## Physics for Doofuses: Mass vs. charge deathmatch

Back in high school, I was struck by the apparent symmetry between mass and charge. For the one you’ve got Newton’s F=Gm1m2/r2, for the other you’ve got Coulomb’s F=Kq1q2/r2. So then why, in our current understanding of the universe, are mass and charge treated so differently? Why should one be inextricably linked to the geometry of spacetime, whereas the other seems more like an add-on? Why should it be so much harder to give a quantum-mechanical treatment of one than the other? Notwithstanding that such questions occupied Einstein for the last decades of his life, let’s plunge ahead.

When we look for differences between mass and charge, we immediately notice several.

(1) Charge can be negative whereas mass can’t.

That’s why gravity is always attractive, whereas the Coulomb force is both attractive and repulsive. Since positive and negative charges tend to neutralize each other, this already explains why gravity is relevant to the large-scale structure of the universe while electromagnetism isn’t. It also explains why there can’t be any “charge black holes” analogous to gravitational black holes. (I don’t mean charged black holes; I mean “black holes” that are black because of electric charge.) Unfortunately, it still doesn’t explain why mass should be related to the geometry of spacetime.

(2) Charge appears to be quantized (coming in units of 1/3 of an electron charge), whereas mass appears not to be quantized, at least not in units we know.

(3) The apparent mass of a moving object increases Lorentzianly, whereas the charge is invariant.

These are interesting differences, but they also don’t seem to get us anywhere.

(4) Gravity is “many orders of magnitude weaker” than electromagnetism.

One hears this statement often; the trouble is, what does it mean? How does one compare the “intrinsic” strength of gravity and electromagnetism, without plugging in the masses and charges of typical particles that we happen to find in the universe? (Help me.)

(5) Gravity is transmitted by a spin-2 particle, whereas electromagnetism is transmitted by a spin-1 particle.

This difference is surely crucial; the trouble with it (to use a pomo word) is that it’s too “theory-laden.” Since no one has ever seen a graviton, the reason we know gravitons are spin-2 particles in the first place must have to do with more “basic” properties of gravity. So if we want a non-circular explanation for why gravity is different from the Coulomb force, it’d be better to phrase the explanation directly in terms of the more basic properties.

(6) Charge shows up in only one fundamental equation of physics — F=Kq1q2/r2 — whereas mass shows up in two equations: F=Gm1m2/r2 and F=ma.

Now we finally seem to be getting somewhere. Difference (6) was the basis for Einstein’s equivalence principle, which was one of the main steps on the road to general relativity.

But while the equivalence principle suggests the possibility of relating mass to spacetime geometry, I could never understand why it implies the necessity of doing so. If we wanted, why couldn’t we simply regard the equivalence of gravitational and inertial mass as a weird coincidence? Why are we forced to take the drastic step of making spacetime itself into a pseudo-Riemannian manifold?

The answer seems to be that we’re not! It’s possible to treat general relativity as just a complicated field theory on flat spacetime, involving a tensor at every point — and indeed, this is a perspective that both Feynman and Weinberg famously adopted at various times. It’s just that most people see it as simpler, more parsimonious, to interpret the tensors geometrically.

So the real question is: why should the field theory of Gmm/r2 involve these complicated tensors (which also turn out to be hard to quantize), whereas the field theory of Kqq/r2 is much simpler and easier to quantize?

After studying this question assiduously for years (alright, alright — I Googled it), I came across the following point, which struck me as the crucial one:

(7) Whereas the electric force is mediated by photons, which don’t themselves carry charge, the gravitational force is mediated by gravitons, which do themselves carry energy.

Photons sail past each other, ships passing in the night. They’re too busy tugging on the charges in the universe even to notice each other’s presence. (Indeed, this is why it’s so hard to build a quantum computer with photons as qubits, despite photons’ excellent coherence times.) Gravitons, by contrast, are constantly tugging at the matter in the universe and at each other. This is why Maxwell’s equations are linear whereas Einstein’s are nonlinear — and that, in turn, is related to why Einstein’s are so much harder than Maxwell’s to quantize.

