to be involved, to have a sensible discussion of any notion of consciousness.

  56. Sniffnoy Says:

    AM #46: That’s not how refuting a proof works? Scholze and Stix aren’t claiming Corollary 3.12 is false, they’re claiming that its proof is invalid. You don’t show a proof is invalid with a proof of your own, you do it by pointing out the error. Yes, obviously if someone has made a false claim, then proving the falsity of their claim is a good thing to do, but it’s a fundamentally seperate thing to do, in that it doesn’t tell you where the error is. (And the error could be in your own proof. Or, technically, in neither, because there’s an inconsistency in mathematics.) In short, writing proofs and refuting proofs are not the same sort of thing, so it does not make sense to complain that, in their refutation, Scholze and Stix do not include a proof of their own.

  57. Scott Says:

    Renato #48: Thanks; I’m glad that my blog post was one of the lucky ones to earn a reply from you! 🙂

    I acknowledge how much care and attention you devote in your paper to the issue of timing. But I contend that, no matter how we formalize the statements in question, and what it means for the agents to “know” the statements, there will some place where we illegitimately cross the temporal Rubicon between before and after Charlie’s brain gets scrambled by a measurement in the Hadamard basis. Somewhat flippantly, I might say: we know this must be the case, because the end result contradicts the predictions of QM! 🙂 More seriously: at two nearby stages of (my version of) your argument, we conclude that Diane’s brain is in the state |1⟩, and then that Diane’s brain is in the state |+⟩. So, I can isolate where I get off your train to somewhere between the former statement and the latter one…

    Incidentally, point taken about the word “consciousness.” But that leads to an interesting question: you say it’s not important if Charlie and Diane are “conscious”; all that matters is whether they’re “agents using quantum mechanics.” But if so, then couldn’t we treat even a single qubit as a “QM-using agent,” in the same sense that one qubit could be said to “measure” another qubit when they’re entangled? In that case, would you agree that the experimental tests of Hardy’s Paradox have already tested your paradox as well?

  58. Job Says:

    What would be the consequences of this result?

    Does it conflict with Quantum Computing in any way? Is that why Scott found it both interesting and annoying?

  59. fred Says:

    mjgeddes #28

    “My new view is that only goal-directed systems that form symbolic representations of reality qualify as ‘computation’ – computers, brains and minds. The *mind* is made of information. Computers and brains too. But most of physical reality is not.”

    We can be more specific by noting that “high level” properties of physical systems are the basis of the symbols. By “high level” I mean from a statistical mechanics point of view, such as temperature, shapes, etc … of big clusters of atoms.

    “Symbolic” means that we see the spontaneous appearance of small and stable systems with microstates that are extremely sensitive to the macro states of some much larger and/or distant systems. E.g. a thermostat is a small system where a few atoms are very sensitive to the average temperature in the room it’s in. Similarly, a few neurons in the brain of a cosmologist are very sensitive to the shapes of very distant and gigantic clumps of atoms (galaxies). This “sensitivity” can be also interpreted as an isomorphism between the properties of two systems of very different size (a massive reduction is going on).
    The micro states of the small systems are also somewhat robust to their own internal noise/randomness. Like, all PCs running a given software have the same values in their registers, even though they’re all different at the atomic level. Resilience to QM randomness is the main property of a “computation”.

    But this picture is not enough to understand one thing:
    Information is relative – e.g. there’s no single answer to the question “how many circles are there in this room?”, or, if we look at an arbitrary system of atoms, we can’t answer questions like “how much software is running in there?”.
    It’s the same difficulty “information integration” theories are running into. They try to extract objective/universal information metrics from systems, but you just can’t do it, because information is relative (the same thing is pointed out by Kolmogorov complexity metrics).

    In other words, we can only consider/recognize the dictionary of symbols in ourselves and in all our human artifacts, but we can’t necessarily recognize the existence of such mappings in external systems (who’s to say that a city isn’t conscious?).
    Another way to see this difficulty is to note that a dictionary (whether an actual book with definitions of words, or an actual brain with connections between all its stored symbols) is really a collection of circular relationships. The definition of every single word/symbol relies on other words/symbols. If it’s all circular, how does get boostrapped?
    Yet, we, as conscious beings, do experience a somewhat grounded/specific interpretation of our world.

    What’s missing in the scientific approach to understanding emergence of consciousness (like information integration) is that they fail to recognize the existence of implicit symbols that are irreducible and beyond their reach, those symbols cannot be expressed in terms of words or broken down by reductionism, they are simply beyond the reach of the scientific method. So the dictionary of our mind isn’t all circular but ends up in basic symbols that are either the content of consciousness or consciousness itself. Like “blue” or “pain”… not the words or sounds of the words, but the bottom experience of “blue” that is instantly recognizable to us, and no amount of extra physical facts about it (blue is this wavelength, it excites certain cells in the eyes, …) is ever going to add anything to the bottom mystery that is experiencing blue.

  60. fred Says:

    Scott #57

    “in the same sense that one qubit could be said to “measure” another qubit when they’re entangled?”

    Isn’t this a bit like reducing something subtle like the halting problem (about the power of Turing Complete machines running other TC machines) to noting that a billiard ball hitting a couple other billiard balls is some sort of classical computing operation too, so it should be enough to cover everything? 😛

  61. Ilya Shpitser Says:

    It was great chatting with you, Scott!

  62. Harry Johnston Says:

    Scott #51, I’ll take your word for it, I guess. But we can perform a two-slit experiment with electrons, right? And we still get an interference pattern despite the fact that the state of the electromagnetic field, if measured sufficiently accurately, would allow us to determine which slit the electron went through. I don’t see how the Schrödinger’s cat experiment is any different.

  63. Scott Says:

    Harry Johnston #62: The dilemma you point out also confused me when I was first learning the subject. It has an actual resolution. Yes, you can do the double-slit experiment with an electron, and yes, that temporarily sets up a superposition over two different configurations of the electromagnetic field. However, that does not mean that any record gets created in the external world about which slit the electron went through. Indeed, if superposing the electron suddenly created records arbitrarily far away in the universe, that would be faster-than-light communication! Rather, the differing field configurations mean only that there’s the potential for a record to be created—if, for example, we put a charged particle in the field, the closer the better, and a record is created of its displacement. The interaction between the superposed electron and the charged particle would be mediated by an exchange of virtual photons, which has some amplitude to happen and some amplitude not to happen. If we succeed in observing interference between the two different paths of the electron, then that very fact tells us that the total amplitude for all the Feynman diagrams that would’ve led to an external record being created was small.

    And again: if maintaining a system in superposition were as easy as personally forgetting its state, then building a scalable quantum computer would be child’s play.

    Actual physicists are welcome to add quibbles, additional explanations, etc.

  64. mjgeddes Says:

    fred #59,

    Yes, I agree with your first couple of paragraphs. Information processing is an emergent property and anyone who thinks reality at base is composed of a string of 0s or 1s (or the qubit generalization) is out to lunch 😉

    I don’t think consciousness and the nature of symbols is ‘beyond the ‘scientific method’ though. It’s just that a full understanding needs to go beyond physics to the world of mathematics. Mathematics, it seems to me, is precisely all about how knowledge is represented or ‘coded’. It does indeed seem that one needs to begin with some irreducible ‘base codes’ or ‘base representations’ if one wants to grasp how minds work. Physical states alone can’t provide an understanding of that. That’s why I’m a mathematical realist – I ascribe actual reality to abstract objects – I think they exist ‘out there’ and are not just a language we use or invent. The combined might of physics *and* mathematics, I believe, should be enough to provide a full explanation of consciousness.

    Draw a 2-d graph with ‘mathematical existence’ along the x-axis, and ‘physical existence’ along the y-axis. I think these two types of existence are orthogonal in the sense that you can’t reduce one to the other or dispense with either if you want a full explanation of reality. You need both.

    Now physical existence is all about the structural properties of things: particles , fields (inc forces) and space-time. Mathematical existence is about abstract patterns, or how knowledge is represented: sets, numbers and functions. One could consider that each has it’s own ‘arrow of time’: physics time (physics) and logical time(mathematics). Then the graph shows the progression of logical time (x-axis), and physics time (y-axis).

    Both ‘arrows of time’ can be unified by the concept of ‘complexity’. ‘Physics time’ is about the complexity of the physical states of a system, whereas ‘logical time’ is about the complexity of ‘mathematical proofs’. Then I can define cognition (inc. mind, ‘computation’ and ‘information’) as a composite (emergent) property built up from both physics time and logical time.

    Thinking of the graph as ‘the dimensions of existence’, then in a real sense, one can say that a new ‘layer’ of reality is being generated as physics time and logical time ‘progress’. The base layers are physical and mathematical existence, and cognition (inc. consciousness) is the emerging new layer! Think of cognition (inc. consciousness) as the ‘high entropy’ state of existence. Both physics and logical time ‘point’ towards the emergence of cognition.

  65. Renato Renner Says:

    I also felt lucky when I saw that my quantum random number generator chose your blog. 🙂 But now, after rethinking the consequences that future Hadamards can have, at least according to your interpretation, I am afraid that the result of my random number generator may not even exist …

    More seriously: I would expect that anyone who claims that our argument is flawed should be able to localise the flaw. So, here is the challenge: Read Table 3 (in the order of increasing superscripts, which specify at what time they are made) and identify the first entry you disagree with. This should be a rather easy task: each entry corresponds to a well-defined statement that you (if you were an agent taking part in the experiment and had observed the outcome indicated in the second column, labelled “assumed observation”) should either be willing to make or not.

    Having said this, I would of course never try to impose homework on you, Scott. 😉 Therefore, starting from your analysis of your simplified “Alice-Bob-Charlie-Diane” argument, I tried myself to reverse-engineer what you would say about our original thought experiment. This reverse-engineering is certainly not unique (partially because you dropped all timing information). However, I found that the only statement to which your concern that we “illegitimately cross the temporal Rubicon” may apply, at least remotely, is the very first of the table, i.e., \bar{F}^{n:02}, for it relates an observation at time n:01 to an observation at time n:31. But my conclusion would then be that you just disagree with Assumption Q (which would of course be fine).

    Unrelated to this: Your question about experimental tests is indeed an interesting one. I’ll comment on it later (to avoid making this comment even longer).

  66. sf Says:

    It may also be interesting to consider the Frauchiger – Renner paper in terms of
    Scott’s definition of
    “State”:
    In physics, math, and computer science, the state of a system is…
    https://www.edge.org/response-detail/27127

    which subtly gets around a lot of non-trivial technical difficulties.

    There is a problem coming from ‘knowing’ being both a physical fact about brains (in QM here), and at the same time a property of observers, more associated with their classical features. The definition of “State” that Scott suggests requires one to choose a minimal description, eliminating redundancies, but also avoiding potential internal conflicts.

    This said, the notions of “State” that are used in physics and computer science are not necessarily (or a priori?) compatible; at the least there’s some coarse graining to go from the continuums of physics to the discrete world of computer science, which may involve some quotienting operation, or an additional notion of identity/equivalence. Giving more global entities some kind of ontological status then seems to cause problems, like in the mind-body problem. The point may be that the equivalence relation should have some physical basis, but it’s usually regarded as some abstract construct of a meta-theory.

  67. asdf Says:

    Neel #14: “That is, can we model both an observer and an experiment as a larger, interacting quantum system, and then derive the Born rule for the observer from an analysis of the joint system?” I think that is what decoherence theory set out to do, unsuccessfully though.

    https://plato.stanford.edu/entries/qm-decoherence/#ConApp

  68. ppnl Says:

    asdf #67:

    Quoting the link:

    ” The measurement problem, in a nutshell, runs as follows. Quantum mechanical systems are described by wave-like mathematical objects (vectors) of which sums (superpositions) can be formed (see the entry on quantum mechanics). Time evolution (the Schrödinger equation) preserves such sums. Thus, if a quantum mechanical system (say, an electron) is described by a superposition of two given states, say, spin in x-direction equal +1/2 and spin in x-direction equal -1/2, and we let it interact with a measuring apparatus that couples to these states, the final quantum state of the composite will be a sum of two components, one in which the apparatus has coupled to (has registered) x-spin = +1/2, and one in which the apparatus has coupled to (has registered) x-spin = -1/2. The problem is that, while we may accept the idea of microscopic systems being described by such sums, the meaning of such a sum for the (composite of electron and) apparatus is not immediately obvious. ”

    Well no I think it is pretty obvious. Yes the measuring apparatus can be seen as being in a superposition of states after the measurement. But if the measuring apparatus is in contact with the rest of the universe then it is in a decohered state. That means any observer also in contact with the rest of the universe will see it as simply a classical object in a classical state. There is no way to tell the difference between decoherence and wave collapse even in principle so they are effectively the same thing. In a weird way we can do away with wave collapse entirely and simply see it as a consequence of decoherence.

    Any macroscopic object looking out at the universe be it human or measuring apparatus will see a decohered universe. That means it will seem to have a coherent past and follow largely classical rules.

    Another way to look at it is all the order in the universe is composed of a vast pattern of superposed states as viewed from inside that superposition. The superposed cat knows very well if he is alive or dead if you ask him. But you have to be in the box in order to ask.

  69. Brad DeLong Says:

    Lemme see if I got this…

    State |ψ>, and Alice and Bob will measure the first and second qubits of this state in the basis {+,-}…

    There are three components to the state |ψ>, and in them:

    1. |00>: If Alice were to measure in {0,1} and Bob were to measure in {+,-}, Bob would measure |+>. If Bob were to measure in {0,1} and Alice were to measure in {+,-}, Alice would measure |+>.
    2. |01>: If Alice were to measure in {0,1} and Bob were to measure in {+,-}, Bob would measure |+>. If Bob were to measure in {0,1} and Alice were to measure in {+,-}, it is uncertain what Alice would measure.
    3. |10>: If Alice were to measure in {0,1} and Bob were to measure in {+,-}, it is uncertain what Bob would measure. If Bob were to measure in {0,1} and Alice were to measure in {+,-}, Alice would measure |+>.

    Frauchiger and Renner then turn these counterfactual subjunctive “were to measure in {0,1}”s into actual measurements by having Charlie and Dianne do their own measurements in the {0,1} basis on the first and second qubits, branching the universe into (1), (2), and (3).

    1. In this branch Charlie knows that Bob will measure |+> were he to get around to measuring before decoherence of the second qubit takes place, and Dianne knows that Alice will measure |+> were she to get around to measuring before decoherence of the first qubit takes place.
    2. In this branch Charlie knows that Bob will measure |+> were he to get around to measuring before decoherence of the second qubit takes place.
    3. In this branch Dianne knows that Alice will measure |+> were she to get around to measuring before decoherence of the first qubit takes place.

    In each branch, Charlie and Dianne write down, respectively, “I have measured qubit 1 in the {0,1} basis, and I may know that Bob will measure |+>” and “I have measured qubit 2 in the {0,1} basis, and I may know that Alice will measure |+>”.

    Frauchiger and Renner then apply the fact that Charlie and Dianne have measured and the principle of the excluded middle to conclude that it is logically impossible—no matter how the branching has taken place—for both Alice and Bob to simultaneously measure |->.

    If we then opened the boxes and decohered Charlie and Dianne, we would be done.

    But…

    Frauchiger and Renner then apply quantum erasers to Charlie and Dianne. The quantum eraser leaves their “I have measured…” messages intact and visible. But the quantum erasers recombines the branches and the restored coherent state is still (or again?) |ψ>.

    And then when Alice and Bob do their measurements in the {+,-} basis, 1/12 of the time we find |- ->

    Is that what is going on here?

    And is the point that either the principle of the excluded middle or the standard use of the subjunctive must fail for QM to be true?

  70. ppnl Says:

    Harry Johnston #62

    ” But we can perform a two-slit experiment with electrons, right? And we still get an interference pattern despite the fact that the state of the electromagnetic field, if measured sufficiently accurately, would allow us to determine which slit the electron went through. I don’t see how the Schrödinger’s cat experiment is any different. ”

    Well a dead cat produces a smell of decomp. We could measure that smell and thus know if the cat is dead or alive right? Except the smell is locked inside the box and no information can pass through the walls of the box.

    The electron has an electric field yes. But that field is locked in a type of box with the electron. That box is created by the distance between the electron and anything that that field could interact with. Remember the field is very weak and the electron is traveling very fast. The chances for any particular electron interacting with anything is small.

    If you do put a detector close enough to the electron to measure the field then its wave will collapse. You have opened the box. And it will collapse even if you never look at the detector. It just being there is enough to open the box.

  71. Schmelzer Says:

    Andrei #42:
    There would be no problem to accept “non-locality”, given that it is only non-Einstein-causality, and perfectly local theories with maximal speed of information transfer of 1.001c have to be named “non-local”.
    Moreover, the “non-locality” is a well-defined one, described by explicit equations which we already use (namely the formula for the Bohmian velocity, which appears as the velocity in the continuity equation for the probability flow which is one half of the Schroedinger equation).
    Essentially all one has to do to preserve realism and causality is to go back to the Lorentz ether interpretation of relativity. It has a preferred frame, which can be used to make faster than light causal influences compatible with classical causality. The generalization of the Lorentz ether to gravity is simple: Consider the Einstein equations of GR (or the equations of whatever covariant metric theory of gravity you prefer) in harmonic coordinates, and interpret the harmonic condition as continuity and Euler equations for the Lorentz ether.
    Instead, superdeterminism is much worse. arxiv:1712.04334 looks at it also from the point of view of Bayesian probability – which, following Jaynes, is simply the logic of plausible reasoning. There, the superdeterminism loophole does not even exist: Once we have no information about, say, how a dice is faked, we have to assume equal probability to all outcomes. This is sufficient to rule out superdeterminism by the way too. Not as a hypothesis about reality (real dices may be faked) but as a consequence of the fact that we have no information about this big conspiracy we cannot take it into account in plausible reasoning.

  72. Harry Johnston Says:

    OK, I’ve read the paper, and there’s something I don’t understand: from the point of view of W and W¯, doesn’t L become entangled with L¯ when F measures the spin S? And doesn’t that mean that when W¯ makes their measurement, it affects not only the state of L¯ but also the state of L? F¯ doesn’t seem to me to be taking that into account when predicting w.

    (I’d also note that the measurement W¯ makes is forcing L¯ into a particular superposition of the F¯-measured-heads and the F¯-measured-tails eigenstates, even if it was originally in one or the other, which is effectively equivalent to winding back that measurement and therefore presumably thermodynamically impossible. But does that depend on your interpretation of what a measurement is?)

    [@ppnl: yes, agreed. One point I’d overlooked was that an electron moving in a straight line doesn’t produce electromagnetic radiation. But I also hadn’t thought the QM math through properly, as was obvious once Scott pointed it out. Careless of me. Sorry.]

  73. Jochen Says:

    It seems to me that Scott raises a valid question. If I understand correctly, then one could also think about this as follows: so suppose \bar(W) surmises that the state of the lab L is |1/2>, i.e. makes the statement “I am certain that F knows that z=+1/2 at time n:11.”. This statement is equivalent to saying “If I were to measure L, I would obtain |1/2> with certainty.”

    Before \bar(W) makes any measurement, we have a state with components |h>|-1/2>, |t>|-1/2>, and |t>|1/2>, where |h> and |t> refer to the states of Lab 1, including the knowledge of F, and |1/2> and |-1/2> refer to the states of Lab 2, including the knowledge of \bar(F).

    If we rewrite this in the {|OK>,|Fail>}-basis of \bar(W), we get something with components |OK>|1/2>, |Fail>|-1/2>, and |Fail>|1/2>, right? So after \bar(W) measures and obtains |OK>, only the component |OK>|1/2> survives. Hence, if she were to measure L, she would obtain |1/2>.

    But if we now re-express that state in the {|h>,|t>}-basis, then we would no longer have a state in which F is certain that W would obtain w=fail, since that state now would have components |h>|1/2> and |t>|1/2>. In essence, the transformation by \bar(W) on the lab has “erased” the prior knowledge of F.

    So the statement \bar(W)(n:22) is correct, in that it refers to the certainty F had at n:11; but the statement \bar(W)(n:23) does not follow—rather, due to the knowledge obtained in her measurement, \bar(W) is now no longer certain that F would predict that W observes ‘fail’; rather, she knows that if she were to ask F now, they’d reply that they have no idea what W will observe.

  74. Schmelzer Says:

    Renninger #65:
    Given that dBB is quite obviously self-consistent, all one has to do is to trace what happens in dBB, and trace the “inconsistency” down to every detail. This is missed in the paper. You have vaguely discussed dBB, with the conclusion “One possibility could be to … add the rule that its predictions are only valid if an experimenter who makes the predictions keeps all relevant information stored.” Even if true: If this is sufficient to restore self-consistency, it was never violated.

    Let’s look at picture 3 and ask ourselves what makes Alice think that \(w\neq ok\). It is the consideration of only a part of the experiment, namely she knows the initial state she gives to Bob, and then considers the final experiment W. This reduction is quite explicit:

    “While the time information contained in the plot \(s^E\) is thus more coarse-grained than that of \(s^{F1}\), it is still sufficient to apply the laws of quantum theory.”

    Fine, indeed, it is. But given that the reduced picture omits the experiment A, which changes the state of F2, the reduced scenario is simply not applicable to the full experiment. Yes, this change of the state of F2 by the measurement of F1 by A is that spooky action at a distance which is related with entanglement, and the Bohmian trajectory of both laboratories will be surrealistic ones, but this does not make them inconsistent.

    The same logical error I see in the derivation is sufficient to prove a classical analog. Alice tells Bob she is communist. Bob will tell Diana what he knows about Alice political views. Knowing that Bob is a honest guy, Alice will surely think that Diana thinks she is communist. Everything fine, no contradiction, given that Alice at that time is communist. In the classical world, somebody who is once communist remains communist forever.

    Now we add the analogon of quantum theory where Charlie can give Alice Solshenizyn for reading, looking at her reaction to measure if she is communist. With some probability for tunneling, that she becomes anti-communist and so Charlie thinks she is anti-communist.

    Alice does not talk to Bob after this, so the prediction remains, Alice will surely think that Diana thinks she is communist. So, there may be multiple outcomes about what people think about Alice being communist or not.

    But Bohm claims that we are in the time of the internet, and once Diana asks Bob about what Alice thinks, he has, as a honest person, to answer “she told me he is communist long ago, but sorry, wait, I will check if this is correct yet”, and then give Diana the actual information about Alice’s political views. And we have, again, a world without different people having different views about what Alice believes.

    Now, apply your argument to this Bohmian internet theory. You consider, for Alice, the reduced version (she tells Bob she is communist, Bob answers Diana’s question). This is a consistent story, you can apply it. Once there is no Solshenizyn reading in this story, Alice remains communist, and Bob will tell Diana that Alice is communist even if he checks the Bohmian internet. But this reduction gives a different result than the full story. Does it follow that the theory is somehow inconsistent?

  75. sf Says:

    Not only do ’we’ know, as Scott points out, “that Alice is going to measure Charlie in the {|+〉,|-〉} basis, which would involve a drastic unitary transformation (specifically, a “Hadamard”) on the quantum state of Charlie’s brain”, BUT EVEN CHARLIE KNOWS THIS.

    The Frauchiger-Renner paper says:
    “We analyse the experiment from the viewpoints of the four agents, F, F’, W, and W’, who have access to different pieces of information (cf. Fig. 2). We assume, however, that all agents are aware of the entire experimental procedure as described in Box 1, and that they all employ the same theory“.
    (F, F’, W, and W’, are C,D,A,B, here)

    So Charlie, Diane even know that they are each just part of an entangled, superposed state which will soon be collapsed in a different basis. It is only when they neglect this in their collective reasoning that the paradox survives. In fact, assumption (Q) is structured to have them selectively neglect such things, but it’s not clear that this makes sense, insofar as it contradicts the quote above.

    We may be able to weaken the assumptions on how much C,D, know, so that they can still reason coherently and unknowingly apply the Born rule to get predictions that are invalid from the viewpoint of higher level observers, such as A,B, or us, but this is essentially coming back to Wigner’s friend.

  76. Brad DeLong Says:

    Re: #75

    So is this the right way to think about this?

    State |ψ>, and Alice and Bob will measure the first and second qubits of this state in the basis {+,-}…

    There are three components to the state |ψ>, and in them:

    1. |00>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>. If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.

    2. |01>: If Alice were to measure in {0,1}, then Alice would know that if Bob were then to measure in {+,-}, Bob would measure |+>.

    3. |10>: If Bob were to measure in {0,1}, then Bob would know that if Alice were then to measure in {+,-}, Alice would measure |+>.

    Frauchiger and Renner then turn these counterfactual subjunctive “were to measure in {0,1}”s into actual measurements by having Charlie and Dianne do their own measurements in the {0,1} basis on the first and second qubits, branching the universe into (1), (2), and (3).

    1. In this branch Charlie knows that if the wave function has collapsed—if the universe has branched—Bob would measure |+> were he to get around to measuring before decoherence of the second qubit takes place. In this branch Dianne knows that if the wave function has collapsed—if the universe has branched—Alice would measure |+> were she to get around to measuring before decoherence of the first qubit takes place.
     
    But Charle and Dianne know that **even though they have done their measurements** they are in their boxes, and hence the wave function has not yet collapsed—the universe has not yet branched.
     
    Thus Charlie and Dianne know that when it comes time for Bob and Alice to do their measurements in {+,1}, there will be contributions not just from the $ \frac{|00>{{\sqrt{3}} $ component of $|\psi>$, but from the $ \frac{|01>{{\sqrt{3}} $ and the $ \frac{|10>{{\sqrt{3}} $ components of $|\psi>$ as well.
     
    And so they do not know that if Bob were to measure in {+,-} Bob would measure |+> and that if Alice were to measure in {+,-} Alice would measure |+>.
     
    Instead, they know that they are uncertain about what Bob and Alice will measure. They know that the facts that Charlie and Dianne know that they have obtained definite results in the {0,1} basis have (or will have had) no consequences for the true wave function, which remains the original $|\psi>$, and will remain $|\psi>$ until Alice and Bob do **their** measurements.

    2. Similar…

    3. Similar…

    ?

    And is the lesson that:

    (A) Many-worlds does not have a problem if agents properly understand what the branching structure of the universe will be when decoherence occurs.

    (B) Other approaches have a big problem, because not even conscious and certain measurement by Turing-Class intelligences justifies a movement from the quantum-superposition to the classical-probabilities level of analysis.

    ?

  77. Andrei Says:

    Harry Johnston #36:

    “@Andrei #27, as far as I’m aware the purpose of the box in the Schrödinger’s cat thought experiment is just to make it clear that the experimenter is not looking directly at the cat during the experiment. It isn’t necessary for the observer to have no way to tell whether the cat is dead or alive, so long as they don’t actually go ahead and make the necessary measurements.

    In other words, it isn’t access to the information that counts, it’s the information you actually choose to collect. Do you have some reason to believe differently?”

    Sorry, I didn’t notice your post so I am answering it only now.

    Let’s consider the case of a double-slit experiment. We know that by placing a particle detector at one slit the interference pattern disappears. It does not matter if you actual notice the detector, or if you look at its output. It is the presence of the detector that changes the behavior of the incoming particles, not your knowledge.

    In the case of a cat in the box I can always place a detector outside the box to determine if the cat is alive or not (by detecting its gravitational field with a very sensitive accelerometer for example). We are still limited by the uncertainty principle, but for a macroscopic object such as a cat it is irrelevant. So, the box is useless. There is no way to place a cat in superposition by placing it in a box.

  78. sf Says:

    Brad DeLong #76

    To start with,

    > 1. |00>: If Alice were to measure in {0,1}, then Alice would know…

    The measurements are done on the superposition (or sum) of the three components, not separately on each component. You correctly insist on the ordering of the two measurements here, which wasn’t so clear in the previous version, #69.

    Jumping to the end, it’s hard to find one definitive way of looking at things here. There are many viewpoints with interesting insights. So far it’s not clear that there’s any consensus on any approach.

  79. Brad DeLong Says:

    Re #78

    Touché…

  80. Andrew Says:

    Quick question — what is the functional difference (if any) between infinite hidden variables and infinite parallel universes? Specifically, if a “complex” system inhabits a world of infinite parallel universes, _or_ an infinite number of “hidden” variables are at play in determining the state of said system, is there any real difference that would manifest itself in the math between those two “interpretations” of what’s “actually” happening beyond what we can observe? I presume the answer is “no”, otherwise we could devise a test to determine which is “true”, but perhaps I’m missing a large chunk of something.

  81. Andrei Says:

    Schmelzer #71:

    “superdeterminism is much worse. arxiv:1712.04334 looks at it also from the point of view of Bayesian probability – which, following Jaynes, is simply the logic of plausible reasoning. There, the superdeterminism loophole does not even exist: Once we have no information about, say, how a dice is faked, we have to assume equal probability to all outcomes. This is sufficient to rule out superdeterminism by the way too. Not as a hypothesis about reality (real dices may be faked) but as a consequence of the fact that we have no information about this big conspiracy we cannot take it into account in plausible reasoning.”

    OK. Three points here.

    1. I will argue that, under acceptable assumptions, Bell’s statistical independence assumption fails, so the “dice is faked”.

    2. I will show that it is not reasonable to ascribe equal probability to all outcomes for a fake dice.

    3. I will show that the argument presented in your paper against superdeterminism is question-begging, so it fails.

    1.

