Would this experiment disprove Bohmian mechanics?

[Demystifier]

I don't see how that's true. The continuity equation only implies that if at time $t_1$, the particle has a probability density of $|\psi(x,t_1)|^2$ of being at any position $x$, then at a later time, this will continue to be true. But you have to assume that it's true initially. Isn't that what the issue of non-equilibrium is all about?

Are you familiar with the H-theorem in classical statistical mechanics? There is a similar quantum H-theorem in BM. See https://en.wikipedia.org/wiki/Antony_Valentini#Quantum_equilibrium,_locality_and_uncertainty

 

[vanhees71]

With all due respect, what is the damage done by Heisenberg and Bohr? That their reasoning has “demolished” the way back to the reality concept of classical 19th century physics or the ontology of materialism?

The damage is that they have obscured a pretty straightforward theory with unnecessarily complicated and superfluous philosophical balast. Of course one doesn't need to follow BM. The only thing that's necessary to use the theory FAPP is the minimal statistical interpretation with Bon's rule as an independent postulate. There's no necessity for a collapse (which is at odds with relativity, contradicting the very results of the most successful theory of matter, i.e. local relativistik QFT, upon which the standard model is based), a quantum-classical cut (which can neither theoretically nor empirically be defined or at least be made heuristically plausible), and complementarity, whose meaning is completely obscure.

BM is in a sense an addition to QM, eliminnating the FAPP argument, as explained in #119. It's only big problem isvthe lack of its complete formulation for standard relativistic QFT. It's far from reestablising a mechanistic worldview of the 19th century. I've no clue what the word reality means. Itvhas been made unusable for scientific discussions by philosophers.

 

[atyy]

The damage is that they have obscured a pretty straightforward theory with unnecessarily complicated and superfluous philosophical balast. Of course one doesn't need to follow BM. The only thing that's necessary to use the theory FAPP is the minimal statistical interpretation with Bon's rule as an independent postulate. There's no necessity for a collapse (which is at odds with relativity, contradicting the very results of the most successful theory of matter, i.e. local relativistik QFT, upon which the standard model is based), a quantum-classical cut (which can neither theoretically nor empirically be defined or at least be made heuristically plausible), and complementarity, whose meaning is completely obscure.

BM is in a sense an addition to QM, eliminnating the FAPP argument, as explained in #119. It's only big problem isvthe lack of its complete formulation for standard relativistic QFT. It's far from reestablising a mechanistic worldview of the 19th century. I've no clue what the word reality means. Itvhas been made unusable for scientific discussions by philosophers.

Heisenberg and Bohr are the advocates of FAPP. It is not correct to pretend that there is a minimal statistical interpretation that is distinct from Copenhagen-type thinking.

BM may not be able to deal with exactly relativistic QFT, but the standard model is not yet such a theory, nor is there a completion of it that is such a theory.

 

[Demystifier]

BM may not be able to deal with exactly relativistic QFT, but the standard model is not yet such a theory, nor is there a completion of it that is such a theory.

Exactly! In addition, it's very likely that relativistic QFT is just an effective theory that ceases to be a good approximation at sufficiently small distances. From that point of view, BM does not need to be able to deal with exactly relativistic QFT.

 

[Lord Jestocost]

The damage is that they have obscured a pretty straightforward theory with unnecessarily complicated and superfluous philosophical balast. Of course one doesn't need to follow BM. The only thing that's necessary to use the theory FAPP is the minimal statistical interpretation with Bon's rule as an independent postulate.

As Hilary Putnam writes in “Philosophical Papers: Volume 1, Mathematics, Matter and Method”:

“The full CI [Copenhagen Interpretation], to put it another way, is the minimal statistical interpretation plus the statement that hidden variables do not exist and that the wave representation gives a complete description of the physical system.” [italics in the original]

 

[vanhees71]

Heisenberg and Bohr are the advocates of FAPP. It is not correct to pretend that there is a minimal statistical interpretation that is distinct from Copenhagen-type thinking.

BM may not be able to deal with exactly relativistic QFT, but the standard model is not yet such a theory, nor is there a completion of it that is such a theory.