When I ran this explanation by non-doofus friends like Daniel Gottesman, they immediately pointed out that I’ve ignored the strong nuclear force — which, while it’s also nonlinear, turns out to be possible to quantize in certain energy regimes, using the hack called “renormalization.” Incidentally, John Preskill told me that this hack only works in 3+1 dimensions: if spacetime were 5-dimensional, then the strong force wouldn’t be renormalizable either. And in the other direction, if spacetime were 3-dimensional, then gravity would become a topological theory that we do sort of know how to quantize.

However, I see no reason to let these actual facts mar our tidy explanation. Think of it this way: if electromagnetism (being linear) is in P and gravity (being nonlinear) is NP-complete, then the strong force is Graph Isomorphism.

My physicist friends were at least willing to concede to me that, while the explanation I’ve settled on is not completely right, it’s not completely wrong either. And that, my friends, means that it more than meets the standards of the Physics for Doofuses series.

### 36 Responses to “Physics for Doofuses: Mass vs. charge deathmatch”

1. Ambitwistor Says:

Point 3, “The apparent mass of a moving object increases Lorentzianly, whereas the charge is invariant”, is evidence of Point 5, “Gravity is transmitted by a spin-2 particle”.

The source of a field has to be a density — charge density, or mass-energy density. Charge density picks up one Lorentz factor gamma (coming from length contraction), while mass-energy density picks up two gamma factors, or a gamma^2 (coming from length contraction and mass-energy increase). If you accept relativity (which you have to, since you’re talking about Lorentz factors), this implies that charge density is a component of a rank-1 tensor (the 4-current), while mass-energy density is a component of a rank-2 tensor (the stress-energy). In turn, these suggest that the electromagnetic and gravitational fields should be spin 1 and spin 2.

However, this chain of logic is not airtight; you could try to write down, say, a scalar gravitational theory which couples to the trace of stress-energy. It has wrong physical implications though (such as gravity being unaffected by electromagnetic fields, whose stress-energy have vanishing trace).

Point 5 is also related to your crucial Point 7. If you try to write down a relativistic spin-2 theory, it ends up being internally inconsistent if you don’t let the field self-couple. So you can’t write down a simple tensor theory that is directly analogous to the electromagnetic vector theory. The corrections needed to restore consistency are the nonlinearities which inevitably give rise to Einstein’s curved spacetime theory. (This argument goes back to Feynman, Deser, etc.)

2. Scott Says:

Thanks, Ambitwistor!

3. Gen Zhang Says:

Actually, the whole spin-2 graviton thing is a bit ambiguous — we call a graviton a small perturbation about a flat, Minkowski spacetime. It so happens that classically, due to the whole gravity only attracting thing, that the disturbances have a quadrapole symmetry, or that it’s symmetric under rotations by $pi$. Upon quantisation of this perturbation field, we (would) get spin-2 particles (if things weren’t non-renormalisable). However, there are several issues with this picture. The biggest one is that there’s no reason for spacetime to be flat asymptotically — in fact observations suggest otherwise.

Actually, a significant issue is that the analogy between “Kqq/r^2″ and “Gmm/r^2″ is a little misleading. Both are the static limits of field theories, but the limits of things are usually simpler than the actual thing. Even though in the (classical) field theories, there are various formal similarities, the conceptual differences are overwhelming. General relativity has at the base the idea that there is no static background spacetime, so no idea of a global anything — simultaneity, etc. Removing more mathematical structure of spacetime makes things icker.

One last point, even the quantisation of EM isn’t as straightforward as many seem to believe. QED has singularities as the theory tends towards smaller and smaller distances, implying that actually the theory isn’t correct. See http://en.wikipedia.org/wiki/Landau_pole. String theory proposes getting rid of it because the intrinsic size of strings are too large to probe the necessary lengths. Loop quantum gravity proposes a finite discreteness to spacetime, thus removing any notion of distance below a certain limit.

4. Moshe Says:

I always liked Weinberg’s viewpoint, after hearing his explanation in QFT course. To paraphrase, we don’t really know the single most important fact that makes “gravity” what it is. It is often assumed that the equivalence principle is the single most important fact, because it is intuitive and easy to understand and everything else follows from it.
\
Weinberg point out that equally, everything (including the equivalence principle itself) follows from the fact that the graviton is spin 2. So the story is that you go about quantizing fields of any possible spin, and low and behold you find that all possible forces are realized in nature (except spin 0 for now…), and obey all the laws forced on you by self-consistency, including the equivalence principle for gravity.
\
The only drawback of this viewpoint, probably the reason why it is not universally adopted :-), is that the fact that everything follows from quantizing spin 2 field (which then has to be unique, and couple universally to matter etc. etc.) has a long and complicated proof (called the Weinberg thm., not to be confused with the Weinberg-Witten theorem) and is not too intuitive. It would be great to come up with intuition why this is the case, but I have nothing too transparent.