    Let’s assume that the quantum world is actually described by a classical, local, field theory. I will use classical electromagnetism as an example.

    One can observe that such a theory does not allow one to split a system (say a source of entangled particles + particle detectors) in independent subsystems. The fields in any region depend on the distribution/momenta of all particles, and the trajectory of each particle depends on the local fields. In fact, for a system of point charges (and in our universe charge is indeed quantized) one can show that the fields in any infinitesimal region is unique for a certain particle distribution/momenta. So, at least at the level of detector/source microstates, Bell’s statistically independence assumption is demonstrably false. It is possible that if all those microstates are correctly counted the statistically independence would be restored, but there is no reason to ascribe a high probability for it to happen.

    In conclusion we have good reasons to believe that the “dice is faked/loaded”.

    2.

    If we know that a dice is faked/loaded we know for sure that ascribing equal probability to all outcomes is the worst possible strategy, because it has 0 chance to succeed. That pretty much follows from the definition of the words. It is better to ascribe a high probability to any value, at random, and you have a 1/6 chance of winning.

    3.

    As far as I understand your rejection of superdeterminism is based on the null hypothesis:

    “Will A increase or decrease the probability of B? Without any information, we have no reason to prefer one of the two answers. The only rational answer is the one which makes no difference – that A is irrelevant for B, that both are independent of each other, P(A ∧ B) = P(A)P(B).”

    This is all nice but the same line of reasoning can be used to reject non-local connections as well. Not only we do not know if a measurement at one location has an instantaneous effect at another, distant location, but everything we know about physics seems to preclude such a behavior.

    Your argument is question-begging because it ascribes a very low probability for superdeterminism (and I agree with that) but does not provide us with any reason to ascribe a higher probability for non-local connections. In fact, the situation is exactly opposite. When confronted with a new type of correlation for which the cause is not known the most reasonable assumption is that we are in the presence of a past, even if unknown cause, not in the presence of a non-local cause. This is the standard way to approach new phenomena in science. Occam’s razor strongly favors a mechanism that does not require new physics, just another, albeit convoluted case of Bertlmann socks over a new entity like a real wave-function which cannot even exist in our 4D-spacetime but nevertheless can move particles around.

  82. John Sidles Says:

    To avoid the need to discuss “minds”, it suffices to have the four agents of the game each certify their predictions, by placing a record of their predictions in a “Newcomb Box” (as we will them). As usual in prediction games, once the prediction-contents of a Newcomb Box have been initialized, all participating agents promise not to alter subsequently, by quantum dynamical interactions, the contents of that Newcomb Box. We will call agents that obey these rules “Newcomb Agents”.

    Working through the dynamical details, and in particular, unraveling projective measurements as Lindbladian dynamical processes, resolves the paradox as follows (as it seems to me anyway): Newcomb Agents are not allowed to “Hadamard brains” (in Scott’s happy phrase), because the projective unravellings that generate Hadamarded brains necessary include (disallowed) Hamiltonian interactions between Newcomb box-contents and measurement reservoirs.

    Specifically, the Newcomb Box certificates, that were originally deposited by agents F and agents F-bar, are subsequently altered by the Lindbladian dynamical processes that generate the projective measurement processes of agents W and W-bar. Hence, with particular reference to Table 3 of the Frauchiger/Renner article, the Newcomb certificates that are associated to the deductions of the first two rows (as generated by agents F and F-bar) necessarily are dynamically altered, ex post facto and contrary to the rules of prediction games, by the Lindbladian generators of the projective observation processes of the second two rows (as imposed by agents W and W-bar).

    In a nutshell, by the usual rules of prediction games, agents W and W-bar are cheating. Yet their cheating method is so delightfully non-obvious (for me at least), that the Frauchiger/Renner analysis acquires the character of an magic trick; a trick that initially astounds us, and subsequently — once the mechanism of the trick is understood — brightly illuminates some of the way(s) that we humans think about predictive processes (and even predict them).

    In summary, a followup-up analysis, in which deductive inferences are certified using Newcomb Boxes, will conclude — as seems likely to me anyway — that “Quantum agents generally cheat at prediction games, but when everyone plays fair, no contradictions arise”

  83. Renato Renner Says:

    Schmelzer #74:

    Good you are mentioning the de Broglie-Bohm theory (dBB). It serves as an excellent example to illustrate how our thought experiment is different from the simplified version that Scott proposed.

    As you are writing, one can indeed apply dBB to our thought experiment and trace in detail what happens. What you will find (our paper does not go into detail here, but it is rather straightforward to do the calculation) is that dBB contradicts statement \bar{F}^{n:02} of Table 3. In other words, according to dBB, the implication “r=tails ==> w=fail” is not correct.

    Conversely, if one applies dBB to Hardy’s paradox, the result is different. Here the statement corresponding to “r=tails ==> w=fail” is always valid.

    So, how can it be that dBB gives a different result when applied to our thought experiment rather than to Hardy’s? The reason is, roughly speaking, that Hardy’s paradox is based on “counterfactual” reasoning, i.e., the different statements are established in different runs of the experiment with different measurement choices. In contrast, in our thought experiment, all measurement outcomes by all agents are obtained in one single run (and hence, in dBB, represented by the corresponding Bohmian particle positions in that single run). One can therefore reason about them without referring to counterfactuals.

  84. David Thornton Says:

    Dr. Renner, please see the entry of 26 September in ‘The Reference Frame’ blog of Lubos Motl where he refutes your proof.

  85. fred Says:

    David #84
    Motl’s short conclusion (in case you don’t want to deal with all the profanity stuff on the blog) :

    “Their invalid “proof” that the “Copenhagen Interpretation” requires to abandon “C” boils down to their incorrect assumption that it doesn’t matter, from some observers’ viewpoints, whether an observable was measured (by someone else). But the measurement of a quantity whose outcome isn’t certain at the moment always changes the situation – and it changes the situation from all observers’ viewpoint.”

  86. fred Says:

    So, if the “alive” version of a Shrodinger’s Cat that’s in the isolated box happens to measure a qubit, it (the collapse) “affects” all observers outside the box, so a measurement is a “universal”/”absolute” event?

    But yet this collapse of the qubit’s wave function would also have to be in superposition with the case where there was no collapse (the cat is dead and couldn’t measure the qubit)?

    Doesn’t seem that obvious to me…

  87. Jochen Says:

    Renato Renner #83:
    “In other words, according to dBB, the implication “r=tails ==> w=fail” is not correct.”

    I’m not totally convinced one can make this inference in ordinary quantum theory. Sure, if \bar{F} assumes their observation collapses the state, that’s OK, but it seems to me that, in order to predict W’s observations, they should apply QM from W’s perspective, which will in the end correctly yield that W could obtain either OK or Fail…

  88. fred Says:

    The paper is fundamentally flawed because its assumption that one can assemble a group of agents who all agree on how to apply QM isn’t a given at all… haha.

  89. Renato Renner Says:

    David #84:

    Next to my random number generator that determines which blogs I should comment (see #48) I have an even more elaborate device that tells me which ones I should not even read. 🙂

  90. ppnl Says:

    fred #86

    ” So, if the “alive” version of a Shrodinger’s Cat that’s in the isolated box happens to measure a qubit, it (the collapse) “affects” all observers outside the box, so a measurement is a “universal”/”absolute” event? ”

    It isn’t clear what precisely you are asking here. But OK first of all the cat interacts with a qubit. It does not matter if the cat is dead or alive when it does so. In order for that interaction to affect observers outside the box it has to be outside the box and that is exactly what the box is intended to prevent.

    The cat is constantly interacting with qubits inside the box. After all the whole point is to have the cat interact with an unstable particle (qubit) in order to place itself into superposition.

    And wave collapse is not universal. We view the cat as being in superposition. But from the cat’s point of view we may be in superposition. In order for us and the cat to agree there must be information flow across the walls of the box.

    Think of wave collapse as a very bad social disease. Any contact at all and you spread the cooties. The box protects the cat from our cooties. And protects us from the cat’s.

  91. Renato Renner Says:

    Jochen #87:

    If r=tails then, according to the protocol, agent \bar{F} must prepare the state as “spin right”. The Born rule is then applied to this state. So, I do not think anything about “state collapses” needs to be assumed here. (Agent \bar{F}’s conclusion is of course only correct if one knows that she indeed saw r=tails. But this is taken into account in the chain of reasoning; see in particular the second row of Table 3, i.e., agent F’s reasoning.)

  92. Dandan Says:


    2. Whenever Diane is in the |1〉 state, she knows that Charlie must be in the |0〉 state (since there’s no |11〉 component).
    3. Whenever Charlie is in the |0〉state, she knows that Diane is in the |+〉 state

    As I see it, this is already a contradiction – Diane in the |1〉state knows that Charlie knows that Diane is in the |+〉state.

    I think the problem here is that Diane’s “discovery of herself” is a measurement with the result unknown to Charlie. But if Charlie knows how Diane measure herself (that is in {|0〉,|1〉} basis) she can update her beliefs from |+〉to a mixed state of |0〉and |1〉. This mixed state is still not equal to |1〉but this discrepancy is justifiable.

    Anyway, this whole thing is very “thought-provoking”. Thank you for awesome exposition!

  93. ppnl Says:

    Andrei #81:

    ” Let’s assume that the quantum world is actually described by a classical, local, field theory. ”

    That would mean that any supposed quantum computer would actually be a classical computer right?

    If they develop large scale quantum computers that give exponential speed up over classical computers would that disprove super-determinism?

  94. Brad DeLong Says:

    #89 seems wise…

  95. Jochen Says:

    Renato Renner #91:
    “So, I do not think anything about “state collapses” needs to be assumed here.”

    Well, the thing is, \bar{F} can reason through the setup in exactly the way we can, to derive that \bar{W} will get the fail-result. And it seems to me that they must know that this is what occurs, in the same way that Wigner’s original friend must know that a suitable experiment performed on their entire lab will show interference. It wouldn’t do to claim that, since the friend observed a certain outcome, they must now predict the non-existence of interference in such an experiment.

    But then, by the same token, it seems to me that \bar{F} ought to reason that the state from the point of view of \bar{W} has components |h>|-1/2>, |t>|1/2>, and |t>|-1/2>, which after W’s measurement is projected onto |OK>|1/2>, which is an equal superposition of |h>|1/2> and |t>|1/2> (see my comment #73 above). Consequently, \bar{F} shouldn’t predict the fail-outcome.

    They should only predict ‘fail’ if the state is equal to |-1/2> + |1/2> to \bar{W}—but it’s not, and \bar{F} knows this.

  96. Jochen Says:

    “Well, the thing is, \bar{F} can reason through the setup in exactly the way we can, to derive that \bar{W} will get the fail-result.”

    This was supposed to be “…may get the OK-result”.

  97. sf Says:

    With apologies to Tim Hardin, crossing over to the silly side:

    If I were a particle,
    and you were a wavelet,
    would you measure me any way,
    would you be my A-gent?

    If entanglement was my trade
    Would you still find me
    Carryin’ the charge I gave
    in our Feynman diagram

  98. Ahron Maline Says:

    It seems to me that the authors of the paper have failed to include, in their list of assumptions, the crucial one: that one who observes a measured value may conclude that the state, after measurement, is an eigenstate corresponding to that value. Without this, the first line of Table 3 in the paper is clearly wrong: when agent Fbar measures r=tails, he has no right to treat the right-polarized atom he is sending as “the true state”, and use that to make predictions about what W will measure. He knows perfectly well that his other self, who measured r=heads, is sending a down-polarized atom, which may affect W’s result. This reasoning by Fbar only makes sense with what amounts to a collapse assumption. Of course this contradicts the assumption that QM can be applied to systems that include observers.

    On the other hand, Fbar is justified, without additional assumptions, to conclude that “if I ever see W’s result, it will be w=fail”. Making predictions from one’s observations to one’s own future observations must be valid in all interpretations, although the justification may vary. But here, What’s measurement ruins the prediction: by Hadamarding Fbar’s brain, he makes it impossible for any continuously-aware version of Fbar to become aware of W’s result. Therefore there is no problem if W in fact measures w=ok.

  99. Andrei Says:

    ppnl #93 October:

    “If they develop large scale quantum computers that give exponential speed up over classical computers would that disprove super-determinism?”

    Not at all. The purpose of superdeterminism is to provide a local explanation for QM, not to deny QM. So, if faster computers are possible according to QM they would be just as possible according to a superdeterminist interpretation of QM.

    Sure, such computers would be classical computers, but they would be a different kind of classical computers because they would make use of a different classical effect, entanglement. An electric engine and a petrol engine are both classical but they need not have the same performance.

  100. Schmelzer Says:

    Andrei #81:

    The objective Bayesian interpretation derives the probabilities from the available information. So, it forces us to accept 1/6 if we have no information which makes a difference between the six outcomes. So, even if we know the dice is faked, as long as we don’t know in which direction it is faked, 1/6 remains the only rational choice.

    Your argument (2) presupposes some reality to probabilities, following the frequency interpretation. But this is not what matters in the logic of plausible reasoning. The point there is logical consistency, and the available information. So, if you don’t use 1/6 for everything, you get a different distribution if you simply use different numbers – but your information remains unchanged, thus, your probabilities should remain unchanged too.

    (1) has essentially the same problem. Your proof (3) fails: “Not only we do not know if a measurement at one location has an instantaneous effect at another, distant location, but everything we know about physics seems to preclude such a behavior.” Sorry, no, we have a theorem that without such instantaneous influence we would have Bell’s inequality.

  101. Schmelzer Says:

    Renato Renner #83:

    So, dBB in your version gives a consistent trajectory, without counterfactual reasoning.

    Where is the inconsistency, then? It appears in the reasoning of Alice thinking that w≠ok. She is reasoning about a counterfactual experiment – one where Charlie does not measure anything, and therefore does not distort Bob’s state.

  102. Scott Says:

    Andrei #99: You’ve given the logical and correct answer to the question, but that’s different from the answer that the “chief superdeterminist,” Gerard ‘t Hooft, gives! ‘t Hooft is on record predicting that it will never be possible to build a quantum computer that outperforms a classical computer, because of the classical cellular automaton that he believes underlies Nature. On the other hand, he also believes that this CA is able to account for the Bell inequality violations, because superdeterminism! So I’ve always wondered: why doesn’t ‘t Hooft point out that superdeterminism could just as easily account for the successful running of Shor’s algorithm (as, in fact, it could account for anything whatsoever)?

  103. Andrei Says:

    Schmelzer #100:

    ” So, even if we know the dice is faked, as long as we don’t know in which direction it is faked, 1/6 remains the only rational choice.”

    This is only true for a single run. If you throw the dice only once you could ascribe equal probability. But if you repeat the experiment many times the equal probability assumption is a certain looser for a loaded dice. Given the fact that a Bell test comprises many measurements we are not in the single-run case. So, the reasonable assumption is that the hidden variable and the settings of the detectors are not independent parameters.

    “(1) has essentially the same problem.”

    I do not understand your point here. In 1 I have provided evidence that a field theory such as classical electromagnetism implies that the “dice is loaded”, in other words, such theories are superdeterministic, according to Bell’s definition. This is about the mathematical structure of the theory, not about prior probabilities.

    “Your proof (3) fails: “Not only we do not know if a measurement at one location has an instantaneous effect at another, distant location, but everything we know about physics seems to preclude such a behavior.” Sorry, no, we have a theorem that without such instantaneous influence we would have Bell’s inequality.”

    You are just proving my point here, about begging the question. Bell’s theorem does not prove the existence of an instantaneous influence. It allows you to choose between such an influence and superdeterminism. So, what you need to prove here is that taking the non-local option is much more reasonable than the superdeterminist option. With 0 evidence for non-local influences (outside the issue of entanglement which is the subject of our debate) and plenty evidence for physical systems that are not independent of each other your job is quite difficult.

  104. Andrei Says:

    Scott,

    The exact quote of ‘t Hooft is (from his paper, The Cellular Automaton Interpretation
    of Quantum Mechanics):

    “Yes, by making good use of quantum features, it will be possible in principle, to build a computer vastly superior to conventional computers, but no, these will not be able to function better than a classical computer would do, if its memory sites would be scaled down to one per Planckian volume element (or, in view of the holographic principle, one memory site per Planckian surface element), and if its processing speed would increase accordingly, typically one operation per Planckian time unit of 10−43 seconds.”

    So, he is not saying that it “will never be possible to build a quantum computer that outperforms a classical computer”, but it will never be possible to outperform a Planck-classical computer. It seems to me that his view is not necessitated by a classical foundation of QM but by the discrete structure of space and time of the CA. A continuous space-time background would not impose any such limitation, so, a classical computer could be equivalent to a quantum one.

  105. Jochen Says:

    Ahron Maine #98:
    “when agent Fbar measures r=tails, he has no right to treat the right-polarized atom he is sending as “the true state”, and use that to make predictions about what W will measure.”

    Yes, this is what worries me, too. It strikes me as being akin to Wigner’s friend concluding that there won’t be any interference if an experiment is performed on the whole lab, where at most they can say that they don’t know.

    It doesn’t strike me as that different from the question of whether two events are simultaneous in special relativity: just that they are to you doesn’t necessarily mean that they are to every observer. In fact, the notion is meaningless without specifying a frame of reference.

    In the same way, ‘the state’ of a quantum may differ according to different observers, and you can’t generally assume that the state you assign to a system is assigned to it by every observer. In particular, this seems to be the case with systems including you as a proper part.

    Wigner’s friend can’t decide whether Winger will observe interference, as this depends on whether they measured a system in an eigenstate of the measurement, or in a superposition. Likewise, \bar{F} can’t decide the outcome of \bar{W}’s measurement, as this, too, depends on whether the coin was in an eigenstate of ‘tails’ or in the superposition specified in the paper. Given the knowledge of the initial state, however, they should conclude that \bar{W} may observe either outcome.

  106. fred Says:

    Scott #102

    “because of the classical cellular automaton that he believes underlies Nature.”

    It’s the same idea that Wolfram had, right?

    While those ideas may be flawed, the real issue is that no-one has any robust theory for what’s going on at the Planck scale, no?
    I.e. coming up with a discrete structure (made of “cells”) for space and time that’s also fitting special and general relativity?
    (I don’t know enough about string theory to tell if it solves this).

  107. fred Says:

    About quantum supremacy and whether the universe is actually a simulation or not (whether an actual QC or a classical computer simulating a QC really poorly).

    Both “classical” and “quantum” computers are digital machines, i.e. reality is described as numbers.

    But reality itself appears analog (until we know WTF is going on at the Planck scale) and magically super-hyper-parallel.

    Reality doesn’t seem to care or struggle to make stuff happen at various scales (from super clusters of galaxies down to the proton), while digital machines need more and more resources to manipulate things consistently at both small scales and large scales.

    Reality doesn’t seem to care whether it’s solving a two-body problem or a trillion-trillion-body problem, it doesn’t need to pretend there such a thing as “isolated systems” to make things happen – every point in space sees the superposition of all the fields (gravity, EM) created by all the particles in the visible universe, no compromise (but apparently that’s still not enough information flowing in a given point of space to cause black holes to spontaneously appear? :P)

  108. bcg Says:

    Andrei #37 (but generally): How does the underlying field determine the angles the researchers choose, such that the researchers are (unknowingly!) conspiring to only present Bell inequality violations? If it’s “I know it must be complicated, and I don’t know how, but it does,” that’s fair, but it seems like a hard sell. If it’s, “That’s not what I’m saying,” then we’re not talking about Bell inequalities.

  109. ppnl Says:

    Andrei #99

    ” Sure, such computers would be classical computers, but they would be a different kind of classical computers because they would make use of a different classical effect, entanglement. An electric engine and a petrol engine are both classical but they need not have the same performance. ”

    But you seem to be postulating a classical process that violates the extended Church/Turing thesis (ECT). If entanglement is a classical process then it should be limited in the same way that all other classical processes are. Transistors are faster than electric relays but they only allow a poly increase in speed. Ditto every other classical process.

    Can you show me a CA that allows a violation of ECT? Do you believe there is such a thing? Does ‘t Hooft postulate any such thing?

    Andrei #104

    “ ‘t Hooft—–Yes, by making good use of quantum features, it will be possible in principle, to build a computer vastly superior to conventional computers, but no, these will not be able to function better than a classical computer would do, if its memory sites would be scaled down to one per Planckian volume element (or, in view of the holographic principle, one memory site per Planckian surface element), and if its processing speed would increase accordingly, typically one operation per Planckian time unit of 10−43 seconds.”

    Neither memory size nor processing speed seem relevant. It is the exponential speed up with size that matters. There are on the order of 2^620 plank unit volumes in the universe. Now imagine a classical computer with that many processors or memory elements that performed an operation in 106^-43 seconds. There seem to be simple problems that this computer could not solve in the age of the universe. But a not overly large quantum computer could. That exponential speedup for some specific problems is hard to beat.

    Now as far as I know (and this is just a hobby for me so…) there only two ways around this. Either BQP is equal to BPP or there is a classical process that violates ECT. I don’t think the smart money is on either of these. By a lot. Showing either would make you famous totally aside from any relevance to super-determinism. In fact I doubt that it would convince anyone that super-determinism is true.

    My understanding – and my understanding is limited – was that ‘t Hooft was claiming that on some scale quantum computers would fail to deliver the exponential speed increase due to the limits of the underlying classical process. This would allow him to avoid the problem with ECT and BQP=BPP. But I have never seem him or anyone else address this directly.

  110. Renato Renner Says:

    Ahron #98 and Schmelzer #101 and Jochen #105:

    “when agent Fbar measures r=tails, he has no right to treat the right-polarized atom he is sending as “the true state”, and use that to make predictions about what W will measure.”

    To make sure I understand your concern, consider a “truncated” variant of the thought experiment where agent Fbar is never subject to a measurement (i.e., Wbar does nothing to her). While you deem the first row of Table 3 as incorrect in the case of the original thought experiment, I guess that you would agree with that row in the case of the truncated experiment, right?

    If yes, then you probably have in mind a restricted version of Assumption (Q) which, along the title of Scott’s blog, we may define as follows:

    (Q_noHadamard): Like Assumption (Q), but the rule is only applicable under the condition that the brain of agent A (who prepared the system S in state psi at time t_0) is never going to be subject to a Hadamard (or any other non-trivial operation).

    If one replaces (Q) by (Q_noHadamard) in our analysis of the thought experiment then I would certainly agree that the contradiction disappears (see my comment #48).

  111. mjgeddes Says:

    fred #107

    Yes indeed,

    The more I really think on this, the more I realize how absurd the idea of ‘physics as computation’/ ‘physics as simulation’ really is, and it’s amazing that anyone fell for this nonsense. Two very smart people (Stephen Wolfram and Gerard de Hooft) are proposing a specific model of computation ( cellular automaton ) as the foundation of physics, which is even more implausible!

    You only need to look at the mathematical foundations of physics to see that it has *nothing* whatsoever to do with the theory of computation. Firstly, physics is mostly based on differential equations, which needs a continuum just for starters. Secondly, no fruitful new physics has *ever* come from theory of computation…it’s explanatory power as regards physics is nada, zip. Thirdly, theory of computation has abstracted away all the structural details of physics – many possible kinds of underlying physics could be compatible with the *same* theory of computation, therefore ToC simply can’t explain these physics details.

    As to the idea of reality as simulation (pan-computationalism), this is just a modern, supped-up version of idealism/solipsism, which can easily be dismissed. Without a physical model of how ‘computation’ is supposed to work, the whole notion of ‘a simulation of the universe’ is simply meaningless, which is just to say, computation needs some underlying hardware, and unless one specifies how this hardware is supposed to work, there’s no coherent theory there. Elon Musk is an example of a really smart guy that fell for this latest incarnation of old recycled nonsense.

  112. Andrei Says:

    bcg #108:

    “How does the underlying field determine the angles the researchers choose, such that the researchers are (unknowingly!) conspiring to only present Bell inequality violations?”

    If I understand your view correctly you imply that superdeterminism requires:

    1. In reality Bell inequality is not violated (QM is wrong)
    2. There is a conspiracy preventing us to measure some of the pairs so that we are under the (false) impression that QM is right.

    I reject both claims above.

    I think that the violation of Bell inequality is a true feature of Nature. My (qualitative) explanation for this fact is the following:

    There is an infinity of states (position velocities of electrons and quarks, electric and magnetic field magnitudes) that the source and the detectors can be in. But, for each physically possible state there is an infinity of states that are not physically possible. Example: take a real, existing state, move a single electron from the source with 1nm and leave everything unchanged. This new state is forbidden because the electric field at any location (including the location of the detector) does not correspond anymore with the charge distribution.

    So, in order to estimate the prediction of classical electromagnetism for a Bell test one needs to only count the states that are physically possible and discard the others. My hypothesis is that when the states are properly counted the violation of the inequality would result.

    You are perfectly justified in disbelieving this hypothesis, but such a disbelief is not enough to rule out the theory. If you claim that the theory cannot violate the inequality you need to actually count those states or come up with a different argument. Bell’s theorem in its present embodiment, that assume the source states and the detector states are independent, is of no use here.

  113. Jochen Says:

    Renato Renner #110:
    I would not want to be that specific in reformulating the assumption. Rather, I would maintain that one can’t in general make predictions about a system of which one is a proper part; furthermore, to me, that’s just applying quantum theory. Otherwise, you already get in trouble in Wigner’s original thought experiment, where the friend might falsely predict the absence of interference.

    There’s also work by Thomas Breuer to the effect that the assumption that one can always predict the results of measurements on systems including oneself yields contradictions, see e. g. “The Impossibility of Accurate Self-Measurements”.

  114. Andrei Says:

    ppnl #109:

    “you seem to be postulating a classical process that violates the extended Church/Turing thesis (ECT).”

    First, I must confess that my knowledge in this field is very limited, so if I say something stupid please accept my apologies.

    OK, let me present the extended Church/Turing thesis:

    http://www-inst.eecs.berkeley.edu/~cs191/fa08/lectures/lecture17.pdf

    “The extended Church-Turing thesis is a foundational principle in computer science. It asserts that any ”reasonable” model of computation can be efficiently simulated on a standard model such as a Turing Machine or a Random Access Machine or a cellular automaton.”

    The lecture continues:

    “But what do we mean by ”reasonable”? In this context, reasonable means ”physically realizable in principle”. One constraint that this places is that the model of computation must be digital. Thus analog computers are not reasonable models of computation, since they assume infinite precision arithmetic. In fact, it can be shown that with suitable infinite precision operations, an analog computer can solve NP-Complete problems in polynomial time. And an infinite precision calculator with operations +, x, =0?, can factor numbers in polynomial time.”

    So, it seems to me that a classical process that uses infinite precision (such as the evolution of a system of charged particles described by classical electromagnetism) is an example of an analog, not digital computer, and such a system can in principle be used to solve the problems that quantum computers are able to solve in comparable time.

    “Can you show me a CA that allows a violation of ECT? Do you believe there is such a thing? Does ‘t Hooft postulate any such thing?”

    I am not going to defend ‘t Hooft’s model as it does not seem to be the most promising path. I would rather go with a theory like stochastic electrodynamics (just classical electrodynamics with a special type of initial state – a real EM field, called the zero-point field, that plays the role of QED vacuum). This theory has passed some non-trivial tests, like giving a classical explanation for:

    Planck’s law
    Nature volume 210, pages 405–406 (23 April 1966)

    Debye law
    Phys Rev A. 1991 Jan 15;43(2):693-699

    electron’s spin
    J. Phys.: Conf. Ser. 504 012007

    “My understanding – and my understanding is limited – was that ‘t Hooft was claiming that on some scale quantum computers would fail to deliver the exponential speed increase due to the limits of the underlying classical process. This would allow him to avoid the problem with ECT and BQP=BPP. But I have never seem him or anyone else address this directly.”

    It seems to me that he is saying exactly that:

    ” these will not be able to function better than a classical computer would do, if its memory sites would be scaled down to one per Planckian volume element”

  115. Renato Renner Says:

    Jochen #113:

    “Rather, I would maintain that one can’t in general make predictions about a system of which one is a proper part; furthermore, to me, that’s just applying quantum theory. Otherwise, you already get in trouble in Wigner’s original thought experiment, …”

    I definitively agree that one cannot make predictions about a quantum system of which one is a part. In fact, avoiding the need for such self-predictions was a main design principle of our thought experiment (see the discussion on the top of the right column on page 5 of our article).

  116. Adam James Says:

    Scott has a good mini-thought experiment in his book(QCSD) regarding counterfactuals and conditional probabilities and observers in superposition and it illustrates the subtle error of reasoning valid in classical but not quantum scenarios that this slightly more complex paradox uses. As another blogger pointed out, Dr. Renner used the same setup to argue for MWI over single world interpretations. It doesn’t do that either. This “paradox” is just standard QM which works for everything: people, particles, or universes.

  117. fred Says:

    mjgeddes #111

    “As to the idea of reality as simulation (pan-computationalism), this is just a modern, supped-up version of idealism/solipsism, which can easily be dismissed. Without a physical model of how ‘computation’ is supposed to work, the whole notion of ‘a simulation of the universe’ is simply meaningless”

    Although I agree that from a physical description of reality point of view, “reality as a simulation” doesn’t get us very far, because we can’t say anything about the “hardware” (since we’re trapped in the system), there’s a different more practical approach to this:

    – consciousness is the only thing that can’t be denied – whether we’re brains in vats, whether the world is a simulation, whether the world is made of particles that are mathematical singularities, whether this is all a dream… the rock bottom truth is our experience of being.