Well, Heisenberg introduced the collapse, and Bohr the cut and complementarity. These are all things unnecessary for the application of the formalism to real-world observations. Stripping this superfluous and misleading "philosophy" from the physics, you end up with the minimal statistical ensemble interpretation, which works FAPP without confusion and esoterics. Some people say it's "only FAPP". I still think it's all we have.

If you need additions to have an ontology, I very recently got convinced that BM is the right thing for non-relativstic QM, because it doesn't alter the physical predictions of QM, which are so well established that it is hard to conceive that we can guess any alterations without a clear guidance from observations. Maybe, one day one sees hints at such contradictions from QM. Then we have to think further how to modify the theory. One example is GRW, which adds a stochastic elements to provide some "spontaneous collapse". As long as there is no hint of such a thing, I'm skeptical why I need this addition. BM is minimal, because it makes only the addition to reinterpret the "wave function" (in the minimal interpretation it has only the probabilistic meaning with the Born Rule as independent postulate) as a "pilot wave", defining deterministic trajectories in configuration space following a non-local time evolution. Then the Born Rule is derivable from the quantum-equilibrium postulate, which however is mathematically unique (see the books by Dürr et al). You end up with an interpretation, which is equivalent with the well-established minimally interpreted theory but offers an ontology for those who need one. That's a very nice compromise, and it can make all these fruitless debates about the "philosophy of QM" superfluous ;-))).

I don't understand what you mean concerning relativistic QFT. Of course, there are mathematical formal problems. What I'm talking about is the physical theory applied to real-world observations, and that's the Standard Model using a renormalized perturbative approach and appropriate resummations to make predictions about real-world observations that are of astonishing precision. Despite the fact that everybody in the HEP community looks for "physics beyond the standard model" as if were the holy grail, there's no established result to this effect. So standard relativistic QFT and the Standard Model are very successful theories, at least FAPP. However, there seems not to be a convincing ontological addition a la BM for non-relativistic QM that can help with the ontological quibbles some philosophers and even some physicists still have with minimally interpreted QFT.

 

[vanhees71]

As Hilary Putnam writes in “Philosophical Papers: Volume 1, Mathematics, Matter and Method”:

“The full CI [Copenhagen Interpretation], to put it another way, is the minimal statistical interpretation plus the statement that hidden variables do not exist and that the wave representation gives a complete description of the physical system.” [italics in the original]

Ok, then take these last statement away. It's just hubris to think that we had a complete description of all phenomena, at least as long as there's no satisfactory unificiation between GR and relativistic Q(F)T of any kind.

That hidden variables do not exist, is for sure a conclusion one cannot draw after Bell's work. The only conclusion one can draw is that there's no "local" deterministic HV theory in accordance with the well-established correlations described by entanglement. Again, with "non-local" I mean long-range correlations not non-local interactions at a distance, which easily get mixed up in the discussion. Maybe one should call this kind of "(non-)locality" "Bell-(non-)locality", which in fact means separability. E.g., for the two-photon-polarization entangled Bell experiments, "Bell-locality" means that there are hidden variables which define for each single photon the polarization state, i.e., the polarization state of both single photons are established "local" facts, which are still not known due to the ignorance about the HVs. This picture is disproven experimentally at high significance through the observation of the violation of Bell's inequality, confirming the predictions of QT, which says that entanglement exists and thus that far-distantly observed parts of a quantum system can be correlated over arbitrary long distances, i.e., QT leads necessarily to inseparability, and this inseparability is well-established empirically by the observed violation of Bell's inequality, which is derived under the assumption of "Bell-locality", i.e., separability.

 

[bolbteppa]

Exactly! In addition, it's very likely that relativistic QFT is just an effective theory that ceases to be a good approximation at sufficiently small distances. From that point of view, BM does not need to be able to deal with exactly relativistic QFT.

Are you really saying that a non-relativistic 'theory' which also claims to be inherently/fundamentally more accurate than current theories does not need to be improved to account for relativistic phenomenon, to least reproduce current results as an approximation to the supposedly more correct theory?

One could have said this kind of stuff about Fermi's beta decay theory being non-renormalizable, and could now say 'oh gravity doesn't need to be compatible with renormalization'...