5. Sean Carroll Says:

“Gravity hard to quantize but E&M is not because gravity is spin-2 and E&M is spin-1″ is a pretty good one-line explanation, but it definitely suffers from all of the above problems, such as theory-ladenness and a clunky justification. Another problem: it’s necessarily perturbative, referring to the properties of small fluctuations about a flat spacetime solution; so it’s not really “fundamental.”

If I were to vote for the best one-line explanation, I’d vote for one that is implicit in your point (4). Of course, you *can’t* compare the intrinsic strength of gravity and E&M, because their coupling constants have different units. (In natural units, the fine-structure constant is dimensionless, whereas Newton’s constant has units of 1/(energy)^2.) When we say “gravity is weaker,” we mean “for ordinary particles that we know and love.” In other words, “gravity is weaker” is a restatement of “Standard Model mass scales are much smaller than the Planck scale.” (Although there’s an interesting paper on this by the world’s funniest physics blogger.)

The size of those scales doesn’t affect the difficulty of quantizing gravity, but the fact that the coupling is dimensionful certainly does. That’s the standard-issue explanation for why GR is nonrenormalizable.

6. Dave Pritchard Says:

This may be too technical a point but consider the doofus-explanation
“… if electromagnetism (being linear) is in P and gravity (being nonlinear) is NP-complete, then the strong force is Graph Isomorphism.”
I understand this fine, being a doofus and all. Do most doofi know all these terms from complexity theory? E.g., does
“Electromagnetism is Homer Simpson and gravity is Optimus Prime, while the strong force is basically beer.”
have any merit?

7. Pseudonym Says:

Gravity is “many orders of magnitude weaker” than electromagnetism.

I’ve always thought that this is only an argument that a particle physicist could appreciate. Surely it’s not that gravity is weak, it’s that subatomic particles are light.

8. Moshe Says:

Just one comment about the spin 2 explanation- I don’t see why it is necessarily perturbative, or relies on the existence of unobserved gravitons. Gravity, including all nonlinearities, seems to be a consequence of having spin 2 field. If we quantize this field perturbatively around flat background we get spin 2 particle, the graviton. But that is an independent step, even if it somehow fails it does not invalidate the first step.
\
With regards to the clunkiness, this is in the eye of the beholder. If you find (like myself) QFT to be an extremely beautiful structure, this is a very satisfying entry point- you quantize all possible fields and simply follow the consequences of fundamental principles like unitarity and Lorentz invariance. In my mind it is remarkable that no further input is required, it is such a minimal explanation it may as well be labeled “fundamental”.

9. DooFus Says:

m is an invariant in QED, the length of the energy momentum 4-vector, so your item (3) is inconsistent with other parts of your discussion.

I don’t really see the point in saying that the m in the non-relativistic expression p = mv needs to be modified when that same modification fails to turn K = p^2/2m into the appropriate relativistic expression. Relativistically invariant quantities are too valuable to discard them so easily in favor of a vague concept like “apparent mass”, but you can be excused if you don’t know that the “apparent mass” of Lorentz has transverse and longitudinal components.

10. Travis Says:

I’ve always thought that this is only an argument that a particle physicist could appreciate. Surely it’s not that gravity is weak, it’s that subatomic particles are light.

I think it’s a more general physicist perspective that gravity is weak rather than electrons light, and not just an opinion confined to particle physics. To put it another way, what’s more “fundamental”: fundamental particles, or fundamental forces?

The (physicist*) answer is that particles are more fundamental (in an epistemological sense), since we observe particles and infer the existence of forces.

* String theorists may argue that forces or perhaps things that are not forces OR particles are more fundamental in an ontological sense; without intending any slight, I exclude them for the purpose of arguing about what the broader physics community believes.

11. Markus Says:

Just as a side remark: I remember, one can geometrize electromagnetism as well, and push it into the underlying space. Instead of a Riemannian space one would end up in a Finsler space. The metric will turn out to be velocity dependent in this case, since the Lorentz force depends on a particles speed.