    – our view of external reality, i.e. the information in our sensory data streams (and all the contents of our consciousness) is computable.

    – the dynamical evolution of external reality (i.e. physics) is such that life spontaneously appears, and life eventually creates computers, lots of them, and those computers keep getting better and better. Basically not only the universe is computable, but eventually it will organize itself into computers.

    – the content of our consciousness can be generated from a computer (aka virtual reality), not only in a way that’s indistinguishable from the external reality, but in ways that transcend external reality (from an evolutionary point of view).

    If you buy all this, it’s then not hard to see where this will lead us.
    And the unlikely situation is the one where we would not already be several recursion deep inside a collection of realities within realities.

  118. JimV Says:

    mjgeddes at 111 says “Firstly, physics is mostly based on differential equations, which needs a continuum just for starters.”

    That turns out not to be the case. Engineering uses differential equations for lots of things that are actually discrete, such as stress and strain and vibration of materials, which are actually made out of discrete molecules (and in the case of alloys, grains that can be seen under low-power magnification). Fluid flow has some famous differential equations, to deal with H20 molecules.

    Calculus is a great approximation to discrete systems. Finite-difference equations also work, and have the same types of solution as differential equations of the same form.

    Meanwhile, Zeno, Democritus, and recently George Ellis, have pointed out that the universe makes more sense in finite, discrete form. With infinities and infinitesimals you get Cantor’s Hotel and other paradoxes.

  119. sf Says:

    Dear Renato,
    I wonder if it would be possible to formulate your result as a theorem about the impossibility of extending the Feynman diagram method (for calculating amplitudes), or if it would get too messy? The idea is that Assumption (Q) corresponds to adding some kind of extra operations to Feynman diagrams, ie the agents correspond to certain ‘subclusters’ in the diagram, and operations on them correspond to the inferences/communications between the agents. This might give a language where the various viewpoints in this discussion could be unified as some theorem about what can and cannot be done legitimately (as inference methods) within the context of Feynman diagrams.

    One motivation; Feynman in some sense refined Bohr’s approach by allowing one to embed QM experiments inside others, in a nested structure, but this required replacing the measurement step by a branching interaction structure. Your paper is also embedding QM experiments inside others, so the Feynman diagram method seems like a natural way to look at things here.

  120. Jochen Says:

    Renato Renner #115:
    “In fact, avoiding the need for such self-predictions was a main design principle of our thought experiment”

    But surely, a measurement on the state of Lbar is a measurement on the state of Fbar? I mean, after that measurement, I know exactly what state Fbar is in, don’t I?

    Anyway, my main point remains: Fbar is only justified in assuming that Wbar obtains ‘fail’ if they’re justified in assuming that the state of the coin is ‘tails’. But I don’t think that’s the case, as the total state of Fbar and the coin is an entangled one.

    W, in other words, would seem to be perfectly justified in reasoning that Fbar’s knowledge of QM and the measurement setup leads them to conclude that they aren’t able to predict Wbar’s measurement outcome—which, of course, is exactly what turns out to be the case.

  121. fred Says:

    Isn’t this expected after all?

    Physics assumes systems can be isolated, but the world is really fully interconnected and deterministic (or deterministic with some pure randomness, whatever that means).

    So, strictly speaking, there’s really no such a thing as a part of a system making a prediction about another part of the system.
    And a system can’t simulate itself fully, a part of the whole by definition has less resources than the whole.

    Also, the “prediction” itself and all its apparatus have been instigated by the initial conditions of the system they belong too. They’re no more independent than any other sequence of events in the system (one wonders why a deterministic system comes up with the notion of “predictions” and “counterfactuals”, it’s not like the “predictions” are going to alter the system’s evolution in some magical independent way… just like other human made concepts, e.g. “free will”).

    Given all this, it’s really not surprising to find that there are limits to the application of physics and contradictions are bound to happen as you try to apply it all recursively.

  122. Harry Johnston Says:

    To answer my own question #72, from F’s perspective S is in a known state so there is no entanglement between Lbar and L.

    It still seems like an impropriety to allow Wbar to perform a measurement that requires the ability to predict the exact microstates of Fbar’s measuring device. Wouldn’t the simplest way to eliminate the apparent paradox be to modify assumption S to explicitly require that a measurement be thermodynamically irreversible, and assumption C to explicitly require that all measurements be thermodynamically possible?

  123. ppnl Says:

    Andrei #114:

    There is no difference between an analog computer and a digital computer. Or more precisely the only difference between them is an abstraction layer. If you zoom in on a digital memory cell past the abstraction layer what you see is an analog computer programmed to emulate a digital memory. Turns out that is the easiest problem for analog computers to solve.

    Why emulate digital computers? Analog computers have a problem with noise. An analog computer without digital emulation will never calculate hundreds of digits of pi because you could never measure the output that accurately. And a fly fart on the other side of the galaxy would disrupt the calculation anyway. Digital computers have calculated sixty trillion digits of pi. In almost every instance the gain you get from the ability to control noise far outweighs the penalty from the emulation layer. Flies are free to fart all they want.

    In short a digital computer can be seen as a particular kind of analog computer algorithm that allows you to control noise. But what that means is that anything that allows you to build better analog computers also allows you to emulate better classical computers. An infinite precision analog computer would allow us to build an infinitely fast digital computer. In a deep sense these are the same thing.

    But infinite precision is a chimera. That would imply infinite information density and your computer would collapse into a black hole dragging the rest of the universe with it. The universe contains a finite number of atoms, finite energy and finite space. As a result it also contains a finite amount of information. This prevents any infinite precision analog computer. Else we would have to junk 99% of all we think we know about physics. There is no simple fix to get around this.

    A quantum computer isn’t faster than a classical computer in the sense of more operations per second or more information density. A quantum computer changes the definition of information and computation in a way that probably allows new algorithms that are exponentially faster on some problems than any possible classical algorithm. That means a comparatively modest quantum computer could outperform any classical computer made with the resources of the entire universe. And necessarily also any analog computer as they have the same limits.

    And remember a quantum computer is only faster on a tiny subset of problems. On most things it is no better than classical. It just isn’t generally faster.

  124. bcg Says:

    Andrei #112

    > So, in order to estimate the prediction of classical electromagnetism for a Bell test one needs to only count the states that are physically possible and discard the others.

    The probability of non-quantized spin being exactly +1/2, or exactly -1/2, is zero. Forget violating BI; how can classical electrodynamics even *obey* BI? This is regurgitated Wikipedia here, so if this is moonman talk, please be kind.

  125. Renato Renner Says:

    Scott,

    I am afraid that it will look as if I’m hijacking your blog if I continue answering the many comments. But I appreciate the variety of reactions that have appeared here, ranging from something like “it has already been done” (either by Wigner or by Hardy) to “it’s really not surprising to find that there are limits to the application of physics” and to “it is fundamentally flawed”. 😉

    For now it’s probably better if I remain silent until someone manages to not merely claim the existence of a flaw but to also localise it (which I think is not too much to ask, for our argument is described step-by-step in the article). Even more because I do not know how to reasonably reply to indirect allegations of the type “I have a simplified version of your thought experiment where no contradiction arises, so your argument must be flawed somewhere”.

    Anyway, my conclusion so far (on the superficial level of the blog’s title) is: Yes, it is hard to think after someone Hadamarded your brain, but certainly not before!

  126. Andrei Says:

    ppnl #123:

    “But infinite precision is a chimera. That would imply infinite information density and your computer would collapse into a black hole dragging the rest of the universe with it. The universe contains a finite number of atoms, finite energy and finite space. As a result it also contains a finite amount of information. This prevents any infinite precision analog computer. Else we would have to junk 99% of all we think we know about physics. There is no simple fix to get around this.”

    I disagree. Nature works with infinite precision because space and time are continuous. This is true in QM and it is also true in general relativity. The magnitudes of fields, locations of particles, etc. are real numbers that have an infinite number of digits. If you introduce a discretisation you run into problems, like violations of symmetries and conservation laws. This is a significant problem for ‘t Hooft’s CA model and he is aware of that. It might be that a solution to this problem exist, but, regardless, our current understanding suggests space-time is continuous.

    GR does not predict that a black-hole appears any time the distance between two objects is not represented by a rational number, so it is clear that there has to be a mistake in your reasoning. My guess is that the mistake originates in the confusion between the information contained in the system itself and the information that can be extracted by using an experimental procedure. For example if you want to measure the location of a particle with infinite accuracy you need a photon of 0 wavelenth, or infinite frequency, and such a photon would carry an infinite amount of energy. It is that energy that creates the black-hole.

    So, a classical, analog computer “computes” with infinite precision, and the only limit is imposed by our ability to measure the initial state (input) and the final state (output).

    “A quantum computer changes the definition of information and computation in a way that probably allows new algorithms that are exponentially faster on some problems than any possible classical algorithm.”

    OK, let’s be precise about what “classical” means here. For the purpose of our discussion a classical theory is a local and realistic theory. Classical electromagnetism, or general relativity are examples of such theories. Now, do you have a proof for your above statement? Can you prove that a computer that is based on local, realistic physics cannot achieve the same performance as a quantum one?

  127. Andrei Says:

    bcg #124:

    The probability of non-quantized spin being exactly +1/2, or exactly -1/2, is zero. Forget violating BI; how can classical electrodynamics even *obey* BI?

    Quantization might be achieved classically as well.

    Please take a look at this paper:

    Emergence of quantization: the spin of the electron (A M Cetto1, L de la Peña2 and A Valdés-Hernández) – J. Phys.: Conf. Ser. 504 012007

    The article can be read here:

    http://iopscience.iop.org/article/10.1088/1742-6596/504/1/012007/pdf

  128. fred Says:

    ppnl #123

    “But infinite precision is a chimera. That would imply infinite information density and your computer would collapse into a black hole dragging the rest of the universe with it. The universe contains a finite number of atoms, finite energy and finite space. As a result it also contains a finite amount of information.”

    But information density, holographic principle, Hawking radiation… that’s still all entirely speculative, no?
    The only thing we’ve ever observed (indirectly) about black holes is their gravity effects (orbits of neighboring stars and gravity waves), and the quantization of space is a difficult nut to crack (https://en.wikipedia.org/wiki/Doubly_special_relativity)

  129. Brad DeLong Says:

    Dear Professor Renner:

    With respect to your “it’s probably better if I remain silent until someone manages to not merely claim the existence of a flaw but to also localise it”, I’m not sure that it’s a flaw, but I would like to ask your reaction to this response:

    Rauchiger-Renner write: “At time n:01 \bar{F} observes tails and thinks: Statement {\bar{F}^{n:02}: ‘I am certain that W will observe w = fail at time n:31.'”

    In fact, even though at time n:01 \bar{F} observes tails \bar{F} is not certain that W will observe w = fail at time n:31, for in fact it is not certain that W will observe w = fail at time n:31.

    What \bar{F} does think, using quantum mechanics, is, rather, this:

    >I have just made a measurement and observed tails. If this measurement of mine were to have branched the multiverse—decohered the state—then I would be certain that W will observe w = fail at time n:31. But I know, looking forward into the future, that my measurement has not branched the universe—decohered the state—or, rather, I know that my brain will be Hadamarded in the future to reconstitute the state, so that nothing will remain in the universe of my measurement of “tails” other than the fact that everyone will agree that I made it.

    >Because I know quantum mechanics, I know that the reconstitution of the state |\psi> requires that my reasoning now, pre-Hadramard, take account not just of what I have observed but of what my ghostly self on the branch that observed heads observed, just as their reasoning must take account not just of what they have observed but of what they see as the ghostly me on this branch that observed tails observed. And when I take account of that, properly using quantum mechanics, I see that even though I know—right now— that the wave function is |0+>, quantum interference with |1+> + |1-> raises the possibility that W will not observe w = fail at time n:31.

    But I am not sure whether I have identified a flaw in your argument. Perhaps I have merely understood what your argument is…

    Yours,

    Brad DeLong

  130. Brad DeLong Says:

    Dear Ahron:

    With respect to “On the other hand, \bar{F} is justified, without additional assumptions, to conclude that ‘if I ever see W’s result, it will be w=fail…’”

    Should that be:

    >\bar{F} is justified, without additional assumptions, to conclude that “if any version of me that retains a memory or any other signal of the fact that I measured tails ever sees W’s result, it will be w=fail…”

    ?

    Yours,

    Brad DeLong

  131. Andrei Says:

    Renato Renner #125:

    For now it’s probably better if I remain silent until someone manages to not merely claim the existence of a flaw but to also localise it (which I think is not too much to ask, for our argument is described step-by-step in the article).

    OK, let me try.

    You write:

    “One observer, called agent F, measures the vertical polarisation z of a spin one-half particle”

    and

    “The other observer, agent W, has no direct access to the outcome z observed by his friend F. Agent W could instead model agent F’s lab as a big quantum system”

    The assumption here is that it is possible to shield the content of the lab from an observer situated outside of the lab. My question is simple. How would you do it? How would you build a lab so that no information about the interior can leak outside. More to the point how can you stop the gravitational, electric or magnetic fields that are correlated to the contents of the lab to be measured from outside?

    Thanks!

  132. Jochen Says:

    Renato Renner #125:
    “For now it’s probably better if I remain silent until someone manages to not merely claim the existence of a flaw but to also localise it”

    Let me just say that I really appreciate your willingness to comment on your work online, but I also understand if it gets a bit… tiresome. Also, even though I don’t think I quite agree with the conclusions of your paper, that doesn’t mean I think it’s not worthwhile—far from it, I think it already has stimulated and galvanized much thinking on the matter, and will continue to do so, which is, to me, definitely a good thing. As the (alleged) Bohr quote goes, the opposite of a profound truth may well be another profound truth.

    That said, to me, it’s becoming more and more clear exactly where I disagree, and I’m gonna use the benefit of having access to a keyboard again to try and explain myself as best I can (for whatever it’s worth). Perhaps I’ll later try and write up something more formal, if I feel my argument contributes anything to the discussion.

    First of all, I’m gonna agree with you that there is indeed a contradiction that arises from your assumptions Q, S, and C. However, I disagree that assumption Q reasonably follows from using quantum theory.

    To localize my disagreement, I do not think that Fbar(n:02) is a statement that Fbar can reasonably make. The reason for this is, essentially, that the inference from observing ‘tails’ to the total state being |t>(1/sqrt(2)(|-1/2> + |1/2>)) does not follow.

    To break this down, Fbar has two lines of reasoning available to them:

    A: “I have observed ‘tails’; hence, I prepare the state 1/sqrt(2)(|-1/2> + |1/2>). Nothing Wbar does changes anything about this, as the total state is the tensor product |tails>[1/sqrt(2)(|-1/2> + |1/2>)]. W’s measurement hence yields ‘fail’, as |ok> = 1/sqrt(2)(|-1/2> – |1/2>) is orthogonal to the state reduced to Lbar.”

    B: “I have observed ‘tails’. However, I know that the coin was prepared in the state |init> = 1/sqrt(3)|heads> + sqrt(2/3)|tails>. Hence, the total state now is |Ψ> = 1/sqrt(3)|heads>|-1/2> + sqrt(2/3)|tails>1/sqrt(2)[|-1/2> + |1/2>] = 1/sqrt(3)(|heads>|-1/2> + |tails>|-1/2> + |tails>|1/2>). Written in the {|okbar>,|failbar>} basis, this is |Ψ> = 2/sqrt(6)|failbar>|-1/2> + 1/sqrt(6)|failbar>|1/2> – 1/sqrt(6)|okbar>|1/2>. This is an entangled state.

    After W observes the outcome ‘okbar’, the total state will be |okbar>|1/2> = 1/sqrt(2)[|heads>|1/2> – |tails>|-1/2>]. But this isn’t orthogonal to |ok>, so W may obtain w = ok.”

    It seems to me that the preferable line of argumentation is B. For one, it has the advantage that it yields the right conclusion, and Fbar must know this in the same way that we do. But more importantly, it doesn’t make the (IMO) unjustified assumption that just because Fbar has made an observation, they can conclude what the total state is for another observer.

    Because in the end, this is a self-measurement: |heads> and |tails> include Fbar’s observation of the coin as ‘heads’ or ‘tails’, and while there’s originally no component |heads>|1/2>, this is there after Wbar’s measurement. So, if we were to tell Fbar after the measurement of W that the outcome was ‘ok’, they’d say: “Of course, that’s very well possible; after all, I observed ‘heads’ at the start!”. So in that sense, no contradiction ever arises—even though one may squirm a little at the ‘undoing’ of Fbar’s knowledge/measurement result.

    But this isn’t even something unique to quantum mechanics: even classically, given the power of re-wiring your brain, I can make you believe that a coin came up ‘heads’ even if you observed it coming up ‘tails’. “I shall then suppose, not that God who is supremely good and the fountain of truth, but some evil genius not less powerful than deceitful, has employed his whole energies in deceiving me…”

    In the general case, we can’t assume Fbar knowing the initial state of the coin, so this seems to prohibit the argumentation B. But then, it doesn’t follow that A is the right way to think. Rather, Fbar ought to reason that they have no way of knowing whether the state, after preparing the spin, is |tails>[1/sqrt(2)(|-1/2> + |1/2>)]: there could well be entanglement between the state of the coin (and consequently, the state of Fbar after observing the coin) and the state of the spin. And by Breuer’s argumentation I have cited above, Fbar cannot decide whether that’s the case. Consequently, they aren’t entitled to derive any conclusions regarding the total state; but this, likewise, blocks the inference of Fbar(n:02).

    This may seem a troubling conclusion in itself, since it implies that there are some things about the total state of the universe (if it’s meaningful to speak of such an entity) that we can’t know; but after all, we can at least derive our own future experiences, and, at least according to what we ever can get to know, this won’t yield any contradictions.

  133. fred Says:

    Jochen #132

    “This may seem a troubling conclusion in itself, since it implies that there are some things about the total state of the universe (if it’s meaningful to speak of such an entity) that we can’t know”

    Why is this troubling or even surprising?
    By definition isn’t the universe made of mostly “stuff” we can’t fully resolve?

    – The part can’t contain (and know) the whole.
    – Perfect knowledge of something is duplication, and the no-cloning theorem says it can’t be done.
    – Short of duplicating a system, we can probe it, and such action is always destructive.
    – The instrument and the object studied can’t be truly independent (for every action there is a reaction), so knowing everything about an object would require knowing everything about yourself perfectly as well.

    The only time we are truly in control is when we’re talking about bits, because they’re relative to us, we made them, they live entirely in our minds!

  134. Ahron Maline Says:

    Renato Renner #110

    Sorry for the delayed response, especially now that you want to withdraw from the discussion. Nevertheless, I’d like to try to further clarify my point.
    What you called “Q-no-Hadamard” is indeed a fair description of the “bottom line” as to when “QM predictions” based on observations are expected to be correct. That is why there is no paradox, and I suspect that Scott intended something similar.
    However, I am making a stronger statement: I believe that your work, which is framed as establishing a new no-go combination of assumptions, does not in fact do so. Your assumption Q is not a sensible position to take, regardless of the other two, and so ruling it out teaches us little.
    If I understand correctly, assumption Q states that if one observes a particular classical reality, he may take the corresponding quantum state and use it to make predictions (at least when the probability is 1), and these predictions will be satisfied by future observations of any possible observer. In our case, Fbar is using his observation r=tails to predict W’s observation as w=fail.
    But there is no sensible reason that this should work! Wigner’s friend experiment presents us with a clear dichotomy. Either:
    A. Observations made, at least by humans, represent the unequivocal reality, with all other possibilities reduced to “might have been”. This is held by the Copenhagen Interpretation, among others. Wigner pointed out that this implies QM will fail if used by an observer outside the lab, and Deutsch spelled out the failure in detail.
    So if A is true, assumption Q is “reasonable”, but known to be false. The other possibility is:
    B. Even after an observation has been made, the other possibilities continue to be “elements of reality” in some form. This may be as “parallel worlds” as in MWI, as “parts of the wavefunction that are empty of Bohmian particles” in dBB, or others. If this is the case, then assumption Q is really quite unreasonable. Why would it make sense for Fbar to ignore the r=heads “branch” when it is understood to be “real”?
    So assumption Q is not something anyone holds, and could not have been.
    Now it may be asked: according to option B, which is quite popular, how can we ever use QM at all? There are always likely to be countless “branches ” different from anything we can know about, so how do we ever make predictions?
    The most common answer to that is decoherence: the assumption that states that are “classically different” will remain too far separated in Hilbert space for any interference to ever be observed. This indeed justifies QM predictions, but of course it does not apply to scenarios where observers are measured in a Hadamard basis.
    And somewhat more generally, what is required for using QM is something like “Q-no-Hadamard”: Predictions made from an observation are valid within the “world” that “remembers” that observation, but not for a world where the observation has been “Hadamarded away”.

  135. David Byrden Says:

    Thank you for your lucid and helpful explanation of the Renner-Frauchiger puzzle.
    It’s immediately obvious that the essence of their puzzle is contained in the 1992 Hardy paradox.

    And, by thinking about that in a geometric way (as vectors in 4 dimensional Hilbert space) I was able to see what is really going on.

    It’s just like Asher Peres said; unperformed measurements have no results. In the {|+〉, |-〉} basis a qubit CANNOT be read as 1 or 0. The apparent “paradox” results from illegally combining facts from different measurement bases.

  136. Ian Says:

    Hi Scott,

    I was wondering if you had any final thoughts on Renato’s comments here? It seems the two camps ( there is a paradox / there is no paradox ) are still solidly separated…

  137. Scott Says:

    Ian #136: Yes, my final thought is still that there’s no paradox, 🙂 for the reasons David Byrden #135 says. I can’t completely localize what I consider the illegal step within the exact language that Frauchiger and Renner use, and I think it would be very worthwhile for someone to take the effort to write a response paper spelling it all out (which I expect will happen). But I can certainly state in broad terms what I consider the issue to be (and did).

  138. David Byrden Says:

    Let me spell out what I visualised.

    The system has 4 physical states (combinations of qubit values), so there are 4 basis vectors spanning its Hilbert space.

    The initial system state is a vector equidistant from three of those basis vectors, and orthogonal to the fourth, which is |11〉. As you wrote, “|ψ〉 has no |11〉 component”

    But Alice and Bob intend to measure in a different basis, namely { |+〉,|-〉} for each qubit.

    In that basis, the state vector is quite close to |++〉and equidistant from the other three vectors, which include |–〉. Don’t try to visualise this unless you are four dimensional !

    Now, the trouble starts. As you wrote:
    “… conditioned on Alice’s qubit being in the state |0〉… ”

    Alice’s qubit will read |0〉only if you measure it. This collapses the state vector into the plane spanned by |00〉|01〉.
    ( don’t forget to renormalise. )

    In its new position, the state vector is orthogonal to |–〉. So of course you cannot get there any more.

    So, in conclusion, when you say “suppose Alice’s qubit were zero” you are really saying “suppose the system were in a different state”.

    But Alice’s qubit is NOT zero. Bob’s qubit is NOT zero. The state vector is pointing out between their ones and zeros, to a spot from which it can collapse into |–〉.

  139. sf Says:

    Scott #137
    It would only make sense to “localize … the illegal step” if you are sure that this is being done in a formally consistent system. But, granting that the precise hypotheses of their article do formally lead to a contradiction, this wouldn’t be the way to resolve the Frauchiger-Renner ‘paradox’; their system would be inconsistent. So which CONSISTENT logical system should one be working in?

    The issue is more likely whether the inconsistency can be ‘localized’ to a smaller set of hypotheses, including some implicit hypotheses. (You suggest in the post some hidden hypothesis, I also made some attempt at this in #75, and was then convinced their system is inconsistent.) There is no objective way to say which hypothesis of an inconsistent system doesn’t belong, unless one passes to a larger context, ie working outside the formal system in question.

    This is also why I suggested Feynman diagrams in #119 as a potentially preferable context. (The divergences of Feynman integrals would have to be avoided, but this isn’t so relevant here).

  140. David Byrden Says:

    Feynman diagrams? There’s no need for anything like that. This is a simple, basic, comprehensible “spot the mistake” puzzle.

    The mistake is: Renner and Frauchiger put their system into a state, then they collect some statements which would each be true in *other* states. Those statements are not true in the *actual* system state.

    Finally they combine the statements, as if they were all true at once, which they are not. It’s like saying “I have just enough money for one beer. I have just enough money for a sandwich. So tonight, I will dine on a beer and sandwich”.

  141. David Byrden Says:

    DarMM #50 :

    I’ll be glad to answer your question.

    > “If \bar{F} gets tails, then he knows … the L lab will evolve into the fail state.”

    That’s true.
    But, in more detail; he knows that F will evolve into a superposition of z=+1/2 and z=-1/2.
    But, the laboratory L contains a quantum device that reads the qubit and passes the results to W without causing decoherence.
    The human being within that lab will read the device and decohere, but no trace of him will emerge from the perfectly sealed lab.
    So, the two superposed versions of data emerging from lab L will combine, and W will measure “fail”.

    > “If agent F measures z=+1/2, F can conclude that \bar{F} knows r=tails.”

    That is true.

    > “F himself would think that since he sees z=+1/2 he and his lab are not in a determined state in the fail,okay basis.”

    F would be right about that.

    > “From that he would think W could get either fail or okay.”

    No!
    F knows that he’s in a superposition. There are two of him, seeing different data.
    And the lab equipment creates constructive interference between his data and his doppelganger’s data.
    They will both contribute to W’s measurement, resulting in “fail”.

    ———–

    Here’s another example of this phenomenon. Imagine a Young’s slit experiment. You are speaking to the photon:

    “Hey, you just went through the Left slit, didn’t you?”
    “Sure did!”
    “Well, there’s a version of you who went to the Right.”
    “I know, he voted for Trump. We’re not on speaking terms.”
    “I have good news. You’re about to meet up and work together!”
    “What? Why?”
    “Because you’re about to hit a wall that doesn’t care about your direction.”

    ———–

    So, in conclusion; the agents in the labs should remember that they themselves are in superpositions, because those superpositions will come into play when the external agents measure everything.

  142. sf Says:

    David Byrden #140
    Basically I agree with you, and the idea is to start with the approach you use. But to respond to the challenge that Renato and Scott were discussing you don’t get the option to finish things up that way. You have to either isolate the mistake within the formalism as Renner and Frauchiger framed it; with agents, ‘knowing’ and inferring things in their ‘partial states’ which aren’t quite quantum or classical states, or you have to say specifically where their setup just doesn’t make sense. Overall no one claims it makes sense, since it gives a paradox, but the issue is if this comes from the global setup or from some more localizable conflict, ie whether there’s anything interesting and deep that’s new about the paradox or just the usual incompatibility of quantum and classical physics as theories of everything, presented in a slightly different way. I completely agree that you can be happy to stop where you do, but this doesn’t satisfy Renato.

    I only meant to use a very rudimentary form of Feynman diagrams; basically a branching Many-worlds interpretation, since one wouldn’t really want to translate things to set theory, but one needs some consistent framework to work in.

  143. David Byrden Says:

    Ah, now I see what you intended with the Feynman diagram.
    Yes, that’s a good idea. So I tried it.
    There are 6 branches.
    Everything is consistent until the final step of the experiment, when Agent W makes his measurement in a different basis to the one that everybody’s been using.

  144. DarMM Says:

    Hi David,

    Thanks for the response. I see what you mean, but by considering himself in superposition F reaches the conclusion that W can never observe “ok”, which seems to be in contradiction to predictions based purely on the quantum state where the chance should be 1/12 (which is the result observed in the Hardy paradox case as Scott mentioned).

    It would seem to me that the agent is simply wrong to not take that his own measurement and collapse (from his perspective, I.m not saying this implies MWI is wrong) into account and shouldn’t reason based on viewing himself in superposition.

    In fact he seems to be composing facts from a collapse and no collapse stand point.

    Collapse to reason that \bar{F} got tails.
    Then no collapse to reason that he should adopt \bar{F}’s view of him.

    It’s only with these composed that he obtains W = fail always, in contradiction with the 1/12 prediction from the actual quantum state.

  145. DarMM Says:

    David,

    Sorry scratch the first part of that. Concluding W cannot get “ok” is fine for the reasons Scott mentioned in the main post. At that point W would get fail. It’s not until \bar{W}’s measurement that this conclusion is invalidated.

    However I’d like to see an interpretation neutral take on F’s two different conclusions. Yours requires something like Many-Worlds.

    It seems F could either consider him and \bar{F} to be in the state:
    |tails,fail>
    or the state:
    |tails,1>

    and both give different predictions for W.

    Now \bar{F} has P(W = fail) = 1, certain. So it seems F would need to adopt the superposition view of himself for superobservers who can make measurements on his lab at the atomic scale.

    Many-Worlds sees this as because there are two F observers. However not all interpretations view superposition like this.

  146. David Byrden Says:

    sf #142

    So I should specify exactly where the paper contains errors. All right, here’s the first error as an example:

    Refer to Table 3. Its first entry reads :

    /F observes r = tails at time n:01

    Now, this agent is in superposition because she could have observed either “heads” or “tails”. In the “many worlds” interpretation, there are two of her in separate worlds. This entry describes only the “tails” copy of agent /F.

