I know in physics we normalize wave function, otherwise it was not legal distribution function.

I talk about different problem,

strong law of large numbers ( what assure us average as n->inf equals expectation) does not hold for all distributions (when first moment does not converges surely ), also some distribution have first moment but infinite variance ( second moment not converges surely ) .

my question is whether wave function can act like this ?

if it is physically possible what does it mean for Uncertainty principle .

if it’s not physically possible wave function , does someone take this into account, so we can add some more constraints for legal wave function?

( i know Cauchy and Levy distribution are is in use in physics world i have no idea if it has any connection to wave function , i have numerous other distribution examples )

in many cases the lazy physicists imagine the experiment to happen in some sort of box (e.g. the laboratory), using appropriate boundary conditions to make sure the integral(s) over the wavefunction(s) converge.

If one talks about the ‘wavefunction of the universe’ etc. your problem could become a real issue (how do yo normalize the universal wavefunction?)

Btw one needs to keep in mind that in real experiments we often do not know the correct physics yet – this is why we do the experiment in the first place. So we do not know the wavefunction before the experiment.

How does a mwi proponent a la Tegmark describe this situation? Did the multiverse split into different branches, with e.g. different masses for the Higgs?

will you consider wave function without surly converges ( lebesgue converges ) of first/second moment ( no SD ) to be the unknown unknowns ?

or will you consider them physically impossible ? ]]>

OK, one more time (I promise it is the last time).

We follow the advice of the famous philosopher Rumsfeld and divide the world into those three parts:

1) the known unknown: the qubits which we can describe with a wavefunction.

2) the unknown unkown: the internal state of the environment, which includes large parts of the observer.

3) the known: my mental state (it is all I really know)

Where one draws the line between 1) and 2) and 3) is up to the particular experimental situation. Perhaps you can arrange it so that nerve cell 563,783,123 in your right eye is part of 1) but in most cases it will be part of 2)

I can ensure you that 1) will always be smaller than 2) and therefore talk about a universal wavefunction is not economic.

I can also tell you that it would not be very economic to describe 3) with a wavefunction, because I know what I know.

So when the wavefunction from 1) entangles with 2) during the experiment, decoherence sets in and when it finally reaches 3) it is reduced.

But again, trying to describe this with one wavefunction would not make much sense … therefore your questions are misguided.

]]>Look, I’m not saying that you shouldn’t adjust your thinking because you happen to come into possession of more information. But don’t tell me you are, as you seem to hint, a hardcore solipsist; if you think that not only the limited world we can observe, and the “universe” we can surmise, but everything there is or could ever be, depends on what you may happen to come up with.

And this is your reason for not being able to at least try and answer my questions? Seriously, give it a try.

]]>Sorry I opened my big mouth again, especially after saying I would retire from commenting lol

It’s Easter, traditionally a time of peace, so I will tread carefully, I will just respond by saying that there is NO *current* experiment which indicates that collapse is not occurring – even the observations made in quantum zeno experiments are entirely consistent with a single path evolution in Hilbert Space – AS LONG AS that path is probabilistically generated! (ie *every single collapse* is probabilistic)

However, as you know, I believe that we will start to observe performance issues which large scale QC which will not be explainable by decoherence issues. The “scale” at which this will happen is of course the thing I should be able to predict, before opening my big mouth again.

Happy Easter!

]]>Like the Grandfather Paradox, not-not-Platonist could mean Scott has a 50% chance of being a Platonist and 50% of being an anti-Platonist. See:

]]>>> What about this ‘collapse’ law?

Your questions are somewhat misguided to a Copenhagener, who is not talking about an “objective collapse’.

*I* decide to reduce the wavefunction after a measurement, because it is not longer the most economic description of reality; This is a matter of convenience and therefore your questions cannot be answered as such.

]]>I thought about some anomaly stuff that exists in the basics of probability theory , that could have some implication in QM: Max Born probabilistic interpretation and Uncertainty principle, and maybe in TCS.

And it will insert some set theory based math to physics( measure theory which is basis of modern probability is based on set theory) .

QM physics and any statistical theory presume strong law of large number holds all the time ( when n->inf average=mean )

But The strong law of large number holds only when the expected value of probability density function converges surely ( by the mean of Lebesgue integration),

there are many probability density function that either the expected value or second moment does not hold this condition( they can converge by other types if integral such as improper reiman or gauge integral

( see here the status on integration definition in math http://www.math.vanderbilt.edu/~schectex/ccc/gauge/

gauge integral also has some connection with QM path integration)

so if some wave function has no first or second moment according to Lebesgue integration then what is the SD and expected value of position for example?

And if there is no such wave functions ( I don’t think it’s true because Cauchy/Lorentzian distribution is in use now) , then such limiting conditions should be taken into account .

( adding to the demand that integral |Psy|^2 dx =1,

integral |x|*|Psy|^2 dx < inf

and

integral x^2*|Psy|^2 dx < inf

)

Quickly scanning sources closely at hand, I’d say that loosely speaking a “world” is a complex, causally connected, partially or completely closed set of interacting sub-systems which don’t significantly interfere with other, more remote, elements in the superposition. Any complex system and its coupled environment, with a large number of internal degrees of freedom, qualifies as a world. An observer, with internal irreversible processes, counts as a complex system. In terms of the wavefunction, a world is a decohered branch of the universal wavefunction, which represents a single macrostate. The worlds all exist simultaneously in a non- interacting linear superposition. Worlds “split” upon measurement-like interactions associated with thermodynamically irreversible processes. How many “worlds” are there? The thermodynamic Planck-Boltzmann relationship, S = k*log(W), counts the branches of the wavefunction at each splitting, at the lowest, maximally refined level of Gell-Mann’s many-histories tree.

This approach accepts the reality of the wave function and the QM formalism without bolting on a collapse postulate. This may not be “coherent” enough for you, and I don’t have the knowledge or background to argue the technical points, but a fair-mined person should, I think, acknowledge that this type of analysis is a reasonable, good faith effort to answer these difficult questions, and that the label “utter hypocrites” is a bit strained.

Now it’s your turn. What about this ‘collapse’ law? Do you have to be conscious to collapse stuff? Can a frog or a robot collapse wavefunctions? At what point does the collapse happen: the optic nerve? the visual cortex? the soul? Or does it just happen whenever you, like, entangle more than some special number of atoms? What is the magic number, then?

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