12. agm Says:

Re point 6:F=ma

This is not the equation you are looking for. Last time I checked, it’s F=dp/dt to get the correct relativistic equation, not to mention correctly quote Newton. More to the point, your bolded caption proposes mass to be in two fundamental physics equations, yet the paragraphs below never discuss the matter. Exactly how does this disparity make any sort of contribution to making a point?

13. agm Says:

Re point 5: This difference is surely crucial; the trouble with it (to use a pomo word) is that it’s too “theory-laden.”

Since when is spin not precisely at the same level of “more basic properties” as mass and charge themselves? Spin current experiments make it plenty clear that spin is as intrinsically important as charge, as opposed to being something less fundamentally important than the other quantities.

14. Joe Fitzsimons Says:

Hi Scott,

I’m surprised that nobody has mentioned it yet, but have you taken a look at Kaluza-Klein theory? Basically it proposes an additional spatial dimension to deal with electromagnetism in the context of general relativity.

I’ve always been curious about the gravity-EM similarities too. Sure charge comes in two varieties, which makes it different from gravity, but we could imagine a universe with only one type of charge. You could certainly propose an equivalence principle for charge and acceleration, in such a system.

As we currently lack a full theory of quantum gravity, there are basically two ways we can compare gravity to EM. The first is at a large scale, where we compare mass to charge in general relativity, and the second is at a small scale where we compare gravitons and photons, etc. It seems to me that it is dangerous to rule out symmetries between the two based on the latter approach, as it seems quite possible that our final theory of quantum gravity will contain some surprising results.

15. Ambitwistor Says:

Actually, the real difference between EM and gravity is not that there are two signs of charge but only one sign of mass — you could postulate “negative mass” (and people have). The real difference is that in EM like charges repel, but in gravity like charges attract. This too goes back to spin 1 vs. 2. You can imagine a universe with only positive charges, but if you want them to attract, you have to consider something like general relativity.

16. Ambitwistor Says:

Joe,

Despite discussion of “gravitons” in this thread, most of the arguments here have nothing to do with quantum gravity. Most of these “spin 2″ arguments, from which the graviton idea originates, go through in classical field theory. Moshe made this point earlier.

17. Dave Bacon Says:

“Why should one be inextricably linked to the geometry of spacetime, whereas the other seems more like an add-on?”

Because Wheeler was never able to get his wormhole throats actings charges idea to work?

18. James Graber Says:

I have to object to one point in Gen Zhang’s comment no3: the statement that “The biggest one is that there’s no reason for spacetime to be flat asymptotically — in fact observations suggest otherwise.”
I agree that there is no known reason that spacetime be asymptotically flat, –except the argument that Gen just gave, that it is necessary to quantize gravity, and the other fact that it is necessary to define a localized mass in GR.
But what I really object to is the statement that observations suggest spacetime is not asymptotically flat. I know inflation is supposed to explain this away, and I know that this is very much a minority position, but if the observations support anything, they support an asymptotically flat universe, confounding expectations that go all the way back to 1919 if not 1915.

19. Greg Kuperberg Says:

I’m surprised that nobody has mentioned it yet, but have you taken a look at Kaluza-Klein theory?

Right. If you take the Cartesian product of 4-dimensional spacetime with a small circle to get a 5-dimensional spacetime, then there is an extra gravitational force between two particles that have velocity in the circle direction. The behavior of this new gravitational effect is equivalent to electromagnetism; the velocity of a particle in the circle direction manifests itself as electric charge. Moreover, if the particles are quantum mechanical, then this manifested charge is quantized, because the velocity in the circle direction is an integer. You might think that the resulting force is weak at the usual experimental scales, as gravity is; however, by making the circle small, you can make the unit of charge as large as you like.

This beautiful geometric idea works so well that you might suppose that it has the ring of truth. It is not a complete idea of course, because it supposes without explanation the stability of the small circle direction. Even so, it is the best idea that people have for making short-range forces a manifestation of gravity. (Maybe even the only viable idea at present; I’m not sure.)

But, be warned: The Kaluza-Klein construction doesn’t yet predict anything new; it only at best explains things that we can already see. It is therefore the stifling dogma of the oppressor class of high-energy theory.

