Do Hidden Variables include sub-structures?

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TL;DR Summary

Bell's Theorem rules out any hidden variables but does it rule out some finer structure to quantum particles?

Summary: Bell's Theorem rules out any hidden variables but does it rule out some finer structure to quantum particles?

At larger scales of the universe, we would see entanglement as cloning. For example, two human clones have the same color eyes because their DNA is identical. I've been reading some on entanglement and wondered if Bell's theorem rules out a finer structure as a hidden variable?

 

[Nugatory]

Yes, any theory that says there is some finer structure that, if understood, would allow us to calculate the results of quantum mechanical observation is pretty much by definition a hidden variable theory.
If you are going to use the eye color analogy... Mendelian genetics itself is a hidden variable theory; the hidden variables are the chromosomes and DNA. The point of Bell’s theorem is that no future discoveries will explain quantum mechanics the way the discovery of chromosomes and DNA explain why eye colors come out the way they do.

Do note that Bell’s theorem does not rule out all hidden variable theories. It rules out a particular type of hidden variable theories, the ones that are casually described as “local realistic” and more precisely described by the assumptions that go into the proof of the theorem. These include pretty much anything that we’d accept as a non-weird explanation of quantum weirdness.

 

[Demystifier]

Summary: Bell's Theorem rules out any hidden variables but does it rule out some finer structure to quantum particles?

First, Bell's Theorem does not rule out any hidden variables. It only rules out local hidden variables. Second, it definitely does not rule out finer structure. For instance, Bell's theorem applied to a proton does not rule out the quark fine structure of the proton.

 

[Elias1960]

I like to object against the "local" hidden variables excluded. What has been excluded is appropriately named "Einstein-local" or "Einstein-causal".

How would you name a theory so that all objects have localization in space, there is also a maximal speed, but one much higher than c? This would be an obviously local theory. But in that naming convention, it would have to be named "nonlocal".

Then, some substructures of objects, say quarks inside protons, would be covered by Bell's theorem as well. One cannot circumvent Bell's theorem by inventing further substructures of the quarks. Such substructures would be some well-defined ontology too, one could describe them with some $\lambda \in \Lambda$.

 

[vanhees71]

Well, if the limiting speed would be much larger than $c$ this would simply mean that light is not described by massless (quantum) fields but by massive ones, and we'd call that limiting speed not "speed of light" but somehow else.

 

[DarMM]

How would you name a theory so that all objects have localization in space, there is also a maximal speed, but one much higher than c?

Bell's theorem also rules that out. In nonlocal theories the signalling has to be instantaneous.

 

[Elias1960]

Bell's theorem also rules that out. In nonlocal theories the signalling has to be instantaneous.

Not really. All one can conclude from Bell's theorem is that the predictions of such a theory cannot be exactly the same as those of QM.

But exact equivalence to QM is not a Holy Grail. What made Bell's theorem interesting is that it allowed to falsify empirically all Einstein-causal realistic theories. Because all that was necessary was to prove that the maximal speed of information transfer has to be higher than c.

But there is clearly no base for hope that one can empirically falsify all local realistic theories. t sufficient to empirically falsify such theories. All one can hope for are results like the maximal speed of information transfer has to be larger than, say, $10^4 c$ (as already obtained) or $10^{400} c$ (which will be unreachable). So, such theories are not ruled out at all.

 

[DarMM]

Well if we're admitting that QM might be wrong, then yes such theories are not ruled out.

 

[Elias1960]

Well, if the limiting speed would be much larger than $c$ this would simply mean that light is not described by massless (quantum) fields but by massive ones, and we'd call that limiting speed not "speed of light" but somehow else.

Not plausible. If light would be massive, we would observe it having very different speeds depending on the momentum. Except if all the light we can observe has already such a high momentum in comparison with its mass that the velocity would be, even if lower than $c$, practically indistinguishable from c. And this could be the case only if $c$ remains almost $c$ and the mass is very small.

