Bohmian mechanics and special relativity

[kurt101]

[Moderator's note: Thread spun off from previous thread due to topic change.]

Good luck but as soon as you posit that there are nonlocal effects and real waves, you run into problems with relativity.
If it weren't for this, nearly everyone would have been onboard with you and BM would have been standard quantum curriculum(it isn't).

Thanks! I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.

 

[PeterDonis]

I am working on understanding why non-local effects violate the special theory of relativity.

They don't as long as you're careful about what you take "non-local effects" to mean. Quantum field theory is consistent with special relativity and predicts violations of the Bell inequalities, which is what "non-local effects" means experimentally. So violations of the Bell inequalities are perfectly consistent with special relativity.

 

[Demystifier]

If the Bohmian interpretation is simply that at some level a particle of sorts is guided by a wave of sorts then the Bohmian interpretation is an interpretation I subscribe to.

Yes, that's what Bohmian interpretation is.

I will try reading your paper, but I suspect it won't provide any additional explanation over Quantum Mechanics as to what is actually happening.

Why do you think so?

 

[Demystifier]

I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.

BM seems incompatible with fundamental relativity, but is compatible with emergent relativity.

 

[kurt101]

Why do you think so?

The discussions on this forum and my initial skim of your paper gave me that impression. However reading it again, has me very interested. I look forward to learning more about it.

BM seems incompatible with fundamental relativity, but is compatible with emergent relativity.

Is there a good link or paper that explains emergent relativity?

 

[EPR]

[Moderator's note: Thread spun off from previous thread due to topic change.]Thanks! I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.

As someone suggested earlier, you need to study the basics and get a good grasp of the notions. At some point you'll notice that most of the 'mysteries' arise not out what and how the fundamental particles are, but from their 'motion'. You'll notice the different approaches to amend the paradoxes, the subtleties, the arguments and the controversies and why some of them remain as deep as ever. But you need a better grasp of what is happening. You can't just jump start from the middle and make up an interpretation.

 

[A. Neumaier]

Is there a good link or paper that explains emergent relativity?

For a discussion of potentials and problems of this approach (including references) see the threads Is QED nonrelativistic? and Lattice QED, and posts #73 and the subsequent discussion from the thread How to derive Born's rule for arbitrary observables from Bohmian mechanics?

 

[martinbn]

BM seems incompatible with fundamental relativity, but is compatible with emergent relativity.

What is emergent relativity!?

 

[Demystifier]

Is there a good link or paper that explains emergent relativity?

What is emergent relativity!?

Loosely speaking, emergent relativity is any theory in which relativistic laws are approximately valid at large distances but not at small distances. Some ideas in that direction can be found in my "Bohmian mechanics for instrumentalists" (linked in my signature below) and references therein.

 

[martinbn]

Loosely speaking, emergent relativity is any theory in which relativistic laws are approximately valid at large distances but not at small distances. Some ideas in that direction can be found in my "Bohmian mechanics for instrumentalists" (linked in my signature below) and references therein.

What about space-time? What is it in such an emergent relativity? It seems that you want space-time to be the one from classical/nonrelativistic physics but somehow to appear to be the one from relativity. Is that even possible?

 

[A. Neumaier]

What about space-time? What is it in such an emergent relativity? It seems that you want space-time to be the one from classical/nonrelativistic physics but somehow to appear to be the one from relativity. Is that even possible?

It might be possible in principle, but so far no one came up with something reproducing QED, let alone the standard model. In view of the nontrivial ''triviality'' issues of lattice approximations it is extremely unlikely that someone ever will. See the discussions referred to in post #7.

 

[Demystifier]

In view of the nontrivial ''triviality'' issues of lattice approximations it is extremely unlikely that someone ever will.

The triviality issue is a problem if one insists on having a well defined continuum limit. But if the fundamental (as yet unknown) theory is not a continuum field theory, then I don't see any reason to insist on having a well defined continuum limit. This is like insisting that the atomic theory should be well defined in the limit in which the Bohr radius is zero because the continuum fluid mechanics corresponds to the limit in which the size of atoms is zero.

 

[Demystifier]

What about space-time? What is it in such an emergent relativity? It seems that you want space-time to be the one from classical/nonrelativistic physics but somehow to appear to be the one from relativity. Is that even possible?

It's possible. The most suggestive evidence is the fact that from a nonrelativistic theory of atoms one can derive an approximative Lorentz invariant wave equation of sound.

 

[martinbn]

It's possible. The most suggestive evidence is the fact that from a nonrelativistic theory of atoms one can derive an approximative Lorentz invariant wave equation of sound.

That is again about properties of matter. I am asking about the properties of space-time. How do you get relativistic(effectively) space-time if fundametally it is classical!

 

[A. Neumaier]

The triviality issue is a problem if one insists on having a well defined continuum limit. But if the fundamental (as yet unknown) theory is not a continuum field theory, then I don't see any reason to insist on having a well defined continuum limit.