 

[Demystifier]

Are you really saying that a non-relativistic 'theory' which also claims to be inherently/fundamentally more accurate than current theories does not need to be improved to account for relativistic phenomenon, to least reproduce current results as an approximation to the supposedly more correct theory?

One could have said this kind of stuff about Fermi's beta decay theory being non-renormalizable, and could now say 'oh gravity doesn't need to be compatible with renormalization'...

A short answer is - yes.

A longer answer is that the so called "elementary particles" of the Standard Model could be just collective excitations of some more fundamental particles described by non-relativistic QM, in the same sense in which phonons are collective excitations of non-relativistic atoms.

 

[Demystifier]

I don't see how that's true. The continuity equation only implies that if at time $t_1$, the particle has a probability density of $|\psi(x,t_1)|^2$ of being at any position $x$, then at a later time, this will continue to be true. But you have to assume that it's true initially. Isn't that what the issue of non-equilibrium is all about?

For more details see the recent review: http://www.mdpi.com/1099-4300/20/6/422

 

[bolbteppa]

A short answer is - yes.

A longer answer is that the so called "elementary particles" of the Standard Model could be just collective excitations of some more fundamental particles described by relativistic QM, in the same sense in which phonons are collective excitations of non-relativistic atoms.

Is classical special relativity derivable from Galilean relativity?

If you think it is - this is demonstrably false (and you know I have a Landau section ready to go )

If you think it isn't - then how in the world could the results of relativistic quantum mechanics be reproduced by the non-relativistic Schrödinger equation in BM?

 

[Demystifier]

Is classical special relativity derivable from Galilean relativity?

Not derivable but emergent. E.g. sound wave satisfies a wave equations which is, to a good approximation, Lorentz invariant (but with the speed of sound instead of the speed of light). And I'm sure there is a Landau section that explains in more detail how the wave equation of sound emerges from motion of non-relativistic atoms.

 

[bolbteppa]

Not derivable but emergent. E.g. sound wave satisfies a wave equations which is, to a good approximation, Lorentz invariant (but with the speed of sound instead of the speed of light). And I'm sure there is a Landau section that explains in more detail how the wave equation of sound emerges from motion of non-relativistic atoms.

Honestly, this is really unbelievable - if special relativity was "emergent" from Galilean classical mechanics, it would contradict the most basic claim of Galilean relativity about interactions being instantaneous which is mandatory in Galilean relativity (c.f. vol. 1 Mechanics sec. 5), there is absolutely no way special relativity can be emergent from Galilean relativity without contradicting Galilean relativity (c.f. vol 1. Mechanics sec. 5 and vol. 2 Classical Theory of Fields sec 1), there's a reason why Einstein is so famous - he fundamentally changed all of classical mechanics with special relativity, it's literally wrong to say SR is "emergent" from Galilean relativity on the most basic grounds.

 

[vanhees71]

A short answer is - yes.

A longer answer is that the so called "elementary particles" of the Standard Model could be just collective excitations of some more fundamental particles described by non-relativistic QM, in the same sense in which phonons are collective excitations of non-relativistic atoms.

Well, this is a bit farfetched since with overwhelming evidence the correct space-time description is relativistic rather than Newtonian. So the fundamental description of matter should be relativistic rather than Newtonian.

 

[Demystifier]

Well, this is a bit farfetched since with overwhelming evidence the correct space-time description is relativistic rather than Newtonian. So the fundamental description of matter should be relativistic rather than Newtonian.

I disagree with this kind of logic. Overwhelming evidence for something does not imply that it must be fundamental. In 18th century the overwhelming evidence was that time was absolute, but it didn't imply that time must be absolute in the fundamental description. Overwhelming evidence tells only about the current state of knowledge, not about possible additional knowledge in the future.

You may object that my claim of fundamental Lorentz non-invariance is a speculation. It certainly is, but speculation is a legitimate method in science.