A theory with a much larger limiting speed would not necessarily be a relativistic field theory. Even if this would be quite plausible that there would be also some Lorentz group playing a role, given that the Lorentz group is the symmetry group of essentially every wave equation.

But the SM fields and gravity would remain to follow the Einstein equations, with good old c as the limiting speed. The higher speeds would be some other, quantum, effects. And if that higher speed Lorentz group would play a fundamental role would be unclear. It would not necessarily be universal and without universality no fundamental Lorentz symmetry.

 

[vanhees71]

Exactly that's what I'm saying. The assumption of a much larger limiting speed than the speed of light is speculative, given the evidence for photons being precisely massless. Of course the experimental "proof" is only a very small upper bound for a putative photon mass, which is (according to the PDB 2018: $m_{\gamma}<1 \cdot 10^{-18} \; \text{eV}/c^2$). Thus to claim that there might be a much large "limiting speed" of relativity is overly speculative (to put it friendly ;-)). There's not the slightest evidence whatsoever for such speculative "alternate theories".

 

[Elias1960]

Exactly that's what I'm saying. The assumption of a much larger limiting speed than the speed of light is speculative, given the evidence for photons being precisely massless.
There's not the slightest evidence whatsoever for such speculative "alternate theories".

Sorry, but the massless photons give you nothing in this regard.

A simple example would be some transparent condensed matter where the sound is described by a simple wave equation. Then, the corresponding phonons would be massless. But light would have nonetheless a much larger velocity that these phonons.

And "not the slightest evidence", seriously? More serious evidence that violations of the Bell inequality are not necessary at all. You have to reject realism as well as causality. But if you do this, and seriously (not only in the single case of Bell inequality violations) no empirical evidence will be ever able to prove anything.

 

[Demystifier]

Exactly that's what I'm saying. The assumption of a much larger limiting speed than the speed of light is speculative, given the evidence for photons being precisely massless. Of course the experimental "proof" is only a very small upper bound for a putative photon mass, which is (according to the PDB 2018: $m_{\gamma}<1 \cdot 10^{-18} \; \text{eV}/c^2$). Thus to claim that there might be a much large "limiting speed" of relativity is overly speculative (to put it friendly ;-)). There's not the slightest evidence whatsoever for such speculative "alternate theories".

That's indeed speculative, but the opposite claim is speculative too. Claiming that relativity theory is valid at all circumstances, including those that are far from the circumstances in currently existing experiments, is speculative too. Is relativity valid at the Planck distance? If one says no, it's speculative. If one says yes, that's speculative too.

 

[martinbn]

That's indeed speculative, but the opposite claim is speculative too. Claiming that relativity theory is valid at all circumstances, including those that are far from the circumstances in currently existing experiments, is speculative too. Is relativity valid at the Planck distance? If one says no, it's speculative. If one says yes, that's speculative too.

To me there is a big difference. Relativity theory is a concrete and specific theory that allows you to solve problems, and has been tested quite extensively. Saying may be it isn't fundamental, or may be it doesn't hold at all scales etc. is, in my opinion, a lot more speculative. In fact it is pointless, because it is just wishfull thinking. It is not enough to say may be it isn't so. You need to at least give enough detail to be able to actually do something with it. Otherwise it is in the same catogory as Russel's teapot.

 

[Elias1960]

To me there is a big difference. Relativity theory is a concrete and specific theory that allows you to solve problems, and has been tested quite extensively. Saying may be it isn't fundamental, or may be it doesn't hold at all scales etc. is, in my opinion, a lot more speculative. In fact it is pointless, because it is just wishfull thinking. It is not enough to say may be it isn't so. You need to at least give enough detail to be able to actually do something with it. Otherwise it is in the same catogory as Russel's teapot.

Sorry, but we know that GR as it is is wrong, because it is not a quantum theory. The straightforward use of standard field-theoretic methods gives an effective field theory on a fixed flat background, but this effective field theory is not renormalizable, thus, fails below a critical length. For this critical length we have a well-motivated guess, Planck length.