QED is defined only in the continuum limit. According to published numerical experiment, triviality of lattice QED sets in already at numerically realizable lattice spacing. Thus the lattice approximates the free theory rather than QED. Decreasing the lattice spacing will not improve this. Thus no lattice approximation will be able to reproduce the highly accurate predictions of the continuum QED.

This is like insisting that the atomic theory should be well defined in the limit in which the Bohr radius is zero because the continuum fluid mechanics corresponds to the limit in which the size of atoms is zero.

No. You cannot even show that a lattice approximation comes anywhere close to reproducing the experimentally verified results of QED.

 

[Demystifier]

According to published numerical experiment, triviality of lattice QED sets in already at numerically realizable lattice spacing. Thus the lattice approximates the free theory rather than QED. Decreasing the lattice spacing will not improve this. Thus no lattice approximation will be able to reproduce the highly accurate predictions of the continuum QED.

Do you have a reference for this claim?

 

[Demystifier]

That is again about properties of matter. I am asking about the properties of space-time. How do you get relativistic(effectively) space-time if fundametally it is classical!

The effective space-time is defined by its effects on matter. In experiments we never measure the space-time itself, we only measure how matter behaves in it. Hence, from an effective point of view, the effect on matter is all what we really need.

 

[A. Neumaier]

Do you have a reference for this claim?

Do you have a reference for the opposite claim?

I repeat some facts from the other threads which amount to almost a proof of my claim:

All formulas of the renormalized, textbook QED, existing since 1948 as witnessed by a Nobel prize given for its discovery, are fully Poincare invariant at every loop order, and make excellent predictions. 1-loop Lorentz invariant QED is fully (and higher loop QED conceptually) constructed without any cutoff or regularization or lattices in Scharf's book on quantum electrodynamics. There is no divergence in any of the Lorentz invariant 1-loop results provided by Scharf, and these give already much better agreement with experiment than lattice QED. 1-loop QED is the version of QED (though with a different derivation) for which Feynman, Tomonaga and Schwinger got the Nobel prize! That each term is finite is enough to claim local Poincare invariance which is the actual mathematical claim of Poincare invariance in perturbative QED, the one that gives outstanding predictions. One gets the 10-decimal agreement of the anomalous magnetic moment only starting with the covariant version (and then making approximations, but not lattice approximations).

Compare this with the poor accuracy obtained by noncovariant lattice theories. They give finite results at each lattice spacing, but none of the lattice spacings for which computations can be carried out gives results matching experiment, and it is not known whether (or in which sense) the limit exists in which the lattice spacing goes to zero. But numerical lattice studies indicate that the limit is a free theory (i.e., the renormalized charge vanishing in the continuum limit) and that this shows already at quite coarse spacing, with lattice sizes ranging from $8^4$ to $24^4$. See, e.g., (all papers with links to the arXiv)

• M. Göckeler et al., Is there a Landau Pole Problem in QED? Phys.Rev.Lett. 80 (1998), 4119-4122.
• Kogut & Strouthos, The Logarithmic Triviality of Compact QED Coupled to a Four Fermi Interaction, Physical Review D 71 (2005), 094012.

At this coarse spacing, the Poincare invariance observed in experiments is badly broken. Hence no high accuracy prediction as in covariant QED is possible. No experimentally verified predictions have ever been made with lattice QED (unlike with lattice QCD, which produces useful predictions and is believed to have a nontrivial continuum limit). In the substantial literature discussing the triviality problem there is not the slightest reason why this should improve at shorter spacing; one expects that one gets even closer to the trivial limit when the lattice spacing is decreased further. See also

• S. Kim et al., On the triviality of textbook quantum electrodynamics, Physics Letters B 502 (2001) 345-349.
• F. Akram et al., Vacuum Polarization and Dynamical Chiral Symmetry Breaking: Phase Diagram of QED with Four-Fermion Contact Interaction, Physical Review D *7 (2013), 01301.
• Section 8, ''IS DESTRUCTIVE FIELD THEORY POSSIBLE?'' of a paper by Gallavotti and Rivasseau from 1984.

For the differences between QED and QCD regarding lattice approximations see this post.

For further information see the discussion and references in my posting at PhysicsOverflow.

 

[Demystifier]

Do you have a reference for the opposite claim?

I don't, but I don't think it's much relevant. I also don't have a reference explaining the flight of airplanes directly from atomic theory (without the use of continuous fluid mechanics) but it doesn't shake my confidence that atomic theory can explain it.

Indeed, it's a common belief in the large part of the community that all known field theories (QED, QCD) are just effective theories valid at large distances, while at smaller distances (such as the Planck scale) they can be completely wrong. The Wilson renormalization theory provides a general justification for such a belief.