20. Dent Says:

This beautiful geometric idea works so well that you might suppose that it has the ring of truth,

You mean “small circle of truth”.

21. Jonathan Vos Post Says:

A related simple question is: what are the domains and ranges of q and m?

You brushed against the range issue with observation of quantization, e/3 was a surprise, of course, to those who assumed that e was the quantum of charge. Don’t forget about fractional charge Hall Effect. Is a Planck length a quantum of length? The length of a loop in Quantum Loop Gravity?

But back to domain. You seem to have implicitly assumed that both q and m are real numbers, Then you appear surprised that m seems to be restricted to the nonnegative subdomain.

But where do you get the implicit axiom that q and m are real?

That strangeness was associated with “hypercharge” hinted that some Physicists were looking for a complex number as charge.

Why should q and/or m not be pure imaginary? Complex? Quaternions? Octonions? Matrices? Something else? There are papers in the literature on each of these, and more.

If you accept F = ma without being careful about domain, then what does a mass of i = sqrt(-1) do when acted on by a real force F. It has to be accelerated along a vector whose magnitude is also imaginary. But in what direction does it move? It can’t be parallel to x, y, z, or t. That leads to speculations such as Kaluza-Klein, and brane theory.

My own simple-minded speculation is outlined in, for instance, the following paper (the long version has many citations on the quaternion and octonion possibilities, and there is a companion paper making experimental predeictions, and looking at a paper by Peter Lynds):

IMAGINARY MASS, FORCE, ACCELERATION, AND MOMENTUM: PHYSICAL OR NONPHYSICAL?

Draft 6.0-Short [for ICCS 2004] of 27 April 2004 [8-page version + 3 pp. Bibliography]

by

Jonathan Vos Post, Andrew Carmichael Post, Christine M. Carmichael

ABSTRACT:

This paper analyzes a possible emergent behavior of subatomic and astrophysical systems, which involves Complexity at four levels: (1) dynamic implications of assigning a Complex value to variables which, by tradition, were assumed real; (2) analysis of the related literature in Newtonian, Quantum Mechanical, Relativistic, and String Theory contexts, which have a social and conceptual complexity from their mutually different assumption; (3) the possibility of pattern formation shortly after the Big Bang, in high-energy events today, and in hypothetical dimensions beyond 4-D space-time; and (4) practical complexity in performing experimental tests of these hypotheses. This paper constitutes a preliminary discussion of a foundational question. Are imaginary mass, imaginary acceleration, imaginary force, and imaginary momentum under any conditions ever “Physical” (i.e. in principal observable by direct or indirect means) or “nonphysical” (i.e. theoretically amenable to calculation, but inherently unobservable in the real world)? The discussion begins by hypothesizing a particle or object of positive imaginary mass in a co-moving frame of reference, and considers some logical consequences. One unusual interpretation is that imaginary mass allows for objects to “disappear” from our ordinary space-time and “leave the brane” to go somewhere perpendicular to ordinary reality. The predictions in this paper are “far out” – even Science Fictional, yet they do not obviously violate Quantum Mechanics, Special Relativity, or General Relativity. They are in the broad context of the scientific literature. They may have both microphysical and macrophysical observability in the laboratory or cosmologically. We review the related literature on mass, in Quantum Mechanics and Special Relativity; return to a pseudo-Newtonian analysis; and then approach the complexity of modern theory and speculation.

22. Zoss Says:

I have a question about point (1)
(1) Charge can be negative whereas mass can’t.
That’s why gravity is always attractive, whereas …

I could understand that mass being always of the same sign would imply that gravity is always either attractive or repulsive, but why pick attractive is a different argument, innit?

Along the same lines, perhaps one could say that another difference between charge and mass is that like charges repulse while like masses attract. That is to say, the signs of them constants in the equations you mentioned are curiously opposite.

23. Jonathan Vos Post Says:

A lovely analysis hit the arXiv today, which may help connect different clumps of publications germane to your question:

http://arxiv.org/pdf/0707.2869
(cross-list from math-ph)
Title: Clifford Algebras and Possible Kinematics
Authors: Alan McRae
Comments: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at this http URL
Journal-ref: SIGMA 3 (2007), 079, 29 pages
Subjects: Mathematical Physics (math-ph)

We review Bacry and Levy-Leblond’s work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all but one of the kinematical groups. We then construct a two-parameter family of Clifford algebras that give a unified framework for representing both the Lie algebras as well as the kinematical groups, showing that these groups are true rotation groups. In addition we give conformal models for these spacetimes.