    She knows this too. But the paper claims that she will use Quantum Mechanics when thinking about things.

    Her deduction is:

    “I am certain that W will observe w = fail at time n:31.”

    From her point of view, this seems a foregone conclusion. She will send a qubit to agent F, in an equal superposition of “up” and “down”. That will put agent F into a superposition. Then agent W will measure agent F, and one of his measurement vectors will coincide exactly with the state vector of agent F. The result of “fail” seems inevitable.

    But she’s doing it wrongly.

    She’s ignoring the other copy of herself, in the parallel “heads” world. That other copy of agent /F will also pass a qubit to agent F. The two qubits may come from separate worlds, but they are coherent and they will combine (like the two paths in a Young’s Slit experiment). Agent F will receive a qubit containing information from BOTH the “heads” and “tails” worlds. The proportions will NOT be fifty-fifty. Agent /F made a wrong calculation.

    She did not use Quantum Mechanics properly, as claimed.

    That’s it, in a nutshell. I could prove it with algebra, I could draw it in 4 dimensional Hilbert space, but I think you have the idea now.

  147. DarMM Says:

    I’m a dumbass, the three observer case I’m asking about is nothing more than the usual oddness for running interference experiments on other observers that one encounters in the usual expanded discussions of Wigner’s friend.

  148. David Byrden Says:

    So, I’m putting my refutation of this paper online at;

    http://byrden.com/quantum/consistency.html

    If there is interest, I will flesh it out. (For example, you might wonder what happens if the labs are unsealed.)

    David

  149. sf Says:

    David Byrden #146

    Thanks. What you say looks right to me, but I’m hoping to have a strong coffee and look at the F-R (Frauchiger-Renner) paper a bit harder soon and possibly play devil’s advocate a bit, just to see if there are still issues of interpretation to be settled. Also, in #75, above, I had some vague hunch related to your point. I’m a bit worried that there are ’straw-men’ littering the terrain; maybe we’re taking the paper to be claiming more than it really does, or maybe F-R is even attacking viewpts that nobody really holds on unlimited use of QM.

    In the meantime I noticed that
    https://fqxi.org
    features a link to a more recent Renner project
    https://fqxi.org/community/articles/display/231
    Dissolving Quantum Paradoxes – The impossibility of building a perfect clock could help explain away microscale weirdness.

    The project coauthor, Lídia del Rio, also nicely presents F-R in a video:

    https://www.perimeterinstitute.ca/videos/journal-club-frauchiger-renner-no-go-theorem-single-world-interpretations-quantum-theory

    I had wondered a bit if there was any issue with taking for granted the fact of giving agents in F-R access to synchronized clocks? But probably this is just a technical point.

    A similar issue is that agents seem to have a way of calibrating their Hilbert space bases; eg the same spin up/down test is shared by the independent labs L, /L. But a priori there shouldn’t be any relation of these bases, especially because F-R assert that labs L, /L are in pure states to start. If they calibrate, then they are entangled. This could be resolved by building in the basis at the outset, but that may have other problems, depending on which interpretation one works in.

  150. David Byrden Says:

    > “agents seem to have a way of calibrating their Hilbert space bases; eg the same spin up/down test is shared by the independent labs L, /L.”

    That’s true, but I thought it would be trivial to do that?

    e.g. if the polarisation of a photon is the shared qubit, then it’s only necessary to have the measuring devices set up with their measurement axes parallel. No special entanglement is needed. I’m sure I’ve seen that done in various quantum experiments.

    Am I missing something there?

  151. sf Says:

    >I’m sure I’ve seen that done in various quantum experiments.

    But the classical measuring devices there are set up using CLASSICAL INTERACTIONS to align them, with measurement axes parallel. Here we have 2 labs that are strongly isolated from each other, as quantum systems. So this ‘classical interaction’ is not available.

    In fact there could be pretty arbitrary unitary operators on the whole quantum computer/lab interfering with alignment after some time passes, insofar as quantum mechanics makes it hard to rule out some initial drift/jitter. There might be a pretty deep problem with getting 2 QM-isolated labs to interact in any meaningful way. I wonder if this has been discussed anywhere?

  152. David Byrden Says:

    Ah, yes, I see. An interesting point. So, we align the measuring devices, then seal them inside “labs”. Will they be aware if they accidentally rotate?

    Well, under SR, your orientation in space is an absolute reference (but not your “speed” or position). So, surely you’d notice if you were rotating? Even when isolated? Because there’s spacetime in the box with you.
    Or, when we build a perfectly isolating “lab”, would it cut you off from the absolute angles of spacetime?

    Which prompts a more fundamental question:
    This experiment, like Schrodinger’s Cat, requires the “box” or “lab” to perfectly block any information coming out from the inside.
    But, wouldn’t both experiments work if information could enter from the outside?

  153. sf Says:

    David Byrden #152
    There’s still a lot to try and clarify here. What seems OK so far is that calibration between labs would involve entanglement, but also that in an orthodox Copenhagen context, a physicist would prepare the 2 (or more) labs so that axes would be aligned for some finite time experiment. Then he/she can apply Born’s rule using that alignment. But I’m not sure the lab agents F,/F, can ‘know’ this; they don’t benefit from the Copenhagen version of Born’s rule, not having prepared this state themselves.

    Your SR point is right (and analogously in Newtonian/Galilean contexts) but there’s a difference between ‘orientation in space is an absolute reference’ and giving access to measuring such absolute orientation to agents in a lab. This is analogous to the issue of time; QM assumes that time-like slices are well-defined, but this doesn’t mean that entities/agents in an experiment can read off this time from some absolute clocks. There’s even an uncertainty principle for time that obstructs this (and more subtle issues of interpretation involved there).

    I don’t know yet if F-R mention any of this, still have to get back to the article.

    The lack of absolute reference for “speed” or position may be enough to rule out access to measuring absolute orientation for lab agents; the (macro but quantum) lab apparatus can tilt by the uncertainty principle for the position of ‘one end’. This may involve one lab implicitly measuring the other’s position though.

    >wouldn’t both experiments work if information could enter from the outside?
    If it’s coming from one lab to the other, which is all that matters here, then there’s still decoherence or entanglement I guess.

  154. Benjamin Says:

    Renato Renner #125

    I don’t think my ideas are new to this thread, but I frame my objections as an error in your Table 3, rather than “identifying and rejecting an additional unstated postulate” as Scott claims he is doing.

    F’^{n:02} should really read “I am certain that W will observe w=fail after n:11 if I still know the S measurement in the |x> basis.”

    F measures in the |z> basis. This alone does not matter to F’, since F’ does not have access to the F measurement. So at this point (t >= n:11) the F’ statement above still holds: a W measurement will yield w=fail. This is not inconsistent with F at this point either.

    If W’ makes a measurement before W, and F measured |+z>, then W’ must find w’=ok’ (assuming consistency (C)). This is again consistent with both F’ and F. However, now F’ cannot know that S is in the |+x> state. Although not a direct measurement on the transferred bit, the W’ measurement fixes S=|+z>. So F’ can no longer be confident that W will observe w=fail — that conclusion was drawn from the knowledge that S=|+x>.

    This is equivalent to Scott’s objection on the grounds of a Hadamard application to the brain, but I think it is helpful to think about what that actually means in terms of the thought process of F’. Before the W’ measurement (which F’ must be aware of), F’ knows S=|+x> because he made it that way. But F’ also knows the Stern-Gerlach experiment, and knows that if S is measured in the |z> basis, the S=|+x> knowledge is lost.

    Now in this thought experiment we already know that F measures S=|+z>, but F’ does not know that so still has confidence that S=|+x>. The important step for F’ is the W’ measurement of w’=ok’. As you state in equation (6) of your paper, the w’=ok’ measurement implies S=|+z>. This is not inconsistent with anything any of our observers have seen so far, but it does mean that F’ loses confidence about S=|+x>. This is not inconsistent with (Q) or (S), but is inconsistent with the idea that labs L and L’ are independent, and I think that is where some of the confusion lies. The S bit, and {F’}’s knowledge of it, are entangled with the L’ lab since F’ prepared the bit and sent it to F. That step alone doesn’t cause concern — it’s the same as Schrodinger preparing his poison-release contraption before he puts it in the cat box. But when W’ measures w’=ok’, he is implicitly making a measurement on that bit in the L lab, even if he doesn’t actually “open the box”.

    I’ll end with a final sanity check to show that F also has a consistent view with the other observers. F, being isolated from F’ and W’, is unaware of the W’ measurement so we are tempted to still see an inconsistency from statement F^{n:14}. But that statement must also be altered in the vein of F’^{n:02}, as it was deduced from an application of (C) to F’. So it is not accurate for F to think “I am certain that W will observe w = fail at time n:31.” Rather, F can only say “If W observes w=ok, then F’ must not know the state of S in the |x> basis, and none of us could have known for certain what W would observe.” A simple calculation shows that the probability of this from the F frame yields the expected 1/12.

  155. tez Says:

    @ David Byrden #146 – note the original title of the paper:

    https://arxiv.org/abs/1604.07422v1

  156. David Byrden Says:

    I’m analysing this Gedankenexperiment and I have a question. I think I know the answer but I’d like someone who has qualifications in QM to tell me what it is.

    Agent /F goes into superposition when she becomes entangled with the randomness generator.

    She prepares a qubit which is sent to the other lab.

    This qubit is not in her own state, but it’s in a state related by a unitary. We can implement that with a machine on the route connecting her lab to the other lab. In that case, agent /F sends out the qubit in her own quantum state.

    So, agent /F is left sitting in her lab, waiting to be measured, in her own quantum state. Meanwhile the qubit is on its way to the other lab, and it’s in the same quantum state.

    I think that runs foul of the No Cloning Theorem.

    I think that the only way around this is for agent /F to read the randomness generator and deliberately set up the qubit in the appropriate state. I think it’s impossible for the randomness generator’s state to “pass through” undisturbed while the agent reads it.

    Why does this matter? Because I want to confirm that reading the state of /F does not collapse the state of F. I want to be clear that they are two distinct states.

    Thank you in advance.

  157. sf Says:

    I’m not at all expert on this, but I think you’re right that there’s an interesting issue there. It would be interesting if you can give your answer in the meantime.

    >”I want to be clear that they are two distinct states”
    If I understand, you mean that it remains a superposition of two distinct branches or components?

    My guess is that when you try to quantize the labs there has to be some allowance for error to creep in. Its crucial to have some quantitative bounds on this error, which may be a problem for F-R.

    See
    https://en.wikipedia.org/wiki/No-cloning_theorem#Imperfect_cloning
    Buzek and M. Hillery showed that a universal cloning machine can make a clone of an unknown state with the surprisingly high fidelity of 5/6. Also,
    https://en.wikipedia.org/wiki/No-broadcast_theorem

    Even to quantize a dynamical system given by polynomials of low degree is problematic, as I recall. The naive approach of using an atomic description/reduction of the labs is not valid because it doesn’t provide an exact description of a Turing machine (or human or whatever the lab is); the latter is an abstraction insofar as its error free etc. and its states are equivalence classes of physical events that aren’t quite physically defined.

    There’s some interesting discussion of classical no-cloning in:
    https://physics.stackexchange.com/questions/296678/what-is-quantum-about-the-no-cloning-theorem

    also to avoid confusion on a related issue from QCSD:
    https://physics.stackexchange.com/questions/266957/no-cloning-and-uncertainty-connections-or-misconception?rq=1

    And while at it…
    There is a sub-wiki on the F-R paper in:
    https://en.wikipedia.org/wiki/Wigner%27s_friend#An_Extension_of_Wigner's_Friend
    and in,
    https://en.wikipedia.org/wiki/Wigner%27s_friend#References
    note 13 lists some papers from many months ago criticising the 2016 preprint of F-R; eg
    Laloë, Franck (2018-02-18). “Can quantum mechanics be considered consistent? a discussion of Frauchinger and Renner’s argument”. arXiv:1802.06396
    or
    “The measurement problem is the measurement problem is the measurement problem”. arXiv:1611.01111

  158. Mateus Araújo Says:

    I’m afraid I’m very late to the party, but I’m a bit intrigued about why nobody mentioned the obvious problem that I see with the argument: the inference from Charlie being in the \(|0\rangle\) state to Bob seeing the outcome \(|+\rangle\) does *not* hold for the original state \(|\psi\rangle\). According to it the probability of Bob seeing the outcome \(|+\rangle\) is 5/6, not 1.

    The language here is rather misleading: if one assumes that \(|\psi\rangle\) describes the situation correctly, then Charlie is not in the state \(|0\rangle\), but rather is this weird entangled superposition. Conversely, if one insists that Charlie is in the state \(|0\rangle\), then \(|\psi\rangle\) should be replaced with \(|0\rangle|+\rangle\).

    Anyway, in both cases the fact that Charlie was Hadamarded after doing his prediction is irrelevant: in the first case the prediction was wrong before and after the Hadamard, and in the second case the prediction was correct before and after the Hadamard.

  159. David Byrden Says:

    The question of whether this exeriment could be set up as described, is an interesting one, but is not relevant to the question of whether an inconsistency has been found in QM.
    So I will set it aside.

    I can now see that the labs are entangled. Measuring one will affect the other (or, if you prefer Many Worlds, then measuring one lab will entangle you with its state, putting you into a world where the contents of the other lab are different).

    The first lab that you measure, has a 1/6 chance of being “ok”. The second lab has a 1/2 chance of being “ok”. This is true BOTH WAYS AROUND. A nice example of entanglement.

    Renner and Frauchinger make a mistake in their analysis. They fail to realise that when you measure one of the two labs, you have changed the system state. Or, equivalently, if you imagine the system to be in its original state while you are reasoning about it, you must take all copies of superpositioned agents into account.

    They say that Agent /F applies the rules of quantum mechanics to a full knowledge of the system. But she doesn’t. She ignores her own superposition. This is where they go wrong.

  160. The flaw in Frauchiger and Renner’s argument | More Quantum Says:

    […] has the argument gone wrong. Several discussions popped up on the internet to do so, for example in Scott Aaronson’s blog, but to my surprise nobody pointed out the obvious mistake: the predictions that Frauchiger and […]

  161. fred Says:

    I’m quite baffled at the fact that everyone (and their grandma) seems to have found some clear problem with the paper, but somewhat all different, but always “obvious”.

    Either the author has no basic understanding of QM, or everyone is equally confused, which is more reflective of QM as a theory that doesn’t quite fit the human brain.

  162. David Byrden Says:

    What means should be used to make it absolutely clear where the problem is? In your opinion.

  163. Mateus Araújo Says:

    fred #161: I am happy to discuss the merits of my objection. I am not interested in discussing the meta-level about what is obvious, why people disagree, and who understands QM.

    I feel the need to respond to your slander, though: I know both Frauchiger and Renner personally, and both are very competent physicists.

  164. Yves Says:

    fred #161:
    I agree, it’s confusing. But let me elaborate on the objections being “somewhat all different”: I don’t think so. For example, Mateus (#158) and David (#159) both agree that agent /F aka Charlie has made a mistake by not considering that the full system (L) as seen by agent W is still (at time 0:02) in a state which is related by a unitary transformation to the initial state. In other words, agent /F should think of herself as a cat in a box, because the assumption is that the full system behaves quantum mechanically (or isn’t it?).

  165. Proposed solution for Riemann hypothesis? — Uncage Says:

    […] case, I hopped over to Shtetl Optimized, Aaronson’s blog. And there, at the end of a long post about the weirdness of quantum theory, was this line: “As of Sept. 25, 2018, it is the official […]

  166. David Byrden Says:

    Fred #161 :

    > “Either the author has no basic understanding of QM, or everyone is equally confused”

    Actually, running my eye down the comments, it seems that most or all of the complainers are pointing at the same error. But they have many different ways to talk about it.

    It is the assumption made by agent /F, when she sees “tails”, that the whole universe will agree with her, and her reasoning about W will hold true for everyone.

    If she were to bust out of her lab, she WOULD find a world where W measured “fail” and everyone agreed with her.

    But as long as she’s sealed in there, the outside world is looking at two superposed versions of her, and both of them contribute different facts to the outcome. Quantum Mechanics is a field where there truly are “alternative facts”.

  167. nikny Says:

    A paper attempting to prove that quantum mechanics can’t consistently describe itself turns out to be impossible to criticize consistently amongst experts of quantum mechanics.

  168. Robert Says:

    My take on this is here: https://atdotde.blogspot.com/2018/10/interfere-and-it-didnt-happen.html (TL;DR I mainly agree with Scot but I think it helps to parametrize the information from inside the box that avoids Hadamardiszation)

  169. David Byrden Says:

    Robert #168:

    Armando Rela ̃no’s paper that you linked to, says what most of us here have been saying. Plus, it has a full mathematical treatment and reasoning.

    To summarise it: you don’t know what’s what until you entangle with the surrounding environment. Agent /F didn’t do so.

  170. Dan Says:

    Scott blogs : “If, on the other hand, you believed both that
    1. collapse is an objective physical event, and
    2. human mental states can be superposed just like anything else in the physical universe,
    then Wigner’s thought experiment probably should rock your world.”

    Scott, I guess I had (naively) supposed that the only reason ever offered (historically and in contemporary philosophy) for upholding (1) is some prior commitment to (not 2). Perhaps your clarifying argument is strong enough to confirm that (not 2) would genuinely be the only reason for supposing (1) after all, given the assumption of correctness of QM? Perhaps that’s too simplistic though…

  171. Renato Renner Says:

    I really appreciate the effort that many commenters have now made in specifying more precisely where they suspect a flaw in our argument. Although it does not look as if there is really an agreement between them, a majority seems to point to the first row of Table 3 of our paper, i.e., they think that statement Fbar^n:02 by agent Fbar does not follow from quantum mechanics.

    Just as a reminder, the claim there is that *if* agent Fbar has observed r=tails at time n:01 then, by reasoning according to (Q), the agent can conclude that w=fail at time n:31.

    I should stress that this is a “conditional statement”, i.e., conditioned on knowing that r=tails. A many-worlder may express it as: “In the branch in which agent Fbar has observed r=tails at time n:01 the agent is allowed to make the claim Fbar^n:02.”

    My suspicion is that many of those who believe Fbar^n:02 is false have overlooked the fact that it is declared as a conditional statement (in the sense above), and that our argument accounts for this. For example, agent F only uses the statement *if* she knows that the condition under which it is obtained holds, i.e., that r=tails at time n:01. Or, again in many-worlds slang, agent F uses Fbar’s statement only if she knows that she is in the branch in which it was made.

    I hope that this clarifies our argument.

  172. Carlos Ungil Says:

    I think that the argument, which relies on /F using QM to predict that W will observe w=’fail’ (as if F had never done a measurement, despite her knowledge that F will do a measurement), can be greatly simplified as follows:

    /F sends a beam of photons across a vertical polarizer in the direction of W

    W has a detector behind an horizontal polarizer.

    (Valid) Statement inferred via (Q) by /F : “I am certain that W won’t detect any photons”

    The setup is modified and F puts a 45-degree polarizer between /F and W.

    (Invalid) Statement inferred via (Q) by /F: “I am certain that W won’t detect any photons”

    W will detect photons. Therefore QM is inconsistent. QED (!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!)

  173. fred Says:

    Mateus #163

    Relax, man.
    It’s no slander.
    My point was that we can’t have our cake and eat it too.
    I.e. we have a curious superposition of two states where two respected physicists come up with a thought experiment, and at the same time everyone else agrees (according to the comments after my comment) to the same “obvious” error (correct me, but I haven’t seen a single comment agreeing with the paper?).
    I really doubt that the difficulty is obvious.

    Anyway, I maintain that this tells a lot about QM as a theory and the difficulty to map it to the human brain…

    I was reading some material about Everett’s dissertation, and the example he gave back in the days seems related (but I could be mistaken), i.e. two observers applying QM recursively (nothing new under the sun?). I think the difficulty is basically of the same nature, going back to the nature of consciousness, which is about what the subjective objectivity of reality 😛

    And, considering what happened to Everett’s thesis at the time of its publication, this again says a lot about QM (and the QM academia?).

    https://www-tc.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf
    (this doesn’t seem like his original thesis because of the term “many worlds” at the top?).

    “To better illustrate the paradoxes which can arise from strict adherence to this interpretation we consider the following amusing, but extremely hypothetical drama.

    Isolated somewhere out in space is a room containing an observer, A, who is about to perform a measurement upon a system S. After performing his measurement he will record the result in his notebook.
    We assume that he knows the state function of S (perhaps a result of previous measurement), and that it is not an eigenstate of the measurement he is about to perform. A, being an orthodox quantum theorist, then believes that the outcome of his measurement is undetermined and that the process is correctly described by Process 1.
    In the meantime, however, there is another observer, B, outside the room, who is in possession of the state function of the entire room, including S, the measuring apparatus, and A, just prior to the measurement. B is only interested in what will be found in the notebook one week hence, so he computes the state function of the room for one week in the future according to Process 2. One week passes, and we find B still in possession of the state function of the room, which this equally orthodox quantum theorist believes to be a complete description of the room and its contents.
    If B’s state function calculation tells beforehand exactly what is going to be in the notebook, then A is incorrect in his belief about the indeterminacy of the outcome of his measurement. We therefore assume that B’s state function contains non-zero amplitudes over several of the notebook entries.
    At this point, B opens the door to the room and looks at the notebook (performs his observation). Having observed the notebook entry, he turns to A and informs him in a patronizing manner that since his (B’s) wave function just prior to his entry into the room, which he knows to have been a complete description of the room and its contents, had non-zero amplitude over other than the present result of the measurement, the result must have been decided only when B entered the room, so that A, his notebook entry, and his memory about what occurred one week ago had no independent objective existence until the intervention by B. In short, B implies that A owes his present objective existence to B’s generous nature which compelled him to intervene on his behalf. However, to B’s consternation, A does not react with anything like the respect and gratitude he should exhibit towards B, and at the end of a somewhat heated reply, in which A conveys in a colorful manner his opinion of B and his beliefs, he rudely punctures B’s ego by observing that if B’s view is correct, then he has no reason to feel complacent, since the whole present situation may have no objective existence, but may depend upon the future actions of yet another observer.
    It is now clear that the interpretation of quantum mechanics with which we began is untenable if we are to consider a universe containing more than one observer.

    We must therefore seek a suitable modification of this scheme, or an entirely different system of interpretation. Several alternatives which avoid the paradox are:

    Alternative 1:
    To postulate the existence of only one observer in the universe.
    This is the solipsist position, in which each of us must hold the view that he alone is the only valid observer, with the rest of the universe and its inhabitants obeying at all times Process 2 except when under his observation.
    This view is quite consistent, but one must feel uneasy when, for example, writing textbooks on quantum mechanics, describing Process 1, for the consumption of other persons to whom it does not apply.

    Alternative 2:
    To limit the applicability of quantum mechanics by asserting that the quantum mechanical description fails when applied to observers, or to measuring apparatus, or more generally to systems approaching macroscopic size. “

  174. fred Says:

    Scott #40

    “No, superdeterminism is still crazy”

    My view of super-determinism is more in the context of something like the “delayed-choice experiment”.

    I find it hard to argue that whether or not there will be a beam splitter at the end of the apparatus isn’t actually already “decided” by the time the photon enters the first splitter.

    If you “reverse the movie” at the moment the photon reaches the end of the apparatus, it looks as if it’s being emitted, and everything has to be consistent with the notion of a static space-time block. Both ends of the space-time block evolve to the other one in the same causal chain (the past implies the future, the future implies the past). There’s really no room whatsoever for “arbitrary” choice (and free will, and time travel where you could change the past), and that’s where the confusion arises.

  175. David Byrden Says:

    Renato #171 :

    Yes, I agree with that. Agent Fbar has predicted an outcome that will hold only if her measurement of “tails” is true. And it’s true within her lab but not outside her lab.

    But she should know better.

    She knows the entire configuration of the experiment, and she knows that her “coin” was a quantum device. She is now “Fbar tails” and she has a twin “Fbar heads” in another MWI “world”. She knows this.

    When calculating the outcome, she should take her twin into account. Both of them jointly emit the qubit, and they emit it coherently even if they have decohered from each other. Both of them contribute to the state of the emitted qubit (this was implied by the description of the experimental setup).

    If agent “Fbar tails” would perform this calculation properly, she would get the same result that we got (i.e. the state “ok /ok” has a one in twelve possibility).

    In ignoring her “twin”, she was NOT using quantum mechanics correctly. Therefore it’s wrong to conclude that QM does not consistently describe its own use.

  176. David Byrden Says:

    fred #173 :

    QM really does predict that “A and B” situation developing as described there. And, as far as I know, all of our observations concur.

    But B’s interpretation is wrong.

    Instead of B magically granting solidity and permanence to one specific state of A, what really happens (according to QM) is that B splits into multiple copies, each one encountering its own A with a different notebook entry.

    A does not collapse; rather, B explodes.

    And this is very relevant to Renner and Frauchiger’s paper. Because if the first lab /L were to be broken open, then agent “Fbar tails” who made the incorrect deductions, would find herself in a universe where her deductions were true.

  177. fred Says:

    Scott
    “human mental states can be superposed just like anything else in the physical universe,
    then Wigner’s thought experiment probably should rock your world.”

    Awareness seems local to a given brain, in time and space. This may seem trivial, but it could have been that awareness is shared across all brains, across the entirety of the space time block. It’s a mystery why awareness, as a true emergent phenomena, works just across all the trillions of atoms of a single brain, as opposed to be limited to single individual atoms, or extending to all the atoms in the universe.

    So, we already have examples of “superposition” of mental states, by the simple fact of the existence of differentiated mental states in time and space.

    1) shifted in time: my mental state as of now and my mental state as of a second ago are differentiated, even though they do exist in the same location in the space-time block.

    2) shifted in space: my mental state and your mental state are differentiated, even though they do exist simultaneously in the space-time block (our two brains could be exactly identical, by some random fluke, or not).

    MWI branching is like adding yet another dimension to this.

    3) shifted in branching: my mental state in this branch and my mental state in another branch are differentiated, even though they do exist simultaneously in the same location in different branches of the space-time block.

  178. Renato Renner Says:

    To David, and everyone else who (still) claims that “quantum theory can consistently describe itself.”

    Here is the task you would need to solve to uphold this claim: Take all agents in our thought experiment to be computers (this avoids invoking ambiguous notions such as consciousness, as I wrote earlier), and program them to be “faithful users of quantum theory”. That is, the computers should be programmed with rules according to the assumptions [Q] and [C] such that, when fed with a description of the experimental setup as well as the specific outcomes of their measurement devices, they output statements like those of our Table 3, but without running into contradictions.

    I promise that you will not succeed. The reason is already apparent from your previous comment. You wrote that Fbar’s statement would be correct if her lab was “broken open”, whereas you also claimed that her statement is incorrect if her lab is later “measured”. So, your program would need to invoke a criterion to distinguish between these cases. However, from a (unitary) quantum viewpoint, there is simply no fundamental difference between them. Measuring a lab and breaking it open both correspond to unitary evolutions of the overall wave function.

    (I described this challenge in more detail in a recent public talk, which you may find here: https://www.video.ethz.ch/speakers/its/2018/autumn/colloquium.html.)

  179. David Byrden Says:

    I’m afraid that I should have been more clear, with regards to opening the lab. Let me spell out that scenario in full detail:

    Consider Agent “Fbar tails” who has already read her quantum coin and got the result “tails”.

    She now configures the qubit to be evenly split between the values “1” and “0” and she sends it to the second lab.

    Then she assumes that they will receive exactly the qubit configuration that she sends, and based on that she makes deductions, coming to a wrong answer.

    All of this is exactly as you described. Now, this is what I say about opening her lab:

    If she were to open her lab, or if somebody outside were to open it, she would find herself in a universe where her assumptions were true. Let’s call it “Universe Tails”.

    BUT

    If one of the outside agents decides that he will open the lab, or if it’s guaranteed that Agent “Fbar tails” will open it, then (a priori) he has a 2/3 probability of finding himself in “Universe Tails”.

    And he has a 1/3 probability of finding himself in “Universe heads”. Or perhaps Agent “Fbar heads” will never open the lab.

    That is exactly what I’m saying, with regards to the opening of the first lab. I want to get that on record. I will answer your question in a subsequent post.

  180. Mateus Araújo Says:

    Renato #171,

    Thanks for joining the discussion again.

    I am well aware that the statement is conditional. The problem is that your assumption about the unitarity of the measurement makes this conditionality toothless. That is, according to (Q), the probability that w=fail is 5/6, independently of whether Fbar observed r=tails,r=heads, or did the measurement at all. For the result of Fbar’s measurement to matter it needs to collapse the state. But this explicitly does not happen.

    A many-worlder would accept such a conditional statement if the measurement in fact resulted in branching. But for a superposition to become a branch it needs to decohere, which again is assumed not to happen. Fbar nows that they are inside this magical box which keeps them coherent, and therefore wouldn’t claim that in the r=tails branch Wigner will observe w=fail with certainty. There is no r=tails branch.

  181. Mateus Araújo Says:

    Renato #178,

    That’s easy, you just need to take into account whether you are inside a decoherence-proof box or a not.

    If you are inside, then you do not use the collapse postulate, but rather base your predictions on the uncollapsed quantum state. If you are outside, then you should use the collapse postulate (it doesn’t matter if it is real collapse or Many-Worlds’ branching).