So there is no "maybe" about GR being not fundamental, it is known not to hold on all scales. And the wishful thinking for a background-independent quantum theory of gravity is on the other side. (In comparison, as a background-dependent QG every more or less plausible regularization of the field theory gives a well-defined candidate.)

 

[PeterDonis]

we know that GR as it is is wrong, because it is not a quantum theory

This assumes that every fundamental theory must be a quantum theory. But that claim itself is also speculative. Most physicists seem to believe it, but that's not the same as actually having evidence for it. (At least one physicist, Freeman Dyson, has IIRC argued that it's possible that there is no quantum theory of gravity, and GR is the most fundamental theory of gravity there is.)

there is no "maybe" about GR being not fundamental, it is known not to hold on all scales

"Known" is much too strong here. We have no evidence that GR fails on any scale. We only have various theoretical arguments that most physicists believe are valid, but which have not been tested (and can't be tested unless and until we figure out how to probe distance scales 20 orders of magnitude smaller than the ones we can probe now).

 

[DarMM]

Also in general it becomes impossible to say anything if every statement about QM has to be appended with 40,000 clauses to prevent "But, but, but what if relativity is wrong, what if QM is wrong, what if spacetime is only the shell of a giant turtle"

 

[Nugatory]

Also in general it becomes impossible to say anything if every statement about QM has to be appended with 40,000 clauses to prevent "But, but, but what if relativity is wrong, what if QM is wrong, what if spacetime is only the shell of a giant turtle"

Yes indeed, and that’s one reason we have the words “as it is currently generally understood and practiced by the professional scientific community” in the mission statement. There’s quite enough complexity just in the mainstream discussion of issues raised in the first post of this thread.

 

[Elias1960]

This assumes that every fundamental theory must be a quantum theory. ... (At least one physicist, Freeman Dyson, has IIRC argued that it's possible that there is no quantum theory of gravity, and GR is the most fundamental theory of gravity there is.)

Ok, let's reformulate: We know that GR, in its current form, is wrong because it is unable to describe quantum effects.

"Known" is much too strong here. We have no evidence that GR fails on any scale. We only have various theoretical arguments that most physicists believe are valid, but which have not been tested (and can't be tested unless and until we figure out how to probe distance scales 20 orders of magnitude smaller than the ones we can probe now).

I agree, but theoretical arguments are not completely worthless. And some aspects of theoretical arguments (in particular, conflicts between theoretical principles) do not depend on empirical support.

Also in general it becomes impossible to say anything if every statement about QM has to be appended with 40,000 clauses to prevent "But, but, but what if relativity is wrong, what if QM is wrong, what if spacetime is only the shell of a giant turtle"

But there is no need to append such things every time. Here, the subdiscussion started with the question that "local" should be named "Einstein-local", given that there are obviously local theories with maximal speed higher than c and to use a convention that forces one to name such theories "non-local" would be Orwellian. And theories different from QM are the very question considered in Bell's theorem too. So, given this context of the discussion, considering these questions here seems justified.

 

[PeterDonis]

We know that GR, in its current form, is wrong because it is unable to describe quantum effects.

That doesn't mean it's wrong, just that it's incomplete. So is our best quantum theory to date, the Standard Model, since it doesn't include gravity. We don't have any complete theory at this point.

theoretical arguments are not completely worthless

That may be true, but having a theoretical argument and nothing else is not the same as knowledge, and my objection was to your use of the word "known".

some aspects of theoretical arguments (in particular, conflicts between theoretical principles) do not depend on empirical support

They do if you want to actually resolve them. Otherwise you just have conflicting theoretical arguments and no evidence either way.

 

[vanhees71]

Sorry, but the massless photons give you nothing in this regard.

A simple example would be some transparent condensed matter where the sound is described by a simple wave equation. Then, the corresponding phonons would be massless. But light would have nonetheless a much larger velocity that these phonons.