24. Coin Says:

I have some doofusy questions.

Charge appears to be quantized (coming in units of 1/3 of an electron charge), whereas mass appears not to be quantized, at least not in units we know.

This is something I wonder about. Does there really appear to be a continuous scale of possible masses? Is there no fundamental lower bound on the resolution with which we can measure something’s mass?

Gravity is transmitted by a spin-2 particle, whereas electromagnetism is transmitted by a spin-1 particle. … the gravitational force is mediated by gravitons

I’m confused here. My first response to these statements (statements that the gravitational force is mediated by spin-2 particles called gravitons) is, how do you know? What if gravity isn’t quantum? We always assume it is, but I’ve never seen an explanation for why we would think gravity is quantum except that it would be really weird if it wasn’t but everything else was. Meanwhile, didn’t you just say above that “mass appears not to be quantized, at least not in units we know”? It seems like there’s a contradiction somewhere here.

It would intuitively seem to me that if the gravitational force is mediated by particles, then it follows from that that gravity is quantized, and if gravity is quantized, then it follows from that that mass is quantized. Where is the flaw in this intuition?

(1) Are “gravity is mediated by spin 2 particles” and “gravity is quantum” not the same statement?*

(2) Is it possible that the force of gravity is quantized, but mass (the “charge” driving the gravitational force) is not? How the heck would that work?

(3) Just to make sure I’m not overlooking something completely fundamental– is there any difference whatsoever between saying “it is quantum” and saying “it is quantized”?

* (There are some statements made in this thread which I don’t quite understand, about gravitons just being “perturbations” in a field, and the statement is made that this field could be classical. What would I need to do to understand what this would mean?)

25. archgoon Says:

Coin:

Gravity has to be quantum because the gravitational field depends on the positions of the masses of objects, but we know from quantum that those ‘things’ don’t have positions.

26. Steve Demuth Says:

Gravity has to be quantum because the gravitational field depends on the positions of the masses of objects, but we know from quantum that those ‘things’ don’t have positions.

I think this overstates what we “know” from quantum theory. Non-local quantum theories, such as Bohm’s, preserve the notion of definite position by using hidden variables and discarding locality. As I understand the literature, there are at least credible attempts to extend this to QFT.

So long as a non-local, property-definite theory gives comparably accurate results to local, property-indefinite QFT, I don’t see how one can discard scientifically the possibility that gravity is non-quantum, and that the matter/energy density defines with zero error the background manifold on which the other forces play out, via the rules of QM/QFT.

Intellectually, of course, non-locality and hidden variable theories are not very statisfying. But then neither are the inaccessibility of the wave function except via measurement and collapse in QM, the the need for perturbative approximations to solve QFT, nor the absence of a respectably testable quantum theory of gravity.

Coin:

is there any difference whatsoever between saying “it is quantum” and saying “it is quantized”?

IIRC we had this discussion on QM at Good Math, Bad Math where we concluded that “modern” QM as opposed to Planck’s combines discrete (“quantized” or “coming in units”, in Scott’s terminology) and continuous states. “Quantized” is a sign that something is “quantum”. (Which we assume for good reasons, but don’t know, that gravity is.)

28. Coin Says:

Torbjörn, we did, and I did remember you trying to explain that to me, I guess I was just still a bit confused. I’m sorry Thanks though.

Coin, the problem with getting into science (whether layman or professional) is that the state of confusion will only deepen. First you don’t know what you don’t know. Then you do know what you don’t know.

30. archgoon Says:

Steve, I was under the impression that Bohm’s theory was equivalent to standard QM. Using his terminology, ‘quantizing’ gravity means incorporating the non-local hidden variables into GR. Would that be correct?

31. Steve Demuth Says:

Archgoon: Bohm’s theory is equivalent to standard QM. So, yes, I guess quantizing gravity a la Bohm would mean introducing the non-locality into gravity. That seems contradictory to the requirements of GR. But then, that’s not a problem, since as far as I know, no one knows how to quantize gravity. Which is really my point: it’s not impossible that gravity is not a quantum force, but rather something that creates a space, time and matter landscape from their mutual interactions, against which the 3 remaining forces play out according to QM and QFT.