    If you insist on using the collapse postulate even when you are inside the decoherence-proof box you will run into contradictions (as indeed your argument shows).

  182. David Byrden Says:

    Renato #178 :

    I’m just an engineer trying to teach himself quantum mechanics. I don’t have the training that you have, and I’m worried that I may be misunderstanding this.

    So, before I try to answer your question, could you clarify something for me, please?

    It is my understanding that if Schrodinger were to open his cat’s box, he would find the cat either alive or dead. Never a mixture of both. Never a “superposition”.

    You can measure the polarisation of a photon (for example) at any angle you choose, because it has no preferred basis. But some quantum systems have preferred basis vectors in their Hilbert space. Such as, “cat alive” and “cat dead”. It was my understanding that you can measure them ONLY in their preferred basis.

    Now, your paper describes “labs” containing agents and other objects. It seems clear to me that these “labs” have preferred basis states. For example, the first lab has “heads” and “tails”. I believe that you cannot encounter an agent in a superposition of her two states.

    But, your paper states that the labs will be measured by the W agents using other bases, “ok” and “fail”.

    If this was a true “measurement” then the labs, and the people in them, should “collapse” to the measured state. No?

    I just don’t see what’s happening here. Can you explain, please?

  183. David Byrden Says:

    Renato #178 :

    I just listened to your lecture at the ITS Science Colloquium. I think that it answers my questions and objections. Because in that lecture, you describe the labs as quantum computers instead of people in boxes.

    I was worried about measuring a human person in an unnatural basis. This is not a problem for a quantum computer.

    I was worried about the how the lab agents could combine their superposed results into qubits. But this is what quantum computers do. It’s not a problem.

    So I willl answer your question now, using the old names “Fbar” “W” and so on, but remembering that these are quantum computers, not people.

    And I will pretend that they are very, very powerful quantum computers, able to think about their own situation and possessing an attention span.

    ———————

    These are the thoughts of Agent Fbar:

    “I have read my coin and it says Tails.”

    “I know that it’s a quantum coin with a 1/3 probability of reading Heads.”

    “Therefore I am in a superposition. I have a twin who saw Heads.”

    “My twin and myself are combining our results into the qubit S.”

    [ ….now we omit some obvious steps…. ]

    “We’re going to be measured in the ok-fail basis.”

    “The result ok,ok has a 1/12 probability of occurring.”

    “However, I will not live to see it, because when I am measured in the ok-fail basis, my quantum algorithm will collapse into the ‘ok’ or ‘fail’ state, which is a mixture of me and my superposed twin.”

    “Surely that will scramble my brain.”

    “I will no longer exist as the entity that saw Tails. In the Many Worlds interpretation, there will no longer be a world where Tails was on the coin. And so there will be no contradiction in quantum mechanics.”

    “Goodbye, everybody.”

  184. Renato Renner Says:

    David #182:

    The concept of a “preferred basis” does not exist in standard quantum theory. In contrast, several interpretations (e.g., Bohmian Mechanics or Many Worlds) depend on the choice of such a special basis (which is usually taken to be the position basis).

    Accordingly, there is nothing in the formalism of standard quantum theory that prevents us, in principle, from measuring Schrödinger’s cat with respect to a superposition basis — it is just extremely hard to actually do it. (The reason is that the information whether the cat is dead or alive is highly redundant, whereas this is not the case for the phase of the superposition.)

    In any case, since our Assumption [Q] is supposed to capture standard quantum theory, it does not constrain measurements to particular “preferred” bases.

  185. David Byrden Says:

    Thank you. I still have a lot to learn.

    So, it seems to me that I can resolve your percieved paradox, even when the agents are people (rather than quantum computers).

    As you said before, “measuring” Fbar is the same as “busting her lab”. And I agree with that. But I was assuming that if we “bust the lab”, we will find agent Fbar in the “heads – tails” basis.

    Now you’re telling me that we can “bust the lab” or “measure” agent Fbar in the “ok / fail” basis. This measurement, you tell me, is “extremely hard” but not impossible.

    If we do THAT, then the version of agent Fbar who saw “tails”, and who deduced that the “ok-ok” result is not possible, ceases to exist.

    And with her, the contradiction ceases to exist.

  186. Yves Says:

    Renato #178: To use Assumption [Q], the agent (or computer) has to know where to draw the boundary between the quantum system and the classical observer. So if we teach (or program) agent Fbar to use quantum mechanics, we have to tell him either one of the following two premises:

    (1) “You are part of a quantum system Lbar, which will (indirectly) interact with system L. The state of system L will later be measured by agent W. Therefore, you must do the prediction of agent W’s observation considering yourself as being part of a unitary evolution starting with the initial state |\psi_init>_R.”

    or

    (2) “You can consider yourself as a classical observer. Therefore, if you observerd the coin being tails, you must take |tails> as the initial state to predict agent W’s observation”.

    To my understanding, the experimental protocol forces you to use premise (1) instead of (2), since the boundaries of the quantum systems L and Lbar as seen from the agents W and Wbar, include the agents F and Fbar. Please correct me if I’m wrong.

  187. Renato Renner Says:

    David #185:

    This is also basically Scott’s point that “it’s hard to think when someone Hadamards your brain.” And, indeed, Wbar’s measurement can be highly detrimental to Fbar.

    Scott’s and your criticism overlooks however a main feature of our argument. As I pointed out earlier, it is deliberately constructed in such a way that Fbar’s statement enters the chain of reasoning *before* she is Hadamarded. Whether Fbar (together with the statement she derived) continues to exist after the Hadamarding is therefore irrelevant.

    Scott’s “simplification” of our thought experiment to Hardy’s paradox obscures exactly this key feature, which is probably the reason why he missed it.

  188. David Byrden Says:

    Renato # 187 :

    So we still disagree.

    I think that our disagreement doesn’t lie in any details of your experiment.

    For example, you just pointed out that Fbar made her measurement and her deductions before her “brain got Hadamarded”. But that’s not relevant. I mentioned her death only to make the point that something comes to an end here.

    According to MWI, agent Fbar existed in a “world” that was restricted to the inside of her lab. In this world certain facts were true, and those facts were not true outside the lab at the same time.

    (This concept should not be new to anybody. Consider Schrodinger’s cat. For the living version of the cat, it’s a fact that he is alive. But for Schrodinger, the cat has only a 50% chance of being alive. That is a different fact.)

    When agent Fbar got measured in the basis ” ok / fail ” then of course it scrambled her brain in some unexplained way. I still find it hard to accept that this is possible for any “classical” object, but you say it’s possible, so I will set that aside.

    But, the scrambling of her brain does not matter. What matters is this; her “world” ceased to exist.

    Now the lab contains a “world” with different facts. There WAS a measurement, made by an agent who was a real solid person, and she measured “tails”, and it was a fact; but now it’s not a fact.

    I get the feeling that you and I disagree here. We disagree on the workings of the Many Worlds Interpretation, not the experiment.

  189. David Byrden Says:

    Prof. Renner # 187 :

    You made a relevant comment in your ITS presentation, concerning “Alternative Facts”. I quote it:

    “In the usual Manyverse implementation, this is not allowed….it would say, in one branch maybe this, and in the other branch that, but not in the same branch on one screen show both things. So that should be disallowed.”

    Now, your paradox is the existence of these two facts;
    1. the W agents measure “ok, ok”
    2. agent Fbar measures “tails”
    and in your paper you prove mathematically that these two facts are contradictory.

    But this does not matter, because the two facts exist in different branches of the Manyverse.

    Fact #1 exists in the “outdoors” branch of your experiment, where both of the W agents live, and their findings are reported to all of us.

    Fact #2 exists in a branch that is physically confined inside the first laboratory. This branch is initiated when the randomness generator is consulted. This is the branch where “tails” is seen, where agent Fbar calculates her predictions and sends her qubit, just as you describe.

    But then agent Wbar measures the lab in the “ok / fail” basis. The branch is destroyed.

    Agent Fbar’s predictions may be known to other agents outside the lab, they may be displayed on screens there, but this does not matter, because they refer to a context, a branch of the Manyverse, which gets destroyed. It never propagates outside the lab and it does not survive past the moment of the measurement.

    So, as you said in your presentation, these two facts do not exist in the same branch of the Manyverse. Therefore, there is no paradox.

  190. Renato Renner Says:

    David #188:

    I am not even sure we disagree. 🙂 I am not excluding the possibility that you have some variant of many-worlds in mind which avoids the paradox.

    However, and that’s the main claim of our paper, whatever theory you have in mind, it can only be consistent if you somehow modify the rule we call [Q]. So, for example, the following cannot be true in general:

    (*) “If I prepare *in my current branch* a particle with spin up and send it to you, knowing that you will measure it in the up/down-basis, then, *in my current branch* I can write in my notebook that I am certain that you will observe up.”

    Your version of many-worlds must now somehow restrict (*) and add something like “but only if my current branch doesn’t cease to exist in the future.”

    The problem is now that it will be difficult to phrase such a restriction of (*) without violating basic physical principles such as causality (at the time when a statement like the one in (*) is made, it may not even be decided whether the branch continues to exist forever). Note also that (*), without any addition, is perfectly compatible with the original Wigner’s friend experiment, as well as with Deutsch’s extension. There, the friend’s statement remains in the isolated box and nobody else knows it, so no contradiction arises (in contrast to our scenario, where agent F learns Fbar’s statement before it gets lost).

    So, to summarise, I think my point is: If you are sure you can come up with a variant of many-worlds that avoids the paradox, then you should certainly go ahead and write it up. But, as I tried to explain, it will be challenging to find an appropriate modification of (*).

  191. Renato Renner Says:

    Yves #186:

    Agent Fbar just applies a rule which, in many-worlds slang, may be phrased like (*) in my previous answer to David. I am not sure whether this means the agent is now “classical”. In fact, she may be well aware that, in a different branch, she prepares the spin differently and therefore, in that other branch, writes a different prediction into her notebook.

    As I wrote to David, it is certainly reasonable to try to restrict this rule to avoid the paradox. For example, you may add to (*) “… only if there exist no other branches in which a different spin was prepared”, which would constrain it to a completely “classical” scenario. But this would be too restrictive (as we are probably not living in such a completely classical world).

  192. Yves Says:

    Renato #191:

    Thank you very much for answering my question! In my previous comment, I attempted to provide a different rule how to use assumption [Q] (Born rule). Namely, I wanted to define a boundary between classical and quantum systems, and assert that the Born rule is only applied when this boundary is crossed. In particular, attempted to solve the problems by introducing quantum-classical boundaries, since that was my understanding of the Born rule (that a measurement crosses this boundary).

    However, when thinking about your reply I noticed that this puts me into a dilemma: either I accept that there is this “magic” crossing between classical and quantum physics, and somebody has to tell me whether I’m classical or not, or otherwise I have to extend this boundary such that it comprises the entire universe, which would mean that I can never apply the Born rule. So the problem remains unsolved and I congratulate you and Daniela for your nice paper!

  193. David Byrden Says:

    Professor Renner #190 :

    I don’t need to modify rule [Q] because rule [Q] does not apply.

    Agent Fbar makes deductions about the state of lab L, assuming that lab L received her qubit in the same quantum state that she sent to them.

    But in fact (from W’s point of view) there was another copy of Fbar who send another qubit, and lab L received the combination of both qubits, and went into a different state.

    Agent Fbar does not include this in her calculations, although the full experimental setup is known to her.

    Instead, she stubbornly assumed that if she SENT a certain qubit state to lab L, then they RECEIVED what she sent.

    And, within a single branch of the Manyverse, that would be true. But the events play out over several branches.

    So, I don’t need to modify rule [Q] or any other rule. I simply need to remind agent Fbar:

    “You CANNOT know what’s happening in other branches of the Manyverse”.

    p.s. It’s not relevant whether agent Fbar’s branch will or will not be destroyed in the future. What matters is whether she will bust out of her lab and extend her branch to include the whole experiment. In THAT case, she will find her assumptions to be true.

  194. David Byrden Says:

    Prof. Renner #191 :

    You proposed an extension to the rule [Q] and then you said it’s “Too restrictive” because it implies a “classical world”.

    I don’t think so. I think that restriction is very real. For example:

    Consider speaking to a photon in a Young’s Slits experiment. You meet the photon downstream of the slits, and you ask it what happened.
    “I just went through the Left slit”, it tells you. “I am sure it was the Left. There will be no interference fringes because I am surely Left.”

    But you reply, “Only if there exists no other branch in which you went through the Right slit”.

    There! That is your proposed restriction. It exists. And it does not imply a “classical scenario”.

  195. Andreas Says:

    Renato Renner #190 (and Jochen #95, David Byrden #146)

    First off, thanks alot for the interesting discussion here and in general as evoked by the paper!

    In my eyes, the way to go when choosing a many worlds interpretation is not to modify (Q), but instead do the following:

    The first line of (Q) says: “Suppose that agent A has established that System S is in state |ψ⟩ at time t0.”

    This is where many commenters have argued: “Fbar must consider the lab to be in a superposition and will then get the correct predictions.”
    This argument is well described in Jochen #95 and David Byrden #146.

    I do think that this perfectly works to resolve the contradiction. But also, that it does so by dropping assumption (S). (Since she assumes that r=tails and r=heads at the same time.) So, this argument would still perfectly lie within the published result of the paper.

    And I think, with the three assumptions you have nicely expressed, what we hope to assume when investigating the world. I mean: It is easy to talk about a closed lab in which only two possibilities coexist. But the same coexistence of alternatives would also apply to everything else. (Even continuous variables like the position of a photon hitting a wall, if I get this correct?) And I think the labs were constructed such, that they contain basically everything you could wish for: A person, heavy equipment etc. So, if the lab can be in a superposition, why shouldn’t the whole world be? Basically the universe can also be considered a closed system and whether there will be a hadamarding or not somewhen in the distant future, we cannot perfectly say.

    Thus, while it would be easy to solve the contradiction in the way described above, it would be quite hard to cope with dropping (S). At least for me. (David Byrden, do you have no problem with that?)

    At the end, just a small detail that I noticed: Renato, you often wrote, that Fbar makes her statement *before* and not *after* Hadamardization. But isn’t the initialization step in the Gedankenexperiment technically also a Hadamard gate? At least in many quantum circuits like the Deutsch-Jozsa algorithm, the production of a superposed state is achieved by applying a Hadamard gate to a classical state.

  196. David Byrden Says:

    Andreas #195 :

    I didn’t pay much attention to [S] because it wasn’t clear to me. Perhaps I didn’t read the paper carefully enough.

    So you’re telling me that [S] is a denial of superposition? It implies that when Fbar sees “tails”, she can DENY that another copy of her may be seeing “heads”? Is that why she ignores that possibility and makes those incorrect deductions?

    Well, I don’t think we can allow [S], if that’s what it means.

    Because then a photon, after passing through Young’s “left” slit, could deny the existence of its own superposition passing through the “right” slit. It would be guaranteed, under [S], no interference fringes.

    Is that what [S] really means?

  197. Yves Says:

    Andreas #195, David Byrden #196:

    Agent Fbar does not need to drop Assumption (S) if she accepts that by measuring the coin, she has put herself into an entangled state with the coin. This is simply because Assumption (S) is stated as an implication rule: the acceptance of the statement “I am certain that x = ξ at time t.” must imply the denial of “I am certain that x ≠ ξ at time t”.

    As always with implications, if the left side of the implication is not true, the right side of the implication also does not need to be true. If agent Fbar accepts that she and her entire lab evolves unitarily, she cannot be certain about the outcome w of the {ok, fail} measurent of agent W. In other words, agent Fbar may well use assumptions (S) for the reasoning about her coin, but she should know that she cannot be certain about agent W’s measurement result. One might object that in general, agent W may not know when she is evolving unitarily, but in the scenario described in the paper, all agents are aware of the entire experimental setup.

    So in conclusion, I do not see why Assumption (S) needs to be dropped. I’m also not convinced that one needs many world interpretations of quantum mechanics to resolve the paradox. Nevertheless, I do see that it would be interesting to come up with refined assumptions, that would hold even in the general case, where the agents are not aware of the experimental setup.

  198. Andreas Says:

    David Byrden #196

    When I had a first look at the paper, it already met my eye, that the authors use (S) only to forbid the case that W measures “w=ok” and “w=fail” at the same time. My thought was: If they consider it possible (or at least define it as possible) to measure a lab in a superposition, why do they not consider (S) violated already at this point. If Wbar gets a result like “wbar=ok” and then also uses this observation to argue, that z must have measured “z=+1/2”, then Wbar certainly assumes the lab to be in a superposition and not only in a statistical mixture, which could also have lead to the results “wbar=ok” or “wbar=fail”. (Do I see this right?)

    The difference between these two branching points (heads/tails vs. ok/fail) would already lead to the question about the level of investigation. I will adress this in the next post.

    Now, back to your question concerning the double slit experiment. I dont think (S) is supposed to completely exclude superposition. It is more concerned with statements that can be made with certainty. Thereby excluding the negation of such a statement.

    In the double slit experiment, when interference patterns occur, people outside do not know whether the photon passed through the lower slit. So they also cannot use (S) to exclude the statement that it passed through the upper slit. Saying that it passed through both slits however is too strong a statement in many interpretations. (Normally in conversations about the topic, it is me who feels like defending the use of such language 🙂

    But now let’s look at the possibility of the photon himself drawing conclusions. I see two differences between the setup of Frauchiger-Renner and Young’s double slit experiment. First of all: Photons cannot talk and reason about their place in the world. However this might be true only on the first glimpse. I would rather consider it sufficient, if the photon or anything else passing the slits, had just one bit of memory, where it could save to himself wheter he went through the upper slit or the lower slit. (This would be the ultra-minimal version of our Friends F and Fbar.)

    And actually this is possible. Many of us know, that the interference pattern can be destroyed, if a detector “knows” wheter a photon did pass at the lower slit or not. But this is still not the same. It would resemble more to someone quickly opening the door of our labs during the experiment and asking the friends what they had measured.

    But there are also versions of the double slit experiment, where the information is actually stored in the photon itself. In its polarization. See for this the wikipedia article about the Qantum erasure experiment:

    https://en.wikipedia.org/wiki/Quantum_eraser_experiment

    “First, a photon is shot through a specialized nonlinear optical device: a beta barium borate (BBO) crystal. This crystal converts the single photon into two entangled photons of lower frequency, a process known as spontaneous parametric down-conversion (SPDC). These entangled photons follow separate paths. One photon goes directly to a detector, while the second photon passes through the double-slit mask to a second detector. Both detectors are connected to a coincidence circuit, ensuring that only entangled photon pairs are counted. A stepper motor moves the second detector to scan across the target area, producing an intensity map. This configuration yields the familiar interference pattern.
    Next, a circular polarizer is placed in front of each slit in the double-slit mask, producing clockwise circular polarization in light passing through one slit, and counter-clockwise circular polarization in the other slit (see Figure 1). This polarization is measured at the detector, thus “marking” the photons and destroying the interference pattern (see Fresnel–Arago laws).”

    If I see this correct, in a first step it is not even necessary to use the crystal and thus the entangled pair. The polarizers alone, when put in front of the slits, should already be enough to destroy the interference pattern.

    This means that if the photon has a mini-consciousness about which path it travelled on, it will exclude its “twin” from the other path to have interference with him.

    However, and i think that is the interesting part of the quantum eraser experiment, if you help the photon to forget about the path by changing its polarization via the entangled other photon, then the interference pattern returns.

    And I would claim that this is also exactly what Wbar and W would have to do to the labs in the Frauchiger-Renner setup: They need to erase all information that is redundant in the labs. They dont need to erase everything, this would not lead to any interesting measurement (just like behind the double slit, you still need to have the phase shifts induced by the length of the two pathways). But they must erase as much as to make it possible to apply a Hadamrd gate to the remaining information (preferably exactly one atom, as a qubit carrying the heads/tails information). Renato #184 has also talked about the redundancy of information in the labs being the biggest obstacle for the Hadamardization. And instead of erasing all redundant information first, you could also try to Hadamard all parts of the lab individually at the same time. But I guess erasing first is way easier.

    Thus, we really have a similar situation in the two setups: The photon can “learn” something about his “branch” and as long as he forgets this again, the superposition can still be measured.

    As a small sidenote about the last (uncited) paragraph in the wikipedia article: (Someone has alread labeled this paragraph as “dubious” It doesn’t have to be the self-interference of the lower photon that magically returns even if the actions of Alice are performed after the lower photon already has hit the detector. But it is rather the selecting of the correct half of the events that have already happened and labeling them through the behavior of the upper photon (as induced by Alice). Thus recovering the interference pattern by selecting the correct subset. Kind of: Selective historical writing in its simplemost form 😉

    Now, the second difference between Frauchiger-Renner and the double slit experiment: The authors chose the lab such, that you have everything inside there that we could wish for (A human and some equipment as stated before). Thereby introducing the possibility to have an objective collapse if any of the proposed (or yet unproposed) collapse theories are true. Thus it is quite well possible, that the photon can be in a superposition and the Friends in the lab cannot. We simply don’t know yet.

    A final remark: It might be that the paper is less explicit in making sure that the setup can proof interference with certainty. There have been other setups considered for example by Deutsch with his modification of Wigner’s friend. His setup is developed exactly with the goal to empirically decide wheter both branches of a system containing a human do arrive at the measurement. This is nicely descibed in the following link by someone who was already commenting here too:

    http://mateusaraujo.info/2016/06/20/if-your-interpretation-of-quantum-mechanics-has-a-single-world-but-no-collapse-you-have-a-problem/

    But I must admit, I did not yet find the time to read the original publications cited there. Neither to think about what outcomes the objective collapse theories would exactly predict in the Frauchiger-Renner setup. What would the change in probabilities be? And can W and Wbar decide if the labs must have been in a superposition if they look at their (repeated) measurement results?

  199. Andreas Says:

    I apologize for my lenghty answer!

    But to me, the following seems important too:

    I see three levels of discussing the same issue, i.e the question whether a system follows unitarity and exists in superpositon or whether an objective collapse happens. Thereby leading to a loss of interference effects (but not necessarily(!)).

    The first level describes microscopic setups. Single photons in a double slit experiment, quantum algorithms beeing executed and the like. Here we already do have empirical observations that make it easy to assume that both “worlds” did happen and “both branches” (or all 4 in the Deutsch algorithm) occur and show interference. But as I said above: This language goes already a bit into interpretation. Alternatively someone can also say: The photon does not take any of the two paths, but rather it is travelling as a wave.

    Then there is the second level: Labs, that are constructed such, that they don’t decohere with its environment and which are being measured in an orthogonal basis form outside. -> The Frauchiger-Renner thought experiment and already Wigners Friend, especially with Deutsch’s modification, allowing interference.

    When you, David, made the photon reason about its other copy not going through the other slit, you made an attempt at upscaling from the first level to the second. At the same time, when Renato Renner, in his talk, describes ways of implementing the thought experiment through the use of (quantum) computers, he does downscaling. At least that’s how I would call it.

    Finally there is the third level: The world that we live in at the very moment. Can it also be considered a “box”? And could it show interference as well? Actually I have had a thought experiment in mind for some years now that would consider exactly this possibility. This is also the reason why I am excited that Renner-Frauchiger have now also considered interference of macroscopically differing worlds. I am at the moment trying to write a paper about this, and if you are interested, I could upload a first version within the next few weeks. (Actually it is only a synopsis/proposal at this stage.) Would you be interested in that?

    There have been other commenters hinting at the implications in our world too:

    For example Renato Renner #48 used his quantum random number generator to decide if he should reply to this blog. And luckily, we happen to be in this branch, where he got a “1” as output. He stated as well: “The key fact to notice here is that both relevant agents, i.e., F and \bar{W}, are in a similar situation as we are (hopefully) now when reading this text. While, from an outside viewpoint, they may be in a superposition state, no Hadamard has been applied to them.” Just a small question: The sentence “Now, we are already in a situation that involves superposed agents, namely me who wrote this reply and you who are reading it.”, shouldn’t this be “situation that involves entangled agents”? Wouldn’t “superposed” rather apply to |Renato and Scott writing and reading the reply⟩+|Renato not having replied and Scott thus not reading a reply⟩? But it might be, that I misunderstood something there.

    Jochen #132 also formulated some implications for our lives in the universe. He kind of solves the problem by saying that we can correctly predict anything, which we are ever going to experience. Since in the Gedankenexperiment, Fbar’s brain will be Hadamarded before she would experience any outcomes contradicting her measurement.

    But anyways, what I want to say is the following: The big question is, whether the same behavior of nature (i.e. the interference of different “possibilities”) that happens on microscopic levels, also does happen in those sealed labs? And if yes, what prevents them from happening on a cosmic scale, i.e. the third level?

    This is what I wanted to hint at in my first post: If Fbar can assume, that another copy of her, measuring the other outcome, has the same way of existing as her (thereby dropping (S), the way I read it), then we would have to assume the same thing about our lives. This is what the many worlds interpretation has been doing for years now, but I just wanted to emphasize that it is not so easy to cope with the assumption that all infinitely many other possibilities do happen in parallel, all the time.

  200. David Byrden Says:

    Yves #197 :

    > “I’m also not convinced that one needs many world interpretations of quantum mechanics to resolve the paradox”

    I find that the MWI gives a nice, intuitive picture of quantum mechanics that allows one to comprehend QM situations.

    But you’re right, one can resolve this paradox without resorting to MWI. I will now describe the paradox in a different way:

    —–

    1. A photon passes through a vertical polariser, then flies across the room, heading for a slanted polariser and followed by a horizontal polariser.

    2. While it’s flying past you, you shout “Hey! Dude! What’s your horizontal component?” and it yells back “Zero! My polarity is DOWN. I have zero horizontal component!”

    3. Then it passes through the other two polarisers successfully.

    4. You ask it “Now what’s your horizontal component?”

    5. It replies “Left. I point to the Left.”

    6. You say “AHA ! Just a moment ago you reported a ZERO horizontal component! That’s a contradiction!”

    7. The photon replies “So what? You can’t combine measurements made in different bases. And polarisers are bases!”

    8. You say “Why not combine them? Why can’t I measure you in more than one basis?”

    9. The photon says “It’s a proven impossibility in quantum mechanics, to measure a state more than once! Because making a measurement will change the state! I truly HAD no horizontal component, then you CHANGED me by measuring me.”

    That is effectively what we’re doing in the Renner experiment.
    The photon corresponds to Agent Fbar.
    The vertical polariser corresponds to the “heads / tails” basis. Agent Fbar gets measured (by herself) in that basis.
    The photon continues its journey NOT collapsed, just like Agent Fbar remains in a superposition, ready to be measured again.
    The horizontal polariser corresponds to the “fail / ok” basis.
    The contradiction arises because measurements in different bases are combined.

    Agent “Fbar-who-measured-heads” has some predictions about the overall result. But she doesn’t participate in it. Her superposition gets mixed with her self, creating a different flavour of Agent Fbar, and THAT is who contributes to the overall result. If this “different mix” of Agent Fbar could think, she would make the correct predictions.

    Is that confusing? If so, then you may prefer the MWI interpretation:

    Agent Fbar measures “heads” in a “world” that never extends beyond her lab.

  201. David Byrden Says:

    Andreas # 198 :

    Regarding the measurements by the W agents, in the “OK / fail” basis, there is an important point to make:

    If the lab contents “collapse” (for example, into the Heads state) then this measurement can proceed, and it will return “ok” or “fail” with 50% probability.
    But, the measurements of the two labs will be independent, and we will not get the desired results.

    For the experiment to work, the labs MUST be in superpositions, and they must be partially entangled (this is achieved by the qubit that they exchange).
    Then will we see the desired results, with a 1/12 probability of “ok – ok”.

    Now, it’s “difficult” to put a human into a superposition! But I think it’s possible with quantum computers. So, when I speak of “Agent Fbar”, I am really thinking of a quantum circuit.

    Regarding the photons and the slits; atoms and molecules have gone through the slits and created interference. Quantum Mechanics does not specify a size limit. So, why not a reasoning computer?

  202. David Byrden Says:

    Andreas # 199 :

    > “it is not so easy to cope with the assumption that all infinitely many other possibilities do happen in parallel, all the time.”

    Yes, this is a difficult pill to swallow !

    I like to tell myself that a MWI “world” is merely the area where a quantum event has influence.

    But, QM leads one to believe that every “world” is a defined reality, that could possibly grow as large as the universe.

    I know that physicists argue about this. Some of them say that all the “worlds” are empty potential ghosts, like the square root of minus one, which don’t have a solid existence, except for a single “world” where we live. Others say that all of the “worlds” are equally real.

    There have been long-range tests of entanglement, and entanglement is a great example of MWI “worlds”. The experiments succeed even at great distances.

  203. Renato Renner Says:

    David #193 and Andreas #195

    While we did not want to use many-worlds slang in our article, let me here rephrase the three assumptions in terms of “branches”. As noted earlier, one may regard the assumptions as rules that the agents are supposed to follow when deriving statements (which they may put down into a notebook):

    [Q] If I am certain that, in the current branch, a system is prepared in state psi, and if the Born rule applied to psi asserts that outcome z occurs with probability 1, then, in my current branch, I can write into my notebook “I am certain that outcome z will occur.”