And "not the slightest evidence", seriously? More serious evidence that violations of the Bell inequality are not necessary at all. You have to reject realism as well as causality. But if you do this, and seriously (not only in the single case of Bell inequality violations) no empirical evidence will be ever able to prove anything.

You have to decide what you claim.

(a) The standard physics (which is very well empirically established)

Photons are massless. The electromagnetic interaction propagates with the limiting speed, usually thus called "the speed of light"

(b) Your personal hypothesis (not in any way established empirically and thus fictitious)

Photons are not massless. The electromagnetic interaction does not propagate with the limiting speed, and thus the limiting velocity is some other larger value than "the speed of light in vacuum".

You cannot have both massless photons and a limiting speed greater than the speed of light.

The violation of Bell's inequality does not contradict this since it has nothing to do with faster-than-light causal influences whatsoever. Relativistic local QFT is the framework upon which the Standard Model is constructed, which is in accord with case (a) and nothing else.

If you want to claim otherwise you have to open another thread in the new "foundations" subforum!

 

[Elias1960]

You cannot have both massless photons and a limiting speed greater than the speed of light.

I can, and I have already given you an example.

Some sufficiently rigid condensed matter, with a wave equation $\square u = 0$ as the equation for sound waves. The phonons of the corresponding quantum condensed matter theory will be massless and have the speed of sound. Nonetheless, there are other things (like light) in this theory that have a much larger speed. So, the speed of sound is not the limiting speed of information transfer.

If you want to claim otherwise you have to open another thread in the new "foundations" subforum!

My original point was about how to name a class of theories that quite obviously can exist. Those theories are local, in any reasonable meaning of local, but they would have to be named nonlocal if one incorrectly abbreviates "Einstein-local" as "local". Your claim that such theories cannot exist is obviously wrong, and my counterexample to your claim is standard condensed matter theory, where you can have massless phonons despite the speed of sound not being the speed limit for information transfer.

 

[vanhees71]

Sound waves have a much lower propagation speed, the speed of sound. Phonons are not massless. I don't know, what you want to prove with this argument.

 

[Elias1960]

Sound waves have a much lower propagation speed, the speed of sound.

Which is the point of the analogy. If there would be a much larger maximal speed of information transfer than c, the speed of light would be an analogon of what is the speed of sound.

Phonons are not massless. I don't know, what you want to prove with this argument.

To quote Wiki-level information:

The speed of propagation of an acoustic phonon, which is also the speed of sound in the lattice, is given by the slope of the acoustic dispersion relation, ∂ωk/∂k (see group velocity.) At low values of k (i.e. long wavelengths), the dispersion relation is almost linear, and the speed of sound is approximately ωa, independent of the phonon frequency.

Thus, in the long-distance limit the acoustic phonons are massless.

The analogy is quite complete, we have a maximal speed of information transfer much larger than the speed of sound, but nonetheless, the acoustic phonons have a speed independent of their frequency as if they were massless particles. What is possible for sound, will be possible for light too, thus, it is not impossible that there is a maximal speed of information transfer much larger than the speed of light, and that the speed of light does not depend on its frequency is not a valid counterargument. So, your argument is invalid.

Here for reference your claims which I reject:

if the limiting speed would be much larger than c this would simply mean that light is not described by massless (quantum) fields but by massive ones
...
You cannot have both massless photons and a limiting speed greater than the speed of light.

 

[Demystifier]

Phonons are not massless.

Yes they are. In the long distance (low energy) limit they obey the dispersion relation
$$\omega^2=c_s^2{\bf k}^2$$
where $c_s$ is the speed of sound. For comparison, photons obey the dispersion relation
$$\omega^2=c^2{\bf k}^2$$
where $c$ is the speed of light.

 

[vanhees71]

If you'd interpret this as "massless", then you'd have tons of "limiting speeds", which is obviously utter nonsense. There's one limiting speed, and that's the speed of light in a vacuum. The speed of a phonon is $c_s<c$ and thus the phonon is not massless.