The fact that we don't have direct computational evidence that lattice QED gives correct results is widely believed to be a mere artefact of the fact that we still don't have sufficiently strong computers. Current computers can simulate 4-dimensional lattices with $20^4$ lattice points or so, which is a very crude approximation and nobody really expects to get very good agreement with observations within such a crude approximation.

Sure, a common belief is not a proof. But the belief that lattice QED would give results in excellent agreement with observations if only we had sufficiently strong computers that can handle $1.000.000^4$ lattice points or so - is a very justified belief.

 

[martinbn]

The effective space-time is defined by its effects on matter. In experiments we never measure the space-time itself, we only measure how matter behaves in it. Hence, from an effective point of view, the effect on matter is all what we really need.

The question remains. How?

 

[Demystifier]

The question remains. How?

How what? Did you read any of the references I mentioned?

 

[PeterDonis]

Moderator's note: An off topic question about the thermal interpretation and EPR experiments has been moved to a new thread:

https://www.physicsforums.com/threads/thermal-interpretation-and-epr-experiment.981290/

 

[martinbn]

How what? Did you read any of the references I mentioned?

Yes, but there is nothing there. It just says that may be (somehow) it could be that way. But my question is how do you get relativistic space-time out of classical one?

 

[A. Neumaier]

Indeed, it's a common belief in the large part of the community that all known field theories (QED, QCD) are just effective theories valid at large distances, while at smaller distances (such as the Planck scale) they can be completely wrong. The Wilson renormalization theory provides a general justification for such a belief.

Originally, Wilson's renormalization theory was about a lattice theory being approximated at a critical point by a nonrelativistic continuum field theory. But he assumes that the limit actually exists! Thus Wilson's theory provides justification for the belief that lattice QED approximates the free limiting theory with zero charge. Indeed, this is what the computer simulations demonstrate.

In its application to relativistic quantum field theory, Wilson's renormalization theory is always described by the Callan-Symanzik equation, which is about a Poincare invariant effective theory approximating another Poincare invariant theory at lower energies. As far as I know, it was never about lattices approximating a known relativistic continuum theory.

Thus Wilson's theory provides no rational justification for your belief. While you are free to believe anything you like with any justification you like, there are no grounds at all why anyone informed should share your belief.

Current computers can simulate 4-dimensional lattices with $20^4$ lattice points or so, which is a very crude approximation and nobody really expects to get very good agreement with observations within such a crude approximation.

I fully agree. But one sees it already converge to the trivial theory, hence there is no reason to expect that nonfree QED results would be obtained by refining the lattice. Thus one will never have very good agreement with observations.

that lattice QED would give results in excellent agreement with observations if only we had sufficiently strong computers that can handle $1.000.000^4$ lattice points or so - is a very justified belief.

No, because the only justification of that belief would be that taking the number of lattice points to infinity would produce exact QED. But all evidence points to that taking the number of lattice points to infinity would produce QED with zero renormalized charge. The numerical evidence for this is already visible at the lattice sizes that can be simulated today, and the observed closeness to triviality grows with lattice size. Extrapolating to $1.000.000^4$ lattice points or so we would see an almost perfect free theory!

 

[Demystifier]

Yes, but there is nothing there. It just says that may be (somehow) it could be that way. But my question is how do you get relativistic space-time out of classical one?

I think I already answered.

 

[Demystifier]

But one sees it already converge to the trivial theory, hence there is no reason to expect that nonfree QED results would be obtained by refining the lattice. Thus one will never have very good agreement with observations.

My point is that agreement of lattice QED with observations is possible (and in fact expected) despite the fact that lattice QED is trivial in the continuum limit. Obviously you disagree. We already exchanged arguments on that issue several times and never came close to an agreement, so maybe it's counterproductive to further argue about that issue.

 

[martinbn]

I think I already answered.

What you said is this.

It's possible. The most suggestive evidence is the fact that from a nonrelativistic theory of atoms one can derive an approximative Lorentz invariant wave equation of sound.

Surely you can understand why I am confused. The phenomenon of sound and the wave equation are entirely classical/nonrelativistic. So I don't know what any if this has to do with relativity as emergent/effective theory!

 

[Demystifier]

The phenomenon of sound and the wave equation are entirely classical/nonrelativistic. So I don't know what any if this has to do with relativity as emergent/effective theory!

Please read Sec. 5.3 of my paper, especially the paragraph around Eq. (29).

 

[martinbn]

Please read Sec. 5.3 of my paper, especially the paragraph around Eq. (29).

I did, it says exactly what you wrote in post #13.

I suppose there is no point in me asking repeatedly. Either I just don't get it or you have a very strange understanding of what relativity is. In any case if I continue I will only be flooding the thread, so I will stop.

 

[Demystifier]

Either I just don't get it or you have a very strange understanding of what relativity is.

For me, special relativity is nothing but measurable consequences of Lorentz symmetry. Do you find it strange?