32. Jonathan Vos Post Says:

I’m not sure that this is the right thread for the following posting, except that Minkowski space is 4-dimensional.

Firest, the Twilight Zone citation, then the Simpson’s parody.

Homer Simpson’s Treehouse of Terror (3), which we all recognize as a clever parody of:
The Twilight Zone, Episode 91, “Little Girl Lost” which was my favorite episode.

Opening Narration —
Narrator: “Missing: one frightened little girl. Name: Bettina Miller. Description: six years of age, average height and build, light brown hair, quite pretty. Last seen being tucked into bed by her mother a few hours ago. Last heard–aye, there’s the rub, as Hamlet put it. For Bettina Miller can be heard quite clearly, despite the rather curious fact that she can’t be seen at all. Present location? Let’s say for the moment–in the Twilight Zone.”

Writer: Richard Matheson,
Director: Paul Stewart,
Star: Rod Serling (Narrator/Host),
Guest Star: Charles Aidman (Bill), Robert Sampson (Chris Miller), Sarah Marshall (Ruth Miller), Tracy Stratford (Tina), Rhoda Williams (Tina’s Voice)

This is the second of Charles Aidman’s two appearances in the original Twilight Zone. Mr. Aidman later went on to narrate the first two seasons of the 80’s version of the series.
The music was so important to this episode that the writer of the score was credited above the director (the only episode to do so)

This episode was likely the inspiration for the 1982 film “Poltergeist.”

This episode is based on the short story “Little Girl Lost” by Richard Matheson. The story was first published in Amazing Stories (November 1953).

Chris: What is it?
Bill: The opening.
Ruth: To what?
Bill: I think… to another dimension.

Closing Narration —
Narrator: “The other half where? The fourth dimension? The fifth? Perhaps. They never found the answer. Despite a battery of research physicists equipped with every device known to man, electronic and otherwise, no result was ever achieved, except perhaps a little more respect for and uncertainty about the mechanisms of the Twilight Zone.”

During the opening narration, the wall behind Rod Serling has the “fourth dimension” boundary lines drawn on it already.

And now (in anticipation of seeing the Simpsons feature film) —

Hibbert: Homer, this is your physician, Dr. Julius Hibbert. Can you tell us what it’s like in there?

Homer: Uh…it’s like…did anyone see the movie “Tron”?
Hibbert: No.
Lisa: No.
Marge: No.
Wiggum: No.
Bart: No.
Patty: No.
Wiggum: No.
Ned: No.
Selma: No.
Frink: No.
Lovejoy: No.
Wiggum: Yes. I mean — um, I mean, no. No, heh.

Professor Frink draws a strange diagram on the wall.

Frink: Well, it should be obvious to even the most dim-witted individual who holds an advanced degree in hyperbolic topology, n’geh, that Homer Simpson has stumbled into…[the lights go off] the third dimension!

Lisa: [turning the lights back on] Sorry.

Frink: [drawing on a blackboard] Here is an ordinary square —

Wiggum: Whoa, whoa — slow down, egghead!

Frink: — but suppose we extend the square beyond the two dimensions of our universe (along the hypothetical Z axis, there).

Everyone: [gasps]

Frink: This forms a three-dimensional object known as a “cube”, or a “Frinkahedron” in honor of its discoverer, n’hey, n’hey.

Homer: [disembodied] Help me! Are you helping me, or are you going on and on?

Frink: Oh, right. And, of course, within, we find the doomed individual.

Wiggum: Enough of your borax, poindexter! We need action —
[fires his gun six times through the wall]
Take that, you lousy dimension!
[the bullets fly toward Homer, but spiral around the widening
hole and get sucked into it]

Homer: Oh, there’s so much I don’t know about astrophysics. I wish I’d read that book by that wheelchair guy.

33. anonymous Says:

Jonathan Vos Post, I think you need to get your own blog.

34. Coin Says:

I kind of think of Jonathan Vos Post as having a “floating” blog that lives in the comments sections of other, randomly selected blogs.

35. Jonathan Vos Post Says:

Anonymous and Coin,

(1) Assume that I exist. Some bloggers assume the contrary. Google “Greatest nerd of all times” and see skeptics in the comments to the original and dig-ed blog. My wife and son are amused that I am hypothesized to be a virgin.