    [C] If I am certain that, in the current branch, agent A’ has written in her notebook “I am certain that outcome z will occur.” then, still in the same branch, I can also write this statement into my own notebook.

    [S] If I am certain that, in the current branch, outcome z will occur, then I cannot, in this same branch, write into my notebook “I am certain that outcome z’ (for z’ different from z) occurs.”

    I hope that this manifestly many-worlds formulation clarifies some of the questions that were raised in this discussion. Note, in particular, that when Fbar follows rule [Q], she merely makes a statement within her current branch (i.e., the statement only appears in the notebook in this branch). The contradiction arises nevertheless.

  204. David Byrden Says:

    Prof. Renner #203 :

    I don’t see a contradiction. This is how I see it:

    Fbar, in her “heads branch”, is absolutely sure that W will measure “fail”.

    Fbar is correct. Within her branch, her predictions are true.

    The branch of Fbar is limited to the inside of lab Lbar. Outside of that lab, there is a different branch. Therefore, the deductions and predictions of Fbar are invalid outside the lab.

    Please note, Fbar’s branch is not defined as “the area within the lab”. It is defined as “the area where it is possible, in principle, to know that Heads was chosen by the coin”. So the second lab L is partially within this branch.

    Agent Wbar now measures the lab Lbar. He uses the basis “ok / fail”. Because Fbar’s branch is defined as the “heads” area, it comes to an end in this “collapse”.

    The predictions of Fbar in the “heads” world are now meaningless. There is no place where they are valid.

  205. Renato Renner Says:

    David #204:

    > “I don’t see a contradiction.”

    But I see one in your answer. 🙂

    You are defining Fbar’s branch as “the area where it is possible, in principle, to know that Heads was chosen by the coin”. I agree that this is a sensible definition. But then you are writing that this branch comes to an end when Wbar measures Fbar. You seem to ignore here that, prior to this measurement, Fbar sent a spin particle to argent F who, if the spin measurement results in +1/2, can know that Fbar got Heads. So, the knowledge that the coin was Heads is still around after Wbar’s measurement. Hence, according to your definition, the Heads branch still exists.

    In fact, the reason why I described the agents as physicists (or computers) who are writing conclusions into notebooks is precisely to keep track of what information is actually available. If an agent, together with her notebook, is subject to a measurement, that information is lost and cannot any longer be used to derive a contradiction — unless the agent made sure the information was transferred to a safe place, e.g., to another agent who put it down in her own notebook.

  206. David Byrden Says:

    You’re right – I will check the math and post it later.

    But I’ll point out immediately that the contents of lab L don’t survive either.
    To obtain the measurement { ok , /ok } the W agents must destroy both lab contents.

  207. Mateus Araújo Says:

    David #204, Renato #205:

    The problem here is what is a “branch”. In Many-Worlds you only have a branch if it has actually decohered, that is, if it has become so much entangled with external systems that its evolution can be successfully approximated to be independent of the other branches.

    By assumption, this doesn’t happen with Fbar. There is no “heads branch” or “tails branch”, as Fbar is assumed to be in this decoherence-proof box that prevents it from entangling with external systems.

  208. Andreas Says:

    Renato Renner #203

    To make sure that our ideas of many worlds are the same, I have to ask you an important question:

    Do you agree, that in the many-worlds view, the universe does not only show branching but also the merging of branches?

    In my eyes this is what happens when Wbar measures Lbar in an orthogonal basis. The branch in which “r=tails” and the branch in which “r=heads” both contribute to the probabilities for the outcomes.

    The same applies to e.g. the Deutsch algorithm: In one branch, the function is being evaluated on “x=0,y=0”, in one branch it is being evaluated on “x=0,y=1” etc. But only if we consider that the 4 branches are being merged again by the Hadamarding and the measurement on the upper wire, we get the results “0” if f is constant and “1” if f is balanced.

    Do you agree with this view on “merging” of branches?

    With this in mind, I think, Fbar cannot say “In my branch I have measured r=tails and thus W will (in this branch) measure w=fail”. Because, by construction of the setup, W’s measurement induces a merging of different branches. And its outcome lives in a branch, that has multiple branches as predecessors.

  209. David Byrden Says:

    Mateus :

    These are questions that I’ve been puzzling over.

    It seems to me that the contents of a literal laboratory “Lbar” would decohere from themselves, even if not from the outside world. There would soon be a difference between “Fbar heads” and “Fbar tails”.

    But then, how can they both contribute to the emitted qubit? They must combine their contributions. The experiment requires it, for the stated probabilities. The qubit values cannot be on completely disconnected branches. The same goes for the measurements by the W agents.

    And because the W agents are measuring in another basis, they also need “merging” or else they will get meaningless fifty-fifty results and the experiment will fail.

    I assumed that the experiment could be realised with quantum computers, not people. But I’m not even sure that quantum equipment could do it.

    Andreas:

    Of course the universe shows “merging” of branches!

    A quick example: Young’s slits.

    1. The particle transits a screen with slits.

    2. There are now three branches, “left slit”, “right slit”, and “ouch I hit the screen” which we can ignore.

    3. The particle (both of it) flies across the air gap to the detector screen. There is no interference in the air gap because the waves are not coherent. They can be distinguished because they carry directional ifnormation.

    4. The particle hits the detector screen. Its wave function blends into the screen’s wave function and continues in there, spreading through objects, causing a “hit” or other result, so eventually the room and the experimenter become affected.

    5. The blending of the particle function and the screen function, did not preserve directional information. From that point forward, these two wave functions are indistinguishable, they add, they blend, to make a single world.

    The interference exists, the experiment succeeds, precisely BECAUSE two branches have merged.

  210. Renato Renner Says:

    Mateus #207 and Andreas #208:

    I would certainly agree that branches can merge again. This happens, for example, in Deutsch’s version of the Wigner’s friend experiment, when Wigner measures his friend in a superposition basis.

    I do not think, though, that many-worlders have ever agreed on a definition of the term “branch”. For some, branches are objective (i.e., branching can occur in a world without observers), for others subjective (any agent has his own branches), for some they are global, for others local, etc.

    Having said this, I do think one can give a minimum criterion that any sensible notion of “branches” must satisfy. Suppose that a measurement during an experiment led to a “branching” of the overall wavefunction into Psi = Psi_0 + Psi_1. Suppose furthermore that an agent has certain information, say he observes a value x=0, that can only occur if the state was Psi_0, but not if the state was Psi_1. Then, clearly, the agent can claim “I am in branch Psi_0.” (And, in particular, this branch Psi_0 “exists” for that agent.)

  211. Mateus Araújo Says:

    Renato #210:

    On the contrary, I don’t think any Many-Worlder would agree with your minimal criterion for branching, as it ignores the fundamental point, that the future evolution of the branches must be independent of each other. See for example here, sections 3 and 4, where Wallace explains the standard notion of branching.

    When talking about this one risks engaging in a sterile discussion about semantics: what is a superposition, a pseudo-branch, a branch, a world, etc. The substantive question is about when it is ok to use the collapse postulate, and I dare you to find a single Many-Worlder that would agree that one should use the collapse postulate when doing a measurement inside a decoherence-proof box.

  212. Mateus Araújo Says:

    David #209:

    Actually, there is already a difference between “Fbar heads” and “Fbar tails”, namely the result of the measurement, heads or tails! And this difference is not small, it makes the quantum states associated to “Fbar heads” and “Fbar tails” orthogonal. They are as different as they can be. The only question (for the experiment) is whether these agents in orthogonal states are capable of sending a qubit in the same state. As I hope to have convinced you in the comments of my blog, there is in principle no problem with that.

  213. Renato Renner Says:

    Mateus #211:

    > “On the contrary, I don’t think any Many-Worlder would agree with your minimal criterion for branching, as it ignores the fundamental point, that the future evolution of the branches must be independent of each other.”

    I am sorry, but here you are wrong; see, e.g., David Deutsch’s “Quantum Theory as a Universal Physical Theory”, especially Section 8, where he writes “[…] according to the Everett interpretation, all copies of the observer are once again identical though they had been different in two branches […]”

    And I do not think you can deny that David Deutsch is a many-worlder.

  214. David Byrden Says:

    And so the conversation rolls on !

    We are having an impressive amount of fun with this simple 4-state quantum system! The debate is fuelled by the things that we do to it; we divide it into two entangled parts and measure them at different times; we change the measurement basis; and we take the “point of view” of its temporary internal states.

    We’re touching on multiple aspects of Quantum Mechanics in this experiment. All of them are interesting.

    Now, I am sure that the “contradiction” alleged here is not real. But it’s interesting to seek where exactly the error lies. There are multiple places where you could say that the logic of the paper goes wrong.

    I have already pointed out the earliest questionable step in the logic. I repeat my claim that agent Fbar, if she measures “tails”, goes into a “world” of the Many Worlds interpretation, which I will call “Fbar tails”.

    As described in the paper, she can predict that agent W will measure “fail” at the end of the experiment. But that will happen only within her “world”, and her “world” exists only inside her lab. She must emerge from her lab if she wishes to see and touch an agent W who measured “fail”.

    She doesn’t need to emerge immediately. She can wait as long as she likes. She can emerge from her lab five minutes AFTER the completion of the experiment. And still, she will find that agent W measured “fail”.

    But we know that the experiment ended with a measurement of “ok ok”, so how is that possible? Does she change events in the past?

    No, she does not. Remember, this experiment has four possible outcomes – the four combinations of “ok” and “fail”. They have different probabilities but they are all possible. So this is another case of “many worlds”. The measurements made by the W agents cause the outside environment to split into four “worlds”.

    When we get our final measurement of “/ok , ok” then we are in a “world” which coexists with three other worlds. In those worlds, the other results happened. When agent “Fbar tails” breaks out of her lab, she will find herself in those other worlds, NOT in our world.

    Let’s put this on a formal basis. When agent Fbar measures “tails”, she puts the system state into 0.707 ( tails,up + tails,down )

    A quick calculation will show you that our measurement, “/ok, ok” is orthogonal to that state. We can never meet the agent “Fbar tails” after we make that measurement.

    So, if we take a hammer and smash the lab open for ourselves, we are guaranteed to find agent “Fbar heads”.

  215. Mateus Araújo Says:

    Renato #213: I’m afraid you are engaging in the sterile discussion about semantics instead of the substantitive discussion about how to make predictions. Deutsch indeed calls these pseudo-branches that can merge again “branches”, but he wouldn’t make the mistake of applying the collapse postulate for an observer in such a pesudo-branch.

  216. Renato Renner Says:

    David #214 and Mateus #215:

    You both seem to argue that Fbar’s use of rule [Q] (which I described in #203 in a many-worlds language) is not allowed, either because her “world exist only inside her lab” or because Fbar’s branch is just a “pseudo-branch” that merges again with another.

    But note the following two points:

    1. Even in an experiment where branches merge (such as in Deutsch’s version of Wigner’s friend experiment) the use of rule [Q] is unproblematic. The reason is that the agent’s prediction (which, according to the rule, is put down in a notebook, which is itself a physical object) will necessarily be erased when branches merge. In other words, a prediction within a branch only exists as long as the corresponding branch does.

    2. In our thought experiment, agent F can know that Fbar’s outcome was “tails” (if her outcome was z=+1/2). She can therefore identify the branch even after Fbar’s lab was measured. That branch therefore still exists.

    The challenge of modifying rule [Q] in a way that avoids the paradox is thus still open.

  217. Andreas Says:

    Mateus Araújo #215

    I also do think we should not be distracted by the semantics. However I also think, that in this particular case, we can discuss the real difference between the two cases. If there is any.

    But first off, let me note, that I also had this picture in mind of already the slightest differences giving rise to different branches. And that a future merging does not change that. If we want to call these pseudo-branches, I do not have a problem with this. At least then, we know what we are talking about. “Pseudo-branches”:= branches that will merge later on. Right?

    But as we have agreed, this would be more of a semantic issue. For me, the real question is the following:

    Can we be sure about normal branches, as you defined them, to not be pseudo-branches as well?

    In other words: Can we say with certainty, that macroscopically different branches, which are not limited to any box, but rather are spreading their difference with huge speed across the universe. Can we say with certainty that such branches will not merge in the very distant future?

    What I have in mind, is the end of the universe. As I have read, there are different scenarios about what is going to happen: The big rip (space gets torn apart), the big crunch (inverse of the big bang), the big chill (heat death) and others. But in all of them, I see a certain possibility for the following to happen:

    This dynamic process at the end of the universe might act as a huge erasure function. It could destroy any difference that has come to exist over the billions of years (at least in some branches). And this would cause, that certain branches might look exactly the same at the end of this process, except for their relative phase. Thereby leading to interference on a cosmic scale. Or as we have called it: It would allow the branches to merge again.

  218. fred Says:

    Renato

    “The concept of a “preferred basis” does not exist in standard quantum theory. In contrast, several interpretations (e.g., Bohmian Mechanics or Many Worlds) depend on the choice of such a special basis (which is usually taken to be the position basis). ”

    I was under the impression that Everett’s original paper (the final revised/public one I had linked) did address the preferred basis objection, that is, there’s no need for a preferred basis.

  219. Mateus Araújo Says:

    Renato #216: A wrong prediction is a wrong prediction. It doesn’t matter if you erase it afterwards, it was still wrong.

    And I find it rather bizarre your claim that Fbar’s use of [Q] is unproblematic. Your own gedankenexperiment shows that their prediction was incorrect, as W observed w=ok, whereas Fbar predicted that he would observe w=fail with certainty.

    Repeating my comment #181: it is very easy to modify [Q] in order to avoid the paradox. Just don’t use the collapse postulate when you are in a decoherence-proof box.

  220. Mateus Araújo Says:

    Andreas #217: Indeed, we cannot be sure that branches won’t merge again. If we have a big crunch (or the solar system is inside a decoherence-proof box as in Greg Egan’s Quarantine) then they must merge. Well, the predictions we make using the collapse postulate will be valid until there is a merging, so we have a bit of time 😉

    But I don’t see a necessity of being able to define sharply what is a branch or a pseudo-branch. This is asking whether the collapse approximation will be valid or not, and the domain of validity of an approximation will necessarily be fuzzy. The fundamental thing, that must be sharply defined and correct, is the evolution of the universal wavefunction. Branches are just emergent concepts that we use to tame its bewildering complexity.

    Not that this matters for the Frauchiger-Renner argument, as there it is clear which branches merge again and which don’t.

  221. David Byrden Says:

    Renato #216 :

    > “You seem to argue that Fbar’s use of rule [Q] is not allowed because her world exist only inside her lab”

    Well, really, her world extends into the other lab, because the labs become entangled.

    So my real argument is this; the world “Fbar tails” does not include the outside agents, W and Wbar.

    > “But… rule [Q] is unproblematic…the agent’s prediction will necessarily be erased”

    I was not claiming that [Q] is invalid. I am claiming that you applied it outside of its scope.

    > “agent F can know that Fbar’s outcome was “tails”…She can therefore identify the branch even after Fbar’s lab was measured. That branch therefore still exists.”

    Yes, that’s true. The branch “Fbar tails” exists in the second lab. And in there, it becomes split into two worlds, 50% probability each.
    Let’s call them “Fbar tails up” and “Fbar tails down”.

    But ALSO, the second lab contains a third world, “Fbar heads down”.

    When agent W measures this lab, he would surely get a “fail” result if the first two worlds were the complete contents of the lab.
    But, because there is a third world in it, he can possibly measure “ok”.

    > “The challenge of modifying rule [Q] in a way that avoids the paradox is thus still open.”

    I will now try to modify [Q] as you suggest. Rule [Q] has three steps. The third step is:

    ….. Statement A(iii): “I am certain that x = ξ at time t.”

    Now, I will add

    ….. Statement A(iv): “but if there are other, coherent copies of system S in other worlds, then I am not certain of anything”

  222. David Byrden Says:

    Andreas # 217 :

    > “Can we say with certainty that such branches will not merge in the very distant future?”

    This is a question that I’m interested in.

    A “world” of the many-worlds interpretation, can merge with other, coherent worlds. This happens if the information distinguishing them becomes erased.

    The obvious example is the Young’s Slits particle. It exists in two worlds after passing the slits; but within the detector screen those two worlds merge. And that is why we get the interference fringes; the observer is literally occupying those two merged worlds.

    So, I assume that many (most?) quantum decisions don’t spread their influence forever. They create worlds that merge. Quantum events happening inside atoms and molecules perhaps cannot be “knowable” in most cases.

    But, even with the more “significant” events, which split our whole planet into multiple “worlds”, perhaps they merge eventually? How many photons from Earth will reach an observer half way across the galaxy? How much information can possibly be carried in those photons?

  223. Renato Renner Says:

    Fred #218:

    Vaidman’s review https://plato.stanford.edu/entries/qm-manyworlds/ contains a short discussion of the problem of choosing a “preferred basis”.

    I think the point is that “pure” quantum theory does not single out any particular basis, so one needs to choose one in order to talk about “branches”. But Everett (and many others, notably Zurek) argue that there exist particular choices that appear to be natural, e.g., because they respect the particular structure of the Hamiltonians that typically occur in Nature.

  224. Renato Renner Says:

    Mateus #219 and David #221:

    Your suggestions for how to modify rule [Q] (or restrict its scope) would indeed resolve the paradox. But they are too restrictive, as they would disallow *any* prediction in quantum theory.

    > “….. Statement A(iv): “but if there are other, coherent copies of system S in other worlds, then I am not certain of anything”

    According to many-worlds, the whole universe is in a big coherent state, i.e., there are always coherent copies of us in other worlds. So, the rule would never be applicable.

    > “Just don’t use the collapse postulate when you are in a decoherence-proof box.”

    According to many-worlds, the whole universe is of course a big decoherence-free box. In addition to that, note that in our thought experiment the information about the outcome of the coin toss is transferred from Fbar to F. Hence, despite of the assumption that Fbar’s lab is otherwise isolated, your “decoherence-proof” criterion does not apply to the lab itself.

    (You talk about the “collapse postulate”, but I guess you mean [Q], as described in #203, for this is the assumption we actually apply, right?)

  225. Mateus Araújo Says:

    Renato #224: You are being disingenuous. Of course modifying [Q] wouldn’t disallow *any* prediction in quantum theory. The only predictions that become disallowed are those regarding the time of the big crunch, if that ever happens. And this is actually a good thing, as predictions based on the collapse postulate will be wrong in this scenario.

    This is anyway besides the point, as you claim to have found an inconsistency in the composite Wigner friend scenario, not in speculations about cosmology. To solve the inconsistency you claim we just need to keep Fbar and F from applying the collapse postulate. And you are again being disingenuous about Fbar and F’s labs. Of course they are decoherence-proof boxes. All decoherence is by assumption blocked, and the only interaction with the external world is carefully controlled.

    > (You talk about the “collapse postulate”, but I guess you mean [Q], as described in #203, for this is the assumption we actually apply, right?)

    [Q] as you describe is the collapse postulate, even though you don’t state this explicitly.

    Here in the blog comments you hide the collapse postulate in your measurement-causes-branching assumption, and in the paper you use it when you say that the agent A has *established* that the system is in state psi. (Which is quite questionable, even without taking Many-Worlds into account; by assumption the state of Fbar is not the collapsed state, so one could argue that Fbar didn’t establish that.)

  226. David Byrden Says:

    Renato # 224 :

    Yes, you are correct. None of us can assume that we’re not in the presence of other “worlds”, though it’s another matter for them to be *coherent* worlds that threaten interference.

    So, I withdraw my suggested Statement A(iv), and I suggest modifying Statement A(iii) in this way, to retain its usefulness:

    …. Statement A(iii): “I am certain that x = ξ at time t. in my world. I will refrain from making assumptions about other worlds.”

    As I’ve been saying, Agent “Fbar tails” could break out of her lab at any time, and she will then find an outside world where W measured “fail”.

    I am convinced that she can do this even after measurement, because I don’t believe in “collapse”.

    But won’t find you and me, i.e. the people who saw “ok, ok”. She will find other versions of you and me.

    So, her predictions will be correct in that case, because they will be predictions about things in her own “world”.

  227. Renato Renner Says:

    David 226:

    Your suggested formulation of [Q] seems to be equivalent to the many-worlds phrasing of [Q] in my comment #203, with an emphasis that statements made in a particular branch are only valid in that branch. Would you agree with this?

  228. Renato Renner Says:

    Mateus #225:

    I tried to figure out from your answers what replacement (or restriction) for [Q] you have in mind. But it seems to me that you are fluctuating between different options, such as:

    [Q1]: Rule [Q] (as phrased in my comment #203) is only applicable in branches that *never* merge again.

    [Q2]: Rule [Q] is applicable in any branch at any time before the branch has merged again with another one. (This would include what you called pseudo-branches.)

    [Q3]: Rule [Q] is only applicable if one is in a lab that is not decoherence-proof (but the universe does not count as such).

    [Q4]: Rule [Q] is only applicable if one does *not* carefully control the interaction with an external world.

    [Q5]: Rule [Q] is sometimes applicable and sometimes not, but one cannot define this sharply.

    Anyway, I fear none of these really matches what you were trying to say. So, would you mind being a bit more specific?

  229. Mateus Araújo Says:

    Renato #228: Sure, with pleasure. First of all, I wouldn’t formulate [Q] like this, because the whole point is discussing the validity of the collapse postulate, which [Q] only does implicitly. But to answer your question: I defend [Q1], [Q3], and [Q4] if you remove the “only” qualifier. [Q2] is confusingly formulated, the point is that the predictions are valid if they refer to events that happen before merging. I would rephrase them like this:

    [Q1]: The collapse postulate is applicable in branches that never merge again.
    [Q2]: The collapse postulate is applicable in any branch to make predictions about events that happen before this branch merges with another.
    [Q3]: The collapse postulate is applicable if one is in a lab that is not decoherence-proof (but the universe does not count as such).
    [Q4]: The collapse postulate is applicable if one does *not* carefully control the interaction with an external world.
    [Q5]: The collapse postulate is sometimes applicable and sometimes not, but one cannot define this sharply.

    About [Q5]: indeed, without defending this I couldn’t defend [Q1-4], as none of them give a sharp domain of applicability. Strictly speaking the collapse postulate is false; it is an excellent approximation in some regimes, but they don’t have sharp boundaries. This is analogous to Newtonian mechanics being an excellent approximation in the low-speed high-decoherence regime, which doesn’t have sharp boundaries.

    All [Q1-5] are true statements that do not contradict eachother, so I’m not sure what is your objection here. Are you looking for a single statement to replace [Q] in your paper? In this case [Q3] suffices.

  230. David Byrden Says:

    Renato # 227 :

    I think that the formulation in comment #203 is not very clear.

    It says that she can “write in her notebook” …. well, she can write anything at any time, it is not a proof!

    Also, it says “in the current branch”. But really, if she is sure about a situation in another branch, then she can make logical deductions about that other branch. (but she cannot visit it)

    Really, I think the original version of [Q] was OK. The paradox was not caused by [Q] and it will not be fixed by changing [Q].

    The paradox appears because of this; you run the experiment until you get the result “ok, /ok”.

    That is a quantum measurement. It splits the outside environment into four “worlds” with the four possible results.

    Then you have agent “Fbar tails” thinking about her situation. And she concludes that agent W measured “fail”. And she is correct. If she comes out of her lab, she will find “fail” recorded in his notebook.

    Because she will be in a different “world” to you.

    So, you are comparing results from two different, parallel worlds. It’s not a paradox.

  231. David Byrden Says:

    Dear everybody:

    You deserve a more formal, demonstrably correct explanation than I gave you in post #230. So let’s find exactly the place in the “paradox” where an error is made.

    I will refer to the argument as it is laid out in the NATURE.COM article at
    https://www.nature.com/articles/s41467-018-05739-8

    Please examine Table 3.

    In the second row, agent F measures z=+1/2 at time n:11.
    She asks herself
    “How could this value of +1/2 come to me from agent /F ?
    “If she got ‘heads’, then surely she would send me z=-1/2
    “She must have got ‘tails’, because only then would she send a qubit that I could read as z=+1/2

    This is the error: Agent F assumes that Agent /F must be in one of two states, “heads” or “tails”.

    She forgets that Agent /F could be in a superposition.

    And the next row of the table depends on such a superposition !

    In row 3, Agent /F is in a superposition of ‘tails’ and ‘heads’ because she was measured in the “ok/fail” basis.

    (Please note, she has this particular superposition state only in the “world” of Agent W. She herself does not sense the superposition. There are two copies of her, and they both feel healthy and normal. One of them saw “tails”, one of them saw “heads”.)

    Then, using equation (6), the authors prove that this superposition causes Agent F to read z=+1/2

    So, the logic used by Agent F is wrong. Specifically : the statement F(n:12) is wrong.

  232. Renato Renner Says:

    Mateus #229:

    Thanks for clarifying. So, if I understand correctly, you are saying that my rule [Q] is not a fundamental law and — even worse — that it is generally false.

    I suppose that this means you have a deeper, i.e., more fundamental, law in mind, from which [Q] emerges in certain practical special cases. Is this right? (You will certainly need something that connects the wave function, which, a priori, is a purely mathematical object, to things we can observe in nature, or test in an experiment.)

    So, as you guessed, I am now asking what you would then suggest as a replacement for [Q] on the level of a fundamental law. I assume that this cannot really be [Q3], which, as you wrote, you consider as an approximation that only works in particular regimes.

  233. Renato Renner Says:

    David #231:

    It’s great you are now very specific about where you think you found an error.

    It seems to me, however, that you are still ignoring the time information contained in the statements. You are arguing that agent Fbar may be in a superposition because “she was measured in the ‘ok/fail’ basis”. But note that this measurement is not carried out until time n:20, whereas statement F^n:12 (which is the one you claim to be wrong) refers to the outcome of Fbar’s coin toss at time n:01.

  234. Mateus Araújo Says:

    Renato #232:

    Indeed, this is precisely what I’m saying. The fundamental law is just unitary evolution under the appropriate Hamiltonian. Figuring out when the collapse postulate applies is a matter of working out when decoherence makes the evolution of the terms of the superposition independent of each other. But I’m not telling you anything new, this is just standard Many-Worlds.

    Not that this matters for your argument. The problem there is not that the domain of applicability of the collapse postulate was incorrectly ascertained, but rather that it was inconsistently applied. From the point of view of Fbar it was, and from the point of view of W it was not. No paradox arises if we either assume that measurement always causes collapse, or that it never causes collapse.

    I wonder, actually, why don’t you present your argument like this. There are lots of people that hold this belief that the collapse can be applied depending on the point of view. You have shown that it cannot.

  235. David Byrden Says:

    Renato #232 :

    I thought that agent Fbar was in a superposition from time n:01, the moment when she tosses her coin. Are you telling me that she’s NOT in a superposition of “heads” and “tails” at n:02 ?

    If you think that Fbar is in a “classical” state, if you think she’s only in “heads” or “tails”, then you don’t need the coin! What is the purpose of the coin? You always want her to begin with “tails” !

    Oh, but you DO need the coin, to finish the experiment! Let me tell you why :

    When agent Wbar measures the lab Lbar, he will get “ok” or “fail”. That is always true. But what is he measuring?

    If agent Fbar is sitting inside the lab in a classical state of “tails”, then she is NOT in a two dimensional Hilbert space.

    Then you cannot apply another basis to the Hilbert space, and equation (6) will not work, and the experiment will fail.

    I’m sorry but this concept of “no superposition at n:02” is not valid.

    Remember, she tosses the coin inside a perfect sealed “lab”. It doesn’t matter if the coin is a quantum device or a classical metal coin. There is no real difference, anyway. What matters is this: information about the result does not reach the outside.

    So, for all of the other agents, Fbar is in a superposition already, at n:02.

  236. Renato Renner Says:

    Mateus #234:

    > No paradox arises if we either assume that measurement always causes collapse, or that it never causes collapse.

    I agree! If you supplement quantum theory with such an objective notion of collapse (one with which every agent agrees) then the contradiction does not arise — otherwise it does.

    I don’t think, though, that many-worlders would agree that the theory allows you to derive such a notion of collapse, i.e., one that’s objective in all situations (including Wigner’s friend type experiments). Recall that decoherence is also just a relative notion, which depends on where you draw the boundaries between systems.

  237. Renato Renner Says:

    David #235:

    All that I am doing is to apply rule [Q]. If you like, I may phrase this using the formulation you suggested in #226. I would then say that, in the world in which agent F observed z=+1/2 at time n:11, she can make the following statement:

    F^n:12: “I am certain that Fbar has recorded the outcome r=tails at time n:01, in my world. I refrain from making assumptions about other worlds.”

    Note that I am not claiming that, from an outside perspective, the joint state of Fbar and F has collapsed to a classical state. Not at all.

  238. Mateus Araújo Says:

    Renato #236:

    > I agree! If you supplement quantum theory with such an objective notion of collapse (one with which every agent agrees) then the contradiction does not arise — otherwise it does.

    Now I see where you’re coming from. What you call “quantum theory” is not textbook quantum theory, but rather QBism.

    But I’m curious about what situation do you have in mind where Many-Worlds can’t give you an objective notion of decoherence/collapse. The whole point of the theory is that it is objective, so I’m rather surprised by your assertion.

  239. David Byrden Says:

    For me, this has become the most interesting mental exercise since I got a Rubic’s Cube in 1980. 🙂

    Before I continue, let me discuss a couple of things, for new readers who are perhaps overwhelmed by the volume of writings here.