 

[Demystifier]

If you'd interpret this as "massless", then you'd have tons of "limiting speeds", which is obviously utter nonsense.

Well, we have many limiting speeds in EU. The limiting speed on German highways is much larger than in the rest of EU. Do you think it's utter nonsense?

Now seriously, the point is that there is no logical contradiction in a possibility that there are different limiting speeds for different objects in different conditions.

There's one limiting speed, and that's the speed of light in a vacuum.

That is indeed so in the Standard Model. But since the Standard Model is just an effective theory, it may not be so at some more fundamental level. Now you will say that there is no any direct experimental evidence for that, but there is at least an indirect one. The experimental violation of Bell inequalities is an indirect evidence that there may exist some influences traveling with an infinite speed. Yes, it's just a hint, an indirect evidence, but it's evidence nonetheless.

The speed of a phonon is $c_s<c$ and thus the phonon is not massless.

So what's the phonon's mass then?

 

[vanhees71]

Let's first get clear what I'm saying: There's one limiting speed in the sense of relativity theory, and that's the speed of light in a vacuum and nothing else.

Phonons are quasiparticles in a medium. That they have formally 0 mass does not mean that there are more then one "limiting speeds" in the sense of relativity.

 

[martinbn]

Now seriously, the point is that there is no logical contradiction in a possibility that there are different limiting speeds for different objects in different conditions.

But if you need an infinite speed of propagation you will run into a problem with relativity that you cannot sweep under the rug "may be relativity isn't exact at other scales". It will be in conflict with tested corollaries.

 

[Demystifier]

Let's first get clear what I'm saying: There's one limiting speed in the sense of relativity theory, and that's the speed of light in a vacuum and nothing else.

Phonons are quasiparticles in a medium. That they have formally 0 mass does not mean that there are more then one "limiting speeds" in the sense of relativity.

I think nobody here doubts that.

 

[Demystifier]

But if you need an infinite speed of propagation you will run into a problem with relativity that you cannot sweep under the rug "may be relativity isn't exact at other scales". It will be in conflict with tested corollaries.

What "tested corollaries" do you have in mind?

 

[vanhees71]

I think nobody here doubts that.

No, there was the claim that there may be another much larger limiting speed than the speed of light in the sense of relativity. That's of course utter nonsense!

 

[Demystifier]

No, there was the claim that there may be another much larger limiting speed than the speed of light in the sense of relativity. That's of course utter nonsense!

I think you misunderstood the claim. It was meant in a sense of generalized relativity. See e.g. my "Bohmian mechanics for instrumentalists", Sec. 5.3.

 

[PeterDonis]

there is no logical contradiction in a possibility that there are different limiting speeds for different objects in different conditions

There might be in the presence of additional premises.

In the context of relativity, isn't there a theorem that there can be at most one finite limiting speed? In other words, that given the principle of relativity, the only two possibilities are Galilean spacetime (no finite limiting speed) and Lorentzian spacetime (one finite limiting speed)?

 

[Elias1960]

[Moderator's note: Rule violation content deleted.]

In the context of relativity, isn't there a theorem that there can be at most one finite limiting speed?

In a discussion about hidden variable theories for quantum theory, the context is not that of relativity.

And you certainly have to make assumptions about the fundamental character of relativistic symmetry. They are necessarily metaphysical, which means, they cannot be supported by observation alone. Else, we have the equations for sound waves, which may be (say, for low-frequency acoustic phonons) $\square u = (\frac{1}{c_{sound}^2}\partial_t^2 - \Delta) u = 0$. This equation, and, therefore, some part of the equations describing this universe, has, then, "relativistic" symmetry with $c_{sound}$ instead of c as the speed used in the Lorentz transformation.

[Moderator's note: Rule violating content deleted.]

 

[PeterDonis]

All you have to do is to go back to the Lorentz ether

This is out of bounds for PF discussion. Please do not mention it again or you will receive a warning.