    The discussion revolves around “superpositions”.

    Now, a superposition is not an absolute, global thing; it is always relative to some other thing. For example, consider the famous Schrodinger’s Cat. The cat is in a superposition of “alive” and “dead”, relative to Mr. Schrodinger who is outside the catbox. But, the living cat does not feel the superposition. He is fully alive, relative to himself. You are always yourself relative to yourself.

    If the box opens, the cat and Mr. Schrodinger will meet but they will disagree about what happened. Mr. Schrodinger will say “I’m glad to meet you! A moment ago, you had a 50% chance of being dead.” and the cat will say “Nonsense, I was fully alive.”

    And because of the perfect, impenetrable catbox, they are both correct.

    This is the feature that makes Quantum Mechanics different from ordinary mechanics: in ordinary life, even if you get no information about an event, it happened. You can assume that the tree which fell in the forest, did make a sound.
    But Quantum Mechanics asserts that if you receive absolutely no information about an event, then it DID NOT HAPPEN (relative to you).
    For Mr. Schrodinger, the cat’s survival literally was not real until the catbox was opened.

    That is the nature of superposition, which is a central feature of this experiment.

    Another thing to understand, is that we can combine information from different “worlds”, from things that are in superposition.

    The two superposed cats, “alive” and “dead”, will never come together or combine in any way because they are too different. They have “decohered”.
    But it’s possible to combine superpositions if they are similar enough. Think of the particle in the Young’s Slits experiment. It’s in a superposition of “left route” and “right route”. But they are similar enough that the detector screen can combine them.

    This experiment that we’re discussing, combines data from superpositions, although it doesn’t need to combine the superposed items. The agents within the labs are in superpositions (at various times). They communicate their state to other agents to measure. The communication must combine information from both superposed copies of the hidden agent, in order for the experiment to work.

  240. Renato Renner Says:

    Mateus #238:

    No, no, I didn’t mean QBism — although you are of course right that QBism agrees with rule [Q], too.

    Rather, what I meant is that, according to Everett’s “Many-Worlds Interpretation of Quantum Mechanics,” quantum jumps (or collapses) are “relative phenomena (i.e., the states of an object-system relative to chosen observer states show this effect), while the absolute states change quite continuously.”

  241. Mateus Araújo Says:

    Renato #240:

    What did you mean then with this sentence: “If you supplement quantum theory with such an objective notion of collapse (one with which every agent agrees).”?

    For it to make sense, “quantum theory” must lack an objective notion of collapse. What is this “quantum theory” then? The only theory I know that allows this collapse-for-me-not-for-you nonsense is QBism.

    As for Many-Worlds, I’m afraid you might be confusing “relative” with “subjective”. For example, in the case of Wigner’s friend, one can consider the relative states \(|\text{friend}_0\rangle \) and \(|\text{friend}_1\rangle \), but it is an objective fact that these are the states relative to the measurement outcomes 0 and 1. All observers agree with this, and all observers agree that the full state of the Wigner-Friend system (relative to the branch where the experiment takes place) is \(|text{Wigner}(|0\rangle|\text{friend}_0\rangle + |1\rangle|\text{friend}_1\rangle) \).

    If you now consider a measurement that is not made inside a decoherence-proof box, then all observers will agree that the collapse postulate will be an excellent approximation, so you get an “objective collapse”.

  242. Renato Renner Says:

    Mateus #241:

    > What did you mean then with this sentence: “If you supplement quantum theory with such an objective notion of collapse (one with which every agent agrees).”? For it to make sense, “quantum theory” must lack an objective notion of collapse.

    By an “objective notion of collapse” I meant a fundamental mechanism for collapse that is imposed on top of standard quantum theory. An example is the one proposed by GRW (see, e.g., https://en.wikipedia.org/wiki/Objective-collapse_theory). Many-worlds doesn’t have that, although something that looks like a collapse “for all practical purposes” can emerge.

  243. Mateus Araújo Says:

    Renato #242:

    Sure, collapse models work, but my question is not about having a fundamental collapse mechanism, but having a collapse that is objective in the sense of happening for all observers.

    Which quantum theory allows for the friend to experience a collapse for themselves but without this collapse happening for other observers? Textbook quantum theory certainly does not. Neo-Copenhagen kind of does, but its defenders usually say that the friend is mistaken. Only QBism insists that the collapse happened for the friend, not for others, and the friend is right.

  244. David Byrden Says:

    Mateus #243 :

    Well, I’m no authority on Quantum Mechanics, but it seems to me that “collapse for you, not for me” is implicit and obvious in the theory.

    Take the canonical Schrodinger’s Cat example. When the radioactive source decays, the (living) cat experiences it as a collapse. But for Schrodinger, the collapse has not happened. The entire contents of the box are still in superposition.

    Personally (if you care) I don’t even think of “collapse” as a quantum system rotating its vector to lie on a vector of the measurement basis (in Hilbert space).

    I imagine that the vector represents the observer, not the quantum system. The observer vector splits into multiple vectors (or “worlds” of MWI). I imagine that other observers may simultaneously retain the original vector, or split into other combinations.

  245. Mateus Araújo Says:

    David #243:

    The question is not about being implicit or obvious, but about what is stated in the axioms of the theory. If you take a textbook on quantum mechanics, usually it states a simplistic collapse postulate along the lines of “if there is a measurement, apply a collapse”. Nothing about the collapse being subjective, you should just collapse the quantum state and use it from then on to make predictions.

    In the case of Schrödinger’s cat, you would either say that the cat caused the collapse, and for Schrödinger it is also collapsed, or say that the cat did not cause a collapse, it is in a superposition, and for Schrödinger it is also in a superposition. In particular, I have never seen a textbook speculating about the subjective experience of a cat in a superposition. If you take a look at the paper where Wigner originally introduced the Wigner’s friend gedankenexperiment, you’ll see how far from obvious this was for him: Wigner couldn’t conceive of what the subjective experience of his friend in a superposition could possibly be, so he concluded that his friend can never be in a superposition, and for that collapse must occur whenever a human consciousness would be superposed.

    What QBism states, and Renato as well, is that from the point of view of the friend there is a collapse, from the point of view of Wigner there is no collapse, and both are right.

    What I am arguing is that this is nonsense. The friend might as well experience a collapse subjectively, but if he states that one actually happened he is mistaken, and if he uses the collapsed state to make predictions they will be wrong. (That, or a collapse really happened, in which case it must also happen for Wigner).

  246. David Byrden Says:

    Renato #237:

    Sorry for that post. I misunderstood what you said. You’re not claiming that the system internals should be treated as a classical system.

    So, I will treat them as a quantum system.

    In the following argument, root(N) means the square root of N.
    These letters have these meanings;

    o = OK state for lab /L
    f = FAIL state for lab /L
    u = +1/2 state for lab L
    d = -1/2 state for lab L
    h = HEADS state for lab /L
    t = TAILS state for lab /L

    I beg your indulgence, but I don’t know how to write superscripts, symbols etc. in these comment windows.

    =====================

    The system state, after initial setup, is

    ( tu + hd + td ) / root(3)

    We consider the event that agent Fbar reads “TAILS”. She sees a “collapse” into

    ( tu + td ) / root(2)

    She sends a qubit over to the other lab, and agent F reads it. We consider the event that she reads “UP”. She has observed a “collapse” into the state

    ( tu )

    Agent F not only knows that she has measured “UP”, but she also knows that agent Fbar is in state “TAILS” because there is no other component to the state that she’s “collapsed” into.

    ———————

    Agent Wbar decides to measure lab /L in the basis { OK , FAIL }

    The system, at this time, still has its original state from his point of view. Agents within the labs have observed “collapses” but the external agents have not. (see post #244 about the illusory nature of “collapse”.)

    We can rewrite the system state with lab /L defined in { OK , FAIL }. It is

    ( fu – ou + 2fd ) / root(6)

    We consider the event that agent Wbar measures “OK”. Therefore he sees a “collapse” into;

    ( – ou )

    Agent Wbar not only knows that he has measured “OK”, but he also knows that agent F is in state “UP” because there is no other component to the state that he’s “collapsed” into.

    ———————

    Now, here is the error in the paper’s logic : the authors assume that ( – ou ) is the same state as ( tu ).

    The error exists in Table 3, row 3, box 3.

  247. David Byrden Says:

    >> “In the case of Schrödinger’s cat, you would either say that the cat caused the collapse, and for Schrödinger it is also collapsed

    That would be the “classical” world.

    >> “or say that the cat did not cause a collapse, it is in a superposition, and for Schrödinger it is also in a superposition.”

    But how does a cat feel when it’s in a superposition? Does it see its own dead body?

    We are all in billions of superpositions at every moment, because quantum events happen in the materials all around us. The cat must feel itself solid, as we feel.

    The second interpretation that you listed, is the common one, and it works well enough with one cat in one box. But it fails in the Renner-Frauchiger experiment.

    As I’ve said already, I don’t believe in “collapse”. In this experiment, you end up wondering how a thing can “collapse” for one observer and not for another. I don’t believe the experiment can work if “collapse” is applied consistently – maybe somebody could try?

    “Many worlds” helps you to think clearly about the experiment, and in the end you will see that the “paradox” does not exist because the contradictory measurements are in different “worlds”.

    The state vectors that I used in post #246 represent some of the seven “worlds” in this experiment. They show clearly how one observer can see the illusion of “collapse” while another does not.

  248. David Byrden Says:

    Mateus #245 :

    > “What QBism states, and Renato as well”

    I am only learning quantum mechanics, so I don’t know what interpretation I am implicitly aligning with. I suspect that it’s Everett’s.

    >> “from the point of view of the friend there is a collapse, from the point of view of Wigner there is no collapse, and both are right.”

    Sounds good to me !

    >> “The friend might as well experience a collapse subjectively, but if he states that one actually happened he is mistaken”

    I agree with that also !

    Renato #210 : I see branches as objective and local.

  249. Renato Renner Says:

    David #246:

    It looks to me as if the place where you believe to have located an error is moving. 🙂 Do I understand correctly that you are now claiming that statement Wbar^{n:23} in Table 3 is wrong? This surprises me, as it is just a direct logical consequence of the earlier statements Wbar^{n:22} (which follows from the considerations in your post) and F^{n:14} (which F can make whenever z=+1/2), isn’t it?

  250. Renato Renner Says:

    Mateus #243 and #245:

    If one enforces an objective collapse upon quantum theory on a fundamental level (i.e., not just as an emergent phenomenon that works for “all practical purposes”) then it is indeed impossible to carry out our thought experiment (because the friends’ measurements, if they really are measurements, would, by assumption, lead to a collapse of the global state).

    But note that, under this assumption, Deutsch’s variant of the Wigner’s friend thought experiment, couldn’t be carried out, either (for the same reasons).

  251. Mateus Araújo Says:

    Renato #250:

    No, it wouldn’t. You just need to deny that the friend’s measurement causes a collapse. And people do this. I have heard neo-Copenhageners saying that yes, measurement causes collapse, but the friend’s measurement is not a real measurement. One could also deny that measurement causes collapse, and say that decoherence does, with similar results.

  252. David Byrden Says:

    Renato #249 :

    Yes, I’m moving the place where I indicate an error. 🙂 because of your comment #237.
    Now, for the first time, I can see the experiment the way that you see it.

    To explain it in “many worlds” terms: I wanted to put all the “worlds” into the calculation.

    But now I see that you are focusing on a single “world”, to find a contradiction within it. You are using your assumptions S,Q,C to navigate through the experiment while remaining in a single “world”.

    >> “you are now claiming that statement Wbar^{n:23} in Table 3 is wrong? ”

    Absolutely! That is the broken link in the chain. That is where you accidentally step from one “world” into another “world” where different facts exist.

    >> “it is just a direct logical consequence of the earlier statements Wbar^{n:22}”

    How can I explain this?

    In quantum systems, there can be states, and combinations of states, that would not be allowed in the classical world.

    You have convinced yourself that when F sees +1/2, the other lab must be “TAILS”. But this is not so. The other lab can have any state.

    Look at your own argument !
    You say that F sees +1/2, and this happened because Wbar measured “OK”.
    Well, what does “OK” mean? It means a mixture of “HEADS” and “TAILS”.
    So, you are saying that the first lab must be “TAILS” ….. because it is a mixture of “HEADS” and “TAILS”.

    We can resolve this with mathematics. Please check my mathematics from post #246.

  253. David Byrden Says:

    Renato #250, Mateus #251 :

    I don’t accept these concepts, “collapse” and “superposition”.

    As far as I can see, quantum mechanics is driven NOT by objects doing multiple things at once, existing in different states at the same time, but by INFORMATION.

    As I said already, in QM, if you have no information about an event, then (for you) it did not happen. And I extend that statement: if you don’t have any information the state of a multi-state system, then (for you) it is in multiple states. You have the *illusion* of superposition.

    Somebody else can have different information than you. For them, the system is in a different state.

    To put it another way:

    When the state vector of a quantum system hovers between the basis vectors in Hilbert space, this does NOT imply that the system itself is in a mixture of states. The vector represents YOUR INFORMATION about the state. And the zone, the district, the area where your information has spread (via the global Wave Function), is a “world” in the MWI.

    So, when you obtain more information about a system (by measuring it) you then change YOUR position in Hilbert space, perhaps to another intermediate position, perhaps to one of the basis state vectors. This move represents a change in YOU, not a change in the system. It’s not a “collapse”.

    This interpretation is, I believe, mathematically equivalent to other interpretations. Correct me if I’m wrong?

    And this interpretation will guide you through the Renner experiment.

    So, for example, agent Fbar makes a “measurement”? That means she obtains information about the system. HER state vector shifts to a new place. The OTHER agents stay where they are because they didn’t get the information. The system itself does not change or “collapse”.

  254. sf Says:

    Mateus Araújo, David Byrden, Renato Renner, #171 — #251

    Having followed the last phase of this discussion from the sidelines, I’m beginning to think there may be a way to reconcile the different viewpoints here. When the debate started up again, around #171, I was already convinced that, from a strictly technical viewpoint, the logic in Frauchiger and Renner is correct, but it depends on a very careful structuring/wording of the hypotheses, and the real question is: what is the significance of the paradox?

    More concretely: does one need some really new insight to get out of the paradox? Or is it just a question of restating or formalizing the principles of Born and Bohr more carefully – ie could it be resolved using things already known, even taken for granted, but not fully included in the formal Assumptions ?

    My suspicion now is that it’s the latter, and there is a need to reconsider the way that Assumption (C ) is formulated. The point is that, in physics, when I use an observation or result that has been recorded by another scientist, there is an implicit understanding that this is a shortcut which is allowed only insofar as I could equally well redo their work and get the same result. That is, there is a “principle of substitution”; that use of the written results could be substituted by doing the same work myself.

    The problem then, in the Frauchiger and Renner context, is that because different observations are being made by agents who have to be isolated from each other in a way that preserves entangled states, it would be impossible for the agent using another agent’s observation to instead make such an observation themselves.

    Since this is not so far from the point that Bohr was making in his debates with Einstein, or from the Asher Peres quote in Scott’s subtitle, this substitution principle may be a standard aspect of their viewpoint that needs to be added back into the Assumption (C ), and such a modification would seem to block the logic leading to the paradox.

    A simpler substitution principle is even involved in Einstein’s most basic formulation of relativity; in the insistence that measurement of time has to be done from a specific frame, though in that case there is a Lorentz transformation that allows others to use the observation, appropriately, so it is less profound than in the QM case, where Bohr introduced a ‘censorship’ on what measurements could be discussed.

    So I would interpret Frauchiger and Renner as asking whether there is any weakening of the substitution principle that could replace Assumption (C ) and still not give a paradox. It seems doubtful, since anything nontrivial along these lines would have to make new predictions, and no one has found alternative versions of QM that can stay consistent. But I don’t know the subject well enough to go beyond such vague generalities.

    PS I just noticed David Byrden #252 but I’m not so sure how this is related; a single world (in MWI) is the key pt for him, and a single agent or observer is the key pt here for me.

  255. David Byrden Says:

    sf #254 :

    Yes, the problem here can be described as one observer using another observer’s facts. But I think the essential thing “worlds” rather than “observers”, because an observer can move from one “world” to another.

    As I’ve said, a “world” is the area where certain information exists. In this experiment, we construct two labs that can confine “worlds” within themselves, but during the experiment we copy and share information in various ways. Counting the outside environment, I think that we make seven “worlds” at various times.

    A “world” can be represented as a state vector for the system. But, as I’ve said, the system itself does not “collapse” into these states; the vectors belong to, and define, the “worlds”. A state vector defines what information YOU have, in your “world”, about the system.

  256. David Byrden Says:

    I’d like to add some detail to my calculations in post # 246.

    Because those calculations are the solution to this paradox. All philosophical musings about QM, all discussions of observers and collapses, can be set aside because those equations make the situation clear.

    As explained in #246, Agent F goes into a “world” represented by the state vector (tu).
    This means TAILS for the first lab and z=+1/2 for herself in the second lab.

    She knows that the first lab is TAILS, but this fact exists in her world, which is defined by the state vector (tu). It does not exist in the outside environment. It does not exist for the other copy of agent F, who has z=-1/2 . It exists for one copy of agent Fbar but not for the other one.
    That is a total of five “worlds”, all with different facts.

    Then, agent Wbar goes into the state (-ou).

    He knows that agent F has z=+1/2 inside her lab. His system state vector (-ou), which contains his information about the system, contains this fact.

    Now, let’s rewrite the state of agent Wbar in terms of { HEADS, TAILS }

    -uo

    = -u (h-t) / root(2)

    = (ut – uh)/root(2)

    So, there you have the mistake.
    Agent Wbar is in a “world” where agent Fbar could have TAILS or HEADS.
    But the proof of the paradox requires her to have HEADS absolutely.

  257. David Byrden Says:

    The logic of this apparent paradox was chained together by three assumptions, S,C,Q.
    I’d like to discuss them now, with reference to the Nature article at
    https://www.nature.com/articles/s41467-018-05739-8

    The situation is:
    at the end of the experiment, agent W has the measurement “OK”. But then, using a chain of logic, he concludes that it should have been “FAIL”.

    Is there a bad link in that chain? If so, where?
    I will read through Table 3 from the last row to the first, looking for the source of this misunderstanding, analysing the steps under the “Many Worlds” interpretation.

    In row 4, agent W hears the announcement by agent Wbar that he measured “/OK” at time n:21.
    Since these two agents are both in the same “world”, i.e. they have the same state vector for the quantum system, then what’s true for one of them is true for the other.

    The reason they’re in a single “world”, despite being separate observers, is that there’s no barrier between them capable of blocking the transfer of information via the universal Wave Function. I don’t see that consciousness of observers plays any part in QM.

    So, statement Wn:26 seems valid to me. Now, instead of continuing with row 4, we must analyse row 3 on which it depends.

    In row 3, agent Wbar measures “/OK” at time n:21. This tells him the state of the lab Lbar, and from that he calculates the state of the partially entangled lab L, using his knowledge of the system.
    This depends on assumption Q.
    He comes to the somewhat surprising conclusion that lab L must be in the state z=+1/2. For convenience, I refer to this state as “UP”.

    How can lab L, containing agent F, be in the state “UP” if it has just been measured in the state “OK” ?

    Well, firstly, agent W didn’t literally measure the insides of the lab. You can’t measure a human being, a chair and other macro objects and find them in a superposition of two states – and, remember, “OK” is a superposition of “UP” and “DOWN”.
    What happens here – and this HAS to happen in order for the experiment to work as described – is, the two agents F and Fbar remain locked inside their labs at all times. They make copies of their state in qubits and send these to the outside world.

    (This does not violate the No Cloning Theorem, because the states are known and orthogonal.)

    So, agent W measured a qubit (e.g. a polarised photon), not agent F herself. Those students using the “collapse” model of quantum mechanics might conclude that his measurement is invalid. The qubit “collapsed”, but agent F did not, because she was untouched.

    This is wrong. This is an example of why “collapse” models don’t work.

    In the “many worlds” interpretation, when agent W measures the qubit, he splits into two copies of himself in different “worlds”. These “worlds” are defined by the system state vector, which has a different value in each “world”. The lab is part of the system. And that means he truly measured the inside of the lab by measuring the qubit.

    So, we can now resolve our puzzlement at row 3. The contents of lab L, including agent F, truly are in the state “UP”, in the “world” occupied by agent W. If lab L should be breached, he will meet agent F saying “my measurement was UP”.

    And when agent W measured the qubit that she sent to him, using the { OK , FAIL } basis, he had a fifty-fifty chance of getting “OK” or “FAIL”. But, as you may recall, we simply repeated the experiment until he got “OK”.

    I will continue in another post….

  258. David Byrden Says:

    Before I continue to analyse Table 3, I want to explain how to find your own way around quantum systems like this one. Let’s examine what happens if agents open a lab. I will use the Many Worlds interpretation, because it works.

    The key to understanding quantum systems is to use Quantum Mechanics. Don’t use “classical” thinking. Use state vectors and the Born rule.

    For example, I defined a shorthand notation for this system, in post #246. Using my notation, the original system state is this vector in Hilbert space;

    ( tu + hd + td ) / root(3)

    Now, if agent W takes a pickaxe and breaks into lab L, what will happen? Why would that change anything? Because he will expose his “world” to the lab’s “world”, entangling their wave functions. This is equivalent to measuring the lab in its basis { u , d }.
    So, in this combined “world”, the state vector will lose all terms containing one of those two states, and the remaining vector will be “renormalised” to unit length.

    The outcome is probabilistic. In one-third of cases he will go into this state, finding that agent F wrote “UP” in her notebook;

    ( tu )

    and in two-thirds of cases he will find that she wrote “DOWN”;

    ( hd + td ) / root(2)

    Note that, in the “UP” case, he not only reads agent F’s notebook, but he can also deduce what’s written in agent Fbar’s notebook, which is hidden in the other lab. His new system state ( tu ) allows for only one possibility. She wrote “TAILS”.

    But in the “DOWN” case, he has no idea what was measured in the other lab. “HEADS” and “TAILS” are equally likely.

    How is it possible that the contents of one lab can affect the unseen contents in a physically disconnected other lab? The answer is, the two labs are partially entangled. This explains nothing, but it’s the official name for what you just saw.

    Now, let’s rewind to the beginning and play it differently. This time, we will let agent F make the first move. She will break out of the lab, instead of W breaking in.

    So, we’re back to the original system state;

    ( tu + hd + td ) / root(3)

    Ah, but wait a minute! I’ve been calling this the “system state”, but really, it’s not the objective state of the system. State vectors belong to the observer, not the system. There can be multiple different state vectors for the same system at the same time. The scope of each one, the area where it’s valid, is called a “world” in the Many Worlds interpretation.

    The above state vector was valid for the “world” outside the labs, including agents W and Wbar, but not inside the labs. In particular, lab L contains agent F who has already measured the qubit S. That measurement split her lab into two “worlds”. We must define which of the two of her will break out of the lab.

    Let’s assume that she decided in advance, when she was still a single entity, to break out only after measuring “UP”. After the measurement of the qubit S, the copy of agent F who intends to break out has this system state vector;

    ( tu )

    It’s important to understand that while she’s in her lab, in a “world” where this is the system state, the agents W and Wbar are waiting outside where the original system state is valid. So we’re looking at three “worlds”; the outside, and the two alternate worlds inside lab L. As an exercise, try counting the additional “worlds” in the other lab.

    Now, the agent F who measured “UP”, breaks out of her lab. She meets the external agents W and Wbar. That is guaranteed. That happens to her 100% of the time. But, for the external agents, there was only a one-in-three chance that agent F would emerge. Different facts exist in different “worlds”.

    The moment when she either emerges, or doesn’t, is a quantum event. It splits the external “world” into two “worlds”, much as I described in the previous example. In this case, if nobody breaks out of the lab, the external agents can conclude that agent F measured “DOWN”. They have read her notebook without entering her lab.

    Once you understand the concept of multiple “worlds”, how they can split and merge, and how they can be partially entwined with each other, you don’t need an explanation for “entanglement”. It’s obviously going to happen and will require no additional mechanisms.

  259. Renato Renner Says:

    Mateus #251:

    OK, it seems you are trying to make a distinction between “non-real” and “real” measurements. If you manage to make such a distinction, that may indeed resolve the paradox.

    But, unfortunately, I did not yet understand how you would distinguish them. I noticed that you are talking about “decoherence”. But recall that this is a highly observer-dependent notion (which you do not want, I guess), depending on where you draw the boundaries around a system. If you draw them around the entire universe, for instance, there is simply no decoherence.

  260. Renato Renner Says:

    David #246-#258:

    While I agree with most of your general comments, I am afraid that they do not provide a resolution of the paradox.

    > Now, here is the error in the paper’s logic : the authors assume that ( – ou ) is the same state as ( tu ).

    You (again) forgot to consider the timing (as Scott did in his original post, which led him to the conclusion that our paper must be flawed). In your notation, (tu) is the state that represents F’s information after having observed outcome z=+1/2 at time n:11, whereas (-ou) is the state that represents Wbar’s information after having observed ok at time n:21.) Note that there is a measurement in between the two times, so the states are indeed not supposed to be identical.

  261. David Byrden Says:

    I will now continue from post #257. I’m looking for an error in Table 3 at https://www.nature.com/articles/s41467-018-05739-8

    As I said in post #257, statement Wbar n:22 in row 3 is correct. I will come back to it shortly and discuss why it is correct.

    The rest of row 3 merely restates row 2, so I will now examine row 2.

    It begins with agent F measuring the qubit S at the time n:11 and getting the result z=+1/2, which I refer to as “UP”.

    The qubit was prepared and sent by agent Fbar, and everybody knows that she put it into one of two states, “DOWN” or “RIGHT”. So how did we get the result “UP” ?

    We got that result because agent F measured in the { UP , DOWN } basis. Those are the only possible results. But what happens then if the qubit is “RIGHT” or “LEFT” or has some other angle?

    It’s a principle of quantum mechanics that, if a system has multiple allowed states, then it can be in any “superposition” of those states. The qubit’s “RIGHT” state can be considered a superposition of “UP” and “DOWN” in equal amounts. Therefore it can be measured as either “UP” or “DOWN”.

    In the body of the article, around equation 5, the authors examine that “UP” measurement to see what they can deduce from it. They imagine what would happen if the qubit were to be sent in the “DOWN” state. Using assumption Q, they show that the measurement result would be “DOWN”.

    Since the result was not “DOWN”, they conclude that the qubit wasn’t in the “DOWN” state. Then they assume it must have been sent in the other state, “RIGHT”.

    But this is the error. It’s an error because the qubit is a quantum system. The qubit can be in a mixture of the “DOWN” and “RIGHT” states. And it’s possible to get a result of “UP” when you measure these superpositions, because they all contain some fraction of “RIGHT” which contains “UP”.

    The three assumptions S,C,Q are not at fault here. The problem is that a quantum system was analysed in a classical way.

    Now, the “RIGHT” state would be sent by agent Fbar only if her own state was “TAILS”. So the authors conclude that agent Fbar must have been in the “TAILS” state. This is written in the next table cell as statement F n:12.

    But this compounds their error. Agent Fbar could potentially be in a superposition of “HEADS” and “TAILS”. If the qubit is in a superposition, then so is she and vice versa. All the subsequent logic in Table 3 needs to be rewritten to allow for this possibility.

    But if it’s just a possibility, perhaps we can ignore it? Does it actually happen during the experiment?

    Look at row 3 of the table again. When agent Wbar measured the lab Lbar, he did so in the { OK , FAIL } basis. These two basis states are superpositions of the lab’s internal states “HEADS” and “TAILS”. (See Table 2, row 3)

    So it’s not just a possibility that agent Fbar was in a superposition; it’s an inevitability. It was forced.

    Of course, agent Fbar herself doesn’t feel like she’s in a mixture of states, but she’s in another “world” with different facts. Actually there are two copies of her in two “worlds”. The paper’s chain of reasoning applies only to the external “world” where agents W and Wbar exist. They could break into her lab, but that would be equivalent to measuring its contents again, in the basis { HEADS , TAILS }.

    In the “world” of agents W and Wbar there exists only the information that agent Fbar is in a superposition. Thanks to the perfectly sealed lab, absolutely no other information about her state can reach them. As I explained in post #253, it’s literally true for them while it is simultaneously untrue for agent Fbar herself (both copies of her). Such is the nature of Quantum Mechanics.

    In the body of the paper, around equation 6, the authors calculate what agent F will see. They prove that she cannot possibly measure “DOWN”. In fact, of all the measurement bases that agent Wbar could have used, his chosen basis { OK , FAIL } is the only one that guarantees agent F will measure “UP”.

    So, there is an error in Table 3, row 2. When agent F reads z=+1/2 at time n:11, it does NOT follow that agent Fbar is in the “TAILS” state. She can also be in a superposition of “HEADS” and “TAILS”.

    Even worse, row 3 of the table is self contradictory. It begins by telling us that agent Fbar is in a superposition, then it proceeds on the assumption that she is not. In the Many Worlds interpretation, contradictory facts may exist in different “worlds”, but not in a single “world”.

    The subsequent chain of logic depends on this assumption and is therefore invalid.

    A full analysis of the experiment (which I have not presented here) finds nothing unusual or contradictory in the results.

  262. David Byrden Says:

    Renato #260 :

    >> “In your notation, (tu) is the state that represents F’s information after having observed outcome z=+1/2 at time n:11”

    At that time there are two copies of F in different “worlds”, and we’re talking about just one of them. But yes, that’s what I am saying about her.

    >> “whereas (-ou) is the state that represents Wbar’s information after having observed ok at time n:21.”

    Again, there are two Wbars at this time.

    But yes, this is the copy of Wbar who shares a “world” with W where they both measured “OK” and they halted the experiment to think about the results.

    This is the “world” that we are in, when we read Table 3. And, as you have calculated, agent F who measured z=+1/2 is also in this “world”.

    Our point of disagreement is the “world” that agent Fbar occupies, or rather, which versions of agent Fbar exist in this “world”, and in what percentages.

    >> “Note that there is a measurement in between the two times, so the states are indeed not supposed to be identical.”

    As I stated in post #244, I don’t believe in “collapse of the wave function”. I think your experiment is a good example of why it doesn’t work.

    I believe that a system state vector, such as ( tu + hd + td ) / root(3), does not represent the system’s objective state. It represents your knowledge of the state. When you “collapse” it with a measurement, the vector moves around in Hilbert space just as the textbooks say, but really it’s your information that changes, not the system itself.

    Your experiment demonstrates that different observers can and must hold different versions of the state of this system, at the same time.

    If we imagine that measurements (like the measurement of “OK” by Wbar) cause a “collapse”, if we imagine that the system itself changes state for everybody when one person measures it, then the experiment cannot work at all. I’d like to see a proponent of the “collapse” model write down an analysis of your experiment!

    Anyway, I have already submitted a post where I spell out the problem in extreme detail, so I will not continue here. Thank you for this really interesting puzzle.

  263. Mateus Araújo Says:

    Renato #259: I’m not doing that myself, I’m just describing what other people do in order to make the point that what you call “quantum theory” is not the consensus quantum theory, but rather a QBist version thereof.

    My solution to the paradox, as I have explained before, is that you cannot use the collapse postulate when you are inside a decoherence-proof box.

  264. David Byrden Says:

    Mateus #207 :

    You said:
    “[branching] this doesn’t happen with Fbar. There is no “heads branch” or “tails branch”, as Fbar is assumed to be in this decoherence-proof box that prevents it from entangling with external systems.”

    Perhaps you could explain what you understand decoherence to be?

    I was under the impression that, as the Heads and Tails versions of Fbar began to differ, that would be sufficient for them to decohere. And I’m talking about very small differences. In my understanding, the information from the random “coin” would have to be quantum-level isolated from the rest of the lab in order to preserve coherence of Fbar-tails and Fbar-heads.

  265. David Byrden Says:

    Looking at my post #261, it disproves the paradox exactly at this sentence:

    >> “The qubit can be in a mixture of the “DOWN” and “RIGHT” states”

    This is where I break the chain of logic. The proof of the paradox requires that qubit to carry either one value or the other, like a classical system. But if it’s allowed to be in a superposition, the proof does not stand.

    The qubit is sent by agent Fbar, and she’s in a superposition, and she sets the qubit value depending on her state, so I’ve assumed that she puts it in a superposition.

    But what if she doesn’t? Then my disproof of the paradox would fail, but would the paradox itself be valid?

    Let’s see what would happen. Let’s make that change and go through the experiment again.

    Imagine that the qubit, sent from agent Fbar, allows agent F to distinguish her two states in all cases. A measurement of “DOWN” that came from “HEADS”, and a measurement of “DOWN” that came from “TAILS”, are not the same.

    Since we have two kinds of “DOWN” state, I need another letter for my equations. I will use uppercase “D” for the “DOWN” associated with “HEADS”.

    Now, the original system state, as seen by the external agents, is:

    ( tu + td + hD ) / root(3)

    Notice the uppercase “D”.

    Agent Wbar intends to measure lab Lbar in the basis { OK , FAIL }, so we convert the equation to that basis;

    ( uf – uo + df -do + oD + fD ) / root(6)

    He measures the value “OK”. For him, the system state is now:

    o ( – u -d + D ) / root(3)

    Well, this is messier than before. If you refer to post #246, you’ll see that we used to have ( –ou ) here.

    In other words; when the qubit was allowed to be in a superposition, the measurement “OK” at the first lab, implied that the second lab was “UP”.

    But now, the measurement “OK” at the first lab puts the second lab into a superposition of three states. It’s no longer guaranteed “UP”. It’s more likely to be one of the “DOWN” states.

    And because it’s not guaranteed “UP”, we can’t continue with the chain of logic from Table 3. We can’t conclude that agent Fbar has “TAILS”.

    Once again, there is no paradox.

  266. David Byrden Says:

    Renato #260:

    Concerning my post #246, you made a comment, and I should answer it precisely. I willl quote you.

    ———–

    >> “(tu) is the state that represents F’s information after having observed outcome z=+1/2 at time n:11”

    Yes, that’s right. At first, the system state information in F’s world is

    ( tu + hd + td ) / root(3)

    Then she reads z=+1/2, which I call “UP”.

    That vector falls into its projection on the “UP” plane. Some people call it a “collapse”.
    The vector components without “u” disappear, and we renormalise.

    Now, her information about the system is:

    ( tu )

    So, in this world, Fbar measured “TAILS”, because the system vector has “t” and no “h”.

    There is another “world” of the MWI where Fbar measured “HEADS” but it has no overlap with this “world”.

    ———–

    > “(-ou) is the state that represents Wbar’s information after having observed ok at time n:21.)”

    We are now talking about a different “world” because Wbar is outside the labs.

    Yes, after the measurement of “OK” on lab Lbar, the system state is

    (-ou)

    in this outside world.

    ———–

    > “Note that there is a measurement in between the two times”

    That’s not relevant. Let me explain how I see this:

    These two states exist in different MWI “worlds” (one is inside a lab, the other is outside). They can be different states because the lab isolates them.

    These vectors don’t represent the objective state of the system. They represent the information about the state that exists in a “world”. So, different “worlds” can hold different state vectors at the same time.

    A measurement does not change the objective system state. It changes the information in a “world”.

    ———–

    > “the states are indeed not supposed to be identical.”

    Look at Table 3, row 3. The first cell says

    /w = /ok at time n:21

    so that is the state (-ou)

    Statement W n:22 follows, and it is indeed true, because this state contains “u”.

    But, the next cell says

    “F is certain that W will observe w = fail ”

    This is true only if Fbar measured “TAILS”.
    So, you’re assuming that the state contains “t” and no “h”.

    You are assuming that (-ou) and (tu) are the same.

  267. David Byrden Says:

    For your reference: my understanding of this problem has been evolving within this thread, so I’d like to correct some things that I said, now that I’ve resolved various questions that were troubling me.

    [1]
    Measurement of labs: I questioned whether one could measure a lab, or other macro object, in an arbitrarily chosen basis such as { OK , FAIL }. I wondered if this made the thought experiment invalid.
    Now I understand that it’s possible in principle. And here is a mechanism:

    a. An agent (e.g. Fbar) fires a photon into a long fiber optic within her lab.
    b. She makes her quantum measurement (e.g. of the randomness generator)
    c. It electronically controls a set of filters downstream of the photon
    d. The photon transits the filters and gets a polarisation representing the lab’s state
    e. The photon is now in a superposition
    f. The photon is guided out of the lab
    g. An external agent measures it in any chosen basis
    h. If the photon got absorbed in the filters, repeat the whole experiment.

    With this approach the two superposed states of the photon remain coherent, even if the rest of the lab’s contents decohere. The external agent receives a photon representing the lab’s contents which are in a superposition of two states (relative to him).

    Contrast this approach with a non-working poorly designed lab where the agent looks at the measurement result and manually prepares a qubit. The two copies of her would inevitably send it at slightly different times, so the two copies of the photon would be distinguishable, making it a “classical” either-or system. I explored the consequences in post #265.

    [2]
    I said in post #185 that unsealing the lab Lbar would implicitly resolve the paradox by putting agent Fbar into a state other than “TAILS”. As the Copenhagers would say, this “collapses” her wave function and ends her superposition.

    I now realise that her wave function can only “collapse” into HEADS or TAILS. To measure her in any other basis, you must use a mechanism such as I outlined in [1]. So this is not a solution to the paradox.

    I also now realise that “collapse” is an illusion. In truth, the observer becomes entangled with the lab and splits into two “worlds”. This experiment is itself a good demonstration that “collapse” interpretations don’t work, because the measurements made by the observers inside the labs would destroy the effect if they “collapsed” anything.

    [3]
    Renato, in post #190 you said that if I had “a variant of many-worlds that avoids the paradox, then you should certainly go ahead and write it up. ”

    After reading summaries of the various QM interpretations, I find that I’ve apparently stumbled into RQM, though I have been using the terminology of MWI.

    Upon reading the Wiki page about RQM I found that it matches my own amateurish understanding of QM. In particular its explanation of entanglement is exactly what I had already figured out.

    So, I have no original or new contributions to make.

  268. Renato Renner Says:

    Relational Quantum Mechanics (RQM) is indeed another interpretation in which all value assignments are relative to observers and their observations, like in QBism and in Everett’s relative state formalism. (@Mateus: This may be of interest to you, as you were asking for examples other than QBism.)

    RQM also satisfies our rule [Q], for it enables the following type of reasoning:

    [RQM] If, for an observer who observed Y, a given system is in state psi, and if the Born rule, used with state psi, assigns probability 1 to a particular measurement outcome x, then the observer can claim “I am certain that the measurement has outcome x relative to me who observed Y.“

    So, the words may differ, but operationally it’s again precisely rule [Q] as used in our argument. The contradiction thus remains a contradiction, also in this interpretation.

  269. Mateus Araújo Says:

    Renato #268:

    Indeed, Relational Quantum Mechanics explicitly defends this nonsense, so you argument implies not only that QBism is inconsistent, but also that Relational Quantum Mechanics is inconsistent.

  270. David Byrden Says:

    Renato #268:

    I am not disputing your assertion [Q].
    But, your contradiction depends on more than [Q].
    I will explain with reference to the “Nature” article at https://www.nature.com/articles/s41467-018-05739-8

    At equation 5, you are examining one possibility:

    “Suppose now that agent F observed z=+1/2 ….”

    Immediately after equation 5, there is written :

    “… it follows from (Q) that S was not in state |↓⟩, and hence that the random value r was not heads.”

    I completely agree with that. I agree with assumption [Q]. The value of r was not “HEADS”.

    So, what was the value of r ?
    Because r is a quantum system, it could be any mixture of “HEADS” and “TAILS”.
    All mixtures contain some fraction of “TAILS”, which in 50% of cases will cause the measurement z=+1/2.

    The article then says:

    “… This is statement Fn:12 of Table 3. ”

    But the statement in the table says this:

    “I am certain that /F knows that r = tails at time n:01.”

    So, you have ignored the possibility of a mixed state. I believe this is an error.

    Can you explain why a mixed state (a superposition of Fbar) was not considered?

  271. Renato Renner Says:

    David #270:

    > Because r is a quantum system, it could be any mixture of “HEADS” and “TAILS”.

    You are right, that’s a possibility. However, from the viewpoint of F who has observed z=+1/2, it is indeed certain that r=tails.

    Although we didn’t do so in the article, one may explain this in many-worlds language if you like. The joint state of r, Fbar, and spin S right before the spin measurement can be written as:

    1/sqrt{3} ( |r=heads>|Fbar observed heads>|down> + |r=tails>|Fbar observed tails>|up> + |r=tails>|Fbar observed tails>|down> )

    Hence, relative to an observer F who measured z=+1/2 (corresponding to “up”), the state of r and Fbar is |r=tails>|Fbar observed tails>, which is obviously a pure state, justifying F^n:12

  272. David Byrden Says:

    Dr. Renner #271 :

    There are two different states for lab Lbar that cause agent F to read “UP”.

    In my notation, they are:

    t

    and

    (h-t) / root(2)

    Therefore, when F reads “UP”, she should not assume that the other lab is ( t ).
    Both of these states may exist in the other lab.

    As I showed in post #246, a measurement of “OK” by Wbar will actually create the second state in Lbar, and cause F to read “UP”.

    Your error is to conflate these two situations.

  273. David Byrden Says:

    Dr. Renner #271 :

    I’d like to extend my response, because I’ve only just realised what you are telling us in that post. I’ve only just noticed the critical words: “obviously a pure state”.

    ————–

    To reprise: there are many, many mixed states of Fbar which could cause F to measure “UP”.
    In the experiment, two of those states arise: (t) and (t-h)/root(2)

    In my view, there is no paradox. You make an illegal jump from one of these states to the other, and that creates the appearance of a paradox.

    ————–

    Specifically: the measurement of “OK” by Wbar changes the system state into

    u(t–h)/root(2)

    This state is valid for Wbar and anything connected to him via the Wave Function, therefore it’s valid for W and the external environment.

    It’s the state of the system *relative* to Wbar and the outside. It’s not the objective state of the system. Other agents may hold other states for the same system at the same time.

    Now, look at the equation. It says that F measured “UP” and Fbar is in a mixed state.

    Because F is in a pure state, we can extend the “world” where this equation is valid.
    The inside of the second lab, holds a “world” where F measured “UP”, and this system state equation is valid in there also. Wbar is in full agreement with F, and for him there is only a single F, no superposition.

    But what do they think about Fbar, inside the first lab?
    The equation tells us that she’s in a superposition (t-h).

    That is the situation in your statement W n:22.

    Then you do something that I consider illegal.
    You move agent F from this state

    u(t–h)/root(2)

    to this state

    (ut)

    and you say it’s because (t) is “obviously a pure state”.

    Well, please explain, why must it be a pure state?

    The lab Lbar has not been opened. Nobody has measured agent Fbar directly. They measured a qubit that she created.

    Why can’t she be, relative to them, in a superposition?

  274. Andreas Says:

    Renato Renner #271

    You did emphasize, that at the time of F’s measurement, the universe can be considered as being split into three branches:

    > Although we didn’t do so in the article, one may explain this in many-worlds language if you like. The joint state of r, Fbar, and spin S right before the spin measurement can be written as:

    > 1/sqrt{3} ( |r=heads>|Fbar observed heads>|down> + |r=tails>|Fbar observed tails>|up> + |r=tails>|Fbar observed tails>|down> )

    You then assume, that F’s measurement happens in each of these 3 branches independently: I.e. the state of the two labs at time n:11 can be written as:

    1/sqrt{3} ( |r=heads>|Fbar observed heads>|down>|F observed -1/2> + |r=tails>|Fbar observed tails>|up>|F observed +1/2> + |r=tails>|Fbar observed tails>|down>|F observed -1/2>)

    My question now focuses on the next step: the measurement performed by Wbar. Let me also assume here, that Wbar gets “okbar” as a result. In the paper you then proceed with the consideration of the orthogonality between the unitarily evolved initial state and |ok〉⊗|↓〉. From this, you have Wbar conclude that F must have measured “z=+1/2”.

    I do see the calculation of the orthogonality, but I wonder: What does this mean in the language of many worlds?

    I assume, a first answer would be, that the two branches in which F measured “z=-1/2” annihilate each other because they were given an opposite phase by the measurement outcome “wbar=okbar”.

    But would this really happen like this? That the measurement that Wbar performs on Lbar causes these two branches, each containing a measurement performed by F, to annihilate each other?

  275. Renato Renner Says:

    David #273:

    > Well, please explain, why must it be a pure state?

    In many-worlds, which seems to be what you are referring to, the global state is usually assumed to be pure. Now, if an agent measures this state with respect to an orthonormal basis (which is always the case in our experiment) and obtains an outcome x then the “relative state” (in the Everett sense) that the agent (who has observed x) assigns to the world around him is still pure. This is generically true, independently of the details of the experiment.

  276. Renato Renner Says:

    Andreas #274:

    > What does this mean in the language of many worlds?

    To see this, it’s useful to rewrite the state described in comment #271 in terms of the states |failbar> and |okbar>:

    sqrt{1}{6} |failbar>|up> – sqrt{1}{6} |okbar>|up> + sqrt{2}{3} |failbar>|down>

    So, I would say that you don’t need to argue about interference here. You can simply say that the measurement outcome okbar of Wbar picks out the branch in which the spin was |up>.

  277. Renato Renner Says:

    Mateus #269:

    I wonder what you would then say about Everett, who not only talks about the (objective) state of the universe, but also very prominently about state assignments relative to observers and, more specifically, relative to their observations. The latter seems to be (at least on the technical level) identical to what Rovelli does in RQM.

  278. David Byrden Says:

    Andreas #274, Dr. Renner #276 :

    I think there’s some confusion here about what “many worlds” is. Let me correct two misapprehensions:

    A “world” not an entire universe. Speed-of-light and causality restrictions make that impossible.

    A state vector may be written in any basis. The resulting equation will have multiple terms separated by “+” or “-“. But those terms don’t correspond to “worlds”, they correspond to whatever basis vectors you chose.

    You can choose “pure states” as your basis vectors. The equation in comment #271 uses a “pure state” basis. In my notation, it’s written as:

    ( hd + tu + td ) / root(3)

    and each term is a “pure state” for both labs. But the terms still don’t correspond exactly to the “worlds” that exist in the experiment.

    Now, this is how I see it :

    A “world” is a branch of reality where the state vector has a specific value. It is limited to a physical area. That’s the RQM interpretation.

    When this experiment is configured, at time n:12, we have five “worlds” :

    1. The external world, where the state is
    ( hd + tu + td ) / root(3)

    2. Lab Lbar where Fbar measured “HEADS”. Her system state is
    ( hd )

    3. Lab Lbar where Fbar measured “TAILS”. Her system state is
    ( tu + td ) / root(2)

    4. Lab L where F measured “UP”. Her system state is
    ( tu )

    5. Lab L where F measured “DOWN”. Her system state is
    ( hd + td ) / root(2)

    At subsequent times, measurements of the system are made. A measurement can change the system state of a “world” because it changes the information about the system that exists in that “world”. It doesn’t affect the system itself or any of the other “worlds”.

  279. David Byrden Says:

    Dr. Renner #275 :

    >> “the global state is usually assumed to be pure.”

    What is “global state”?

    Are you saying that the outside world, surrounding an experiment, has a special status?

    So, Schrodinger’s cat may be in a mixed state, but Schrodinger must always be in a pure state?

    I don’t see a distinction.
    I see two regions of space, separated by the cat’s box.
    I believe that Schrodinger can use a poison device, just like the cat’s device.
    I believe that Schrodinger and the entire “global” environment will have a superposition of “Schrodinger alive” and “Schrodinger dead”, relative to the cat.

    So, the term “global state” doesn’t make sense to me.

    And even if the “global state” had a special status; surely W and Wbar are the agents in the “global” state here?
    But we’re discussing the state of Fbar, who is inside a lab.

    >> “Now, if an agent measures this state….and obtains an outcome x, then the relative state (in the Everett sense) that the agent (who has observed x) assigns to the world around him is still pure.”

    But Agent F does not measure Agent Fbar directly.

    She measures the qubit. The result need not correspond to a pure state for Agent Fbar.

    Look at Agent Wbar, who measures the SAME lab and gets “OKbar”, which is a mixed state.
    He’s doing exactly what you said was impossible !

  280. Mateus Araújo Says:

    Renato #277:

    The difference is that Rovelli insists that the friend is right, and moreover that the relative states are all that is. For Everett, the fundamental object is the universal wave function, from which you derive relative states in order to obtain the perspective of each observer. In particular, Everett would sustain that the friend is wrong.

    Rovelli defends this pretty explicitly in his Relational Quantum Mechanics paper. Take a look at “Objection 7” on page 5.

  281. Renato Renner Says:

    David #279:

    > “OKbar”, which is a mixed state.

    No, OKbar is, by definition, a pure state.

    Could it be that you are using a non-standard notion for what you call “pure” and “mixed” states? This may explain your disagreement with the argument in our paper.

  282. David Byrden Says:

    Dr. Renner #281 :

    You are absolutely right. My apologies. I didn’t understand the meaning of “mixed state”.

    I will re-read your argument in this light and come back here.

    I hope I’m right to assume that the article in Nature is your complete argument and not a summary?
    https://www.nature.com/articles/s41467-018-05739-8

  283. David Byrden Says:

    Dr. Renner #281 :

    Well, this concept of “mixed state” is fascinating. I had analysed your experiment on the assumption that all its states were pure. So, of course, I might have been on a different track to you.

    Rather than risk misinterpretations, I will ask you now to put me on the right track.

    When agent Fbar reads the “random generator”, does this put her into a superposition, or a mixed state?
    (relative to other observers, of course.)

    When agent F measures the qubit with polarisation “RIGHT”, she measures it in the { UP , DOWN } basis. Does this put her into a superposition, or a mixed state?

    Thank you.

  284. David Byrden Says:

    Dr. Renner #268:

    Now that I know (vaguely) the meaning of “mixed state”, I will rewrite my post #270 and I hope that I will use the correct words this time !

    ——- post #270 version 2 ——-

    I am not disputing your assertion [Q].
    But, your contradiction depends on more than [Q].
    I will explain with reference to the “Nature” article at https://www.nature.com/articles/s41467-018-05739-8

    At equation 5, you are examining one possibility:

    “Suppose now that agent F observed z=+1/2 ….”

    Immediately after equation 5, there is written :

    “… it follows from (Q) that S was not in state |↓⟩, and hence that the random value r was not heads.”

    I completely agree with that. I agree with assumption [Q]. The value of r was not “HEADS”.

    So, what was the value of r ?
    Because r is a quantum system, it could be any superposition of “HEADS” and “TAILS”.
    All superpositions contain some fraction of “TAILS”, which can lead to the measurement z=+1/2.

    The article then says:

    “… This is statement Fn:12 of Table 3. ”

    But actually you are making an assumption. The statement Fn:12 says this:

    “I am certain that /F knows that r = tails at time n:01.”

    So, you have ignored the possibility of a superposition? I believe this is an error.

    Can you explain why a pure superposition state in lab /L was not considered as a possible cause of the “UP” measurement?

  285. Scott Says:

    Renato, David Bryden, et al.: Sorry, but I’m going to close down this thread in a few days, since otherwise it looks like I’ll have this thread to deal with in my moderation queue for the remainder of eternity. 🙂 So please get in any final thoughts soon! Thanks very much.

  286. Andreas Says:

    Renato Renner #276

    I think you make a good point by mentioning that the state

    1/sqrt{3} ( |heads>|down> + |tails>|up> + |tails>|down> )

    is equal to the state

    sqrt{1}{6} |failbar>|up> – sqrt{1}{6} |okbar>|up> + sqrt{2}{3} |failbar>|down>

    However I would argue, that interference is still involved there. I guess when you did the calculation, you also got as a Zwischenresultat:

    1/sqrt{6}(|failbar>|down>+|okbar>|down>+|failbar>|up>-|okbar>|up>+|failbar>|down>-|okbar>|down>)

    where the term |okbar>|down> appears twice, but with an opposite phase.

    In addition I would also claim, that the cancellation of these two terms is what makes the difference between the two parts of your argumentation in the paper.

    When F measures “up”, she can be certain, that in her past Fbar must have measured “tails”. Agreed. But she is not the complete future of “tails”. Behind her back there is also the other half of “tails”, i.e. |tails>|down>. And also |heads>|down>. Now the experiment is designed such, that whenever this crazy state gets measured as |okbar>, all terms containing |down> and reaching “okbar” cancel each other out.

    So in fact, there is nothing behind F’s back, exactly because the two components from “heads” and “tails” featuring |down> cancel each other out. At least towards a future world where Wbar measures “okbar”.

    And this cancellation would not happen if Fbar only measured “tails”, which then later on would lead to W not being able to measure “ok”.

  287. Andreas Says:

    But your reply is a good reminder, that I cannot simply say this cancellation would happen at the time of Wbar’s measurement. Since it is just a mathematical reformulation that applies already before the measurement.

    It almost seems as if the future measurement of Wbar has an influence on which events do happen in the past and which not. At least in the language of your argumentation in the paper.

    And in fact this might be quite similar to an idea that I have had in my mind in the last years. As I have written above (Comment #217) my setup of choice is not consisting of labs with friends inside, but is considering the whole universe and the assumption, that its last phase, e.g. a big crunch, could act as a big eraser function, allowing for interference between macroscopically differing branches.

    If for a certain event, one outcome exclusively leads to an endstate with complete destructive interference, could this not cause the event to not take that outcome at all?

    Your Gedankenexperiment of course allows for a much more exact analysis than my general considerations about potential interference in endstates of the universe. But a similarity seems to be, that in both scenarios, we are interested not only in the outcome after the “interference in a box”. But also, what the situation would mean for the histories on the inside, especially for the results and conclusions of persons (or computers) within the setup.

  288. Andreas Says:

    Dear Scott,

    I am very thankful for the opportunity that you have given us. Your post and also the technical side of your blog have offered us a very nice setup to discuss these ideas. Thanks!

    I can also totally understand, that you don’t have infinite resources to host this discussion forever. (The lack of infinite resources seems to be one of the strongest driving factor in your field of computation theory 😉 ).

    @ Renato Renner, David Byrden, Mateus Araújo and others. What do you think? I could make a post on reddit, either in my personal subreddit that nobody reads or in another subreddit. Reddit also has some skillful people interested in quantum mechanics. Whichever you prefer. In general: Reddit offers the possibility to reply to specific comments and thus allows a branching structure of the comments section 🙂 . This can be very helpful. Nevertheless I also enjoyed the straight time line here.

    Do you know any other place that you would prefer? Or are you also at a point where you think the discussion should be brought to an end?

  289. Mateus Araújo Says:

    Scott #285: Thanks for putting up with us for so long! I hope you got some enjoyment out of it.

    Andreas #288: I don’t think there is anything left to discuss. In my point of view the contradiction comes from the assumption that both Wigner’s and the friend’s perspectives are equally valid. Renato agrees that this assumption is necessary, but for him it is just quantum mechanics. I think this assumption is nonsense, and moreover only defended in QBism and RQM, so one can hardly claim that it is just quantum mechanics. In any case, I doubt that further discussion will resolve this disagreement.

  290. David Byrden Says:

    Scott:

    I also thank you for hosting this prolonged discussion. I wonder have you checked the analytics. Are we alone here, talking in an echo chamber?

    Andreas #287: you said:

    >> “it seems as if the future measurement of Wbar has an influence on which events do happen in the past”

    I began to study this Gedankenexperiment without a clear picture of how QM works, and this experiment steered me into the RQM interpretation, precisely because it doesn’t require a rewriting of history.

    In RQM there is no objective state of the system. Every “observer” holds a different version of the state, and this gets changed when they make a “measurement”, but there is no collapse and it changes for them only.

    Consciousness is not involved. State information spreads via the Wave Function, and the region over which it’s available (e.g. the inside of a Lab) can be visualised as a “world”. Multiple “worlds” can coexist in the same region, and a “measurement” does indeed split them off as branches.

    So, in this interpretation: Wbar and W exist in the same “world”, the external environment.
    The system state *relative to that world*, is (at first):

    ( tu + td + hd ) / root(3)

    and, as you said, we can rewrite this in other bases.

    The beauty of RQM is that it allows F and Fbar to “see” different system states from their branches and worlds inside their labs.
    For example, the state seen by F, in the branch and “world” where she measured “UP”, is:

    (tu)

    about which you wrote:

    >> “Behind her back there is also the other half of “tails”, i.e. |tails>|down>”

    It’s not really “behind her back” – it’s in another “world”, accessible to some agents but not to her.

  291. Renato Renner Says:

    Scott et al.: Thanks for the discussion! My final thought is that the debate has a clear outcome:

    “Users of quantum theory cannot consistently decide whether the theory can consistently describe its own use.” 🙂

    (This includes professional users, see, e.g., https://www.quantamagazine.org/frauchiger-renner-paradox-clarifies-where-our-views-of-reality-go-wrong-20181203.)

  292. Clara Says:

    Isn’t the second step already fishy? Diane can infer that Charlie is in state |0> given herself being in state |1> only given the ‘old’ quantum state |PSI>, right? Once Alice has measured Charlie’s state to be |– >, the quantum state of Charlie+Diane has changed (the reduced state should be some mixed state now, I suppose?), and so the inference is no longer a valid one. (But that solution to the problem seems almost too simple. Am I missing something here?)

  293. David Byrden Says:

    Dr. Renner #291 :

    I am surprised to see your “last word”. I thought that I’d asked a simple, clear question that cuts to the heart of this problem. And you have not answered it.

    To take a geometric approach; this system can be drawn in 4 dimensional Hilbert space. In that space, there is a plane corresponding to the measurement z=+1/2.

    In statement /W n:22, when you deduce that z=-1/2 is not the case, it implies that the state vector (relative to you) is on this plane. Since it’s a unit length vector, that leaves it with one degree of freedom. The intersection of the Bloch sphere with the plane is a circle.

    Then you assume one specific state vector. And you carry on with that assumption.

    What is your justification for ignoring the rest of this plane?

  294. Mateus Araújo Says:

    Renato #291:

    I would conclude instead that

    “Users of quantum theory cannot consistently decide what quantum theory is.”

    Once we are clear about what quantum theory is, then deciding about its consistency is easy. For instance, I think we agreed here that QBism and RQM cannot consistently describe their own use.