 

[Demystifier]

Honestly, this is really unbelievable - if special relativity was "emergent" from Galilean classical mechanics, it would contradict the most basic claim of Galilean relativity about interactions being instantaneous which is mandatory in Galilean relativity (c.f. vol. 1 Mechanics sec. 5), there is absolutely no way special relativity can be emergent from Galilean relativity without contradicting Galilean relativity (c.f. vol 1. Mechanics sec. 5 and vol. 2 Classical Theory of Fields sec 1), there's a reason why Einstein is so famous - he fundamentally changed all of classical mechanics with special relativity, it's literally wrong to say SR is "emergent" from Galilean relativity on the most basic grounds.

I don't think you understood my point based on sound waves.

 

[vanhees71]

Sound waves are very different from electromagnetic waves, because they are waves of the medium (air, liquid, solid), and thus there's a physically preferred (local) frame of reference, i.e., the (local) rest frame of the medium. That's why the Doppler formula is different for the cases, whether the observer or the source (or both) is (are) moving. That's also true for sound waves within relativity. That's why your analogy doesn't make, no matter whether you argue within Newtonian or relativistic physics.

 

[bolbteppa]

I don't think you understood my point based on sound waves.

I don't think you've thought about the assumptions going into the derivation of the wave equation in a Galilean world, for all intents and purposes the wave equation in Galilean classical mechanics is completely irrelevant regarding the fundamentals of the theory, hinges on the laws of motion of the constituent particles in the wave, and talks about the aggregate behavior of multiple particles each separately satisfying Galilean motion...

 

[Demystifier]

Sound waves are very different from electromagnetic waves, because they are waves of the medium (air, liquid, solid),

There is no proof that electromagnetic waves are not waves of the medium. The fact that they are not in the Standard Model is not a proof that they cannot be in any model. There is no any no-go theorem of that form. Indeed, in Lorentz theory EM waves are waves of the medium. The Einstein's theory prevailed not because he proved that there is no ether, but because the theory without ether looked simpler. The Michelson-Morley experiment excluded the simplest version of ether theory, not any version of ether theory.

and thus there's a physically preferred (local) frame of reference, i.e., the (local) rest frame of the medium.

Again, there is no proof that a preferred frame doesn't exist. Sure, we didn't find it yet, but so what? We also didn't find supersymmetry, extra dimensions, axions, fourth generation of quarks, ..., but it doesn't stop physicists at LHC to search for it. There is a whole bunch of beyond the standard model physics studied by theoreticians, and theories which violate Lorentz invariance are a part of it.

That's why the Doppler formula is different for the cases, whether the observer or the source (or both) is (are) moving. That's also true for sound waves within relativity. That's why your analogy doesn't make, no matter whether you argue within Newtonian or relativistic physics.

I don't understand. Are you saying that Doppler formula for moving source differs from Doppler formula for moving observer?

 

[Demystifier]

Another hint for fundamental Lorentz non-invariance, independent on Bohmian interpretation, is this. Relativistic QFT is mathematically not well defined. The source of problem lies in the infinite number of degrees of freedom, that is, in UV divergences. The simplest way to remove UV divergences is to introduce a cutoff that violates Lorentz invariance. One may think that it is unacceptable because all existing experiments are consistent with Lorentz invariance. However, if the cutoff is put at a sufficiently small length (say the Planck length), then this hypothetical fundamental violation of Lorentz invariance is not in contradiction with any of the existing experiments.

What will be the mainstream "standard model" of fundamental physics in 1000 years from now? Nobody knows, but if I could bet, I would bet that fundamental Lorentz invariance will not be a part of it.

 

[vanhees71]

I don't comment on aether speculations in this forum.

I don't understand. Are you saying that Doppler formula for moving source differs from Doppler formula for moving observer?

Sure, you find this in any elementary textbook about sound waves. It's even derived in Wikipedia

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

For the important specialty of light wave, where the Doppler effect depends only on the relative velocity (of course in the correct relativistic sense!) as it must be, because for light there is no medium (or aether), at least not if you "believe" in relativity, which is so overwhelmingly confirmed by observation that I really don't see, how you want to justify an speculations of an "aether". If there is an "aether" in any sense, it's most probably not a naive one as thought in the 19th century!

For the relativistic treatment of the Doppler effect for arbitrary waves, including he special case of light in vacuo, see

http://www.mathpages.com/rr/s2-04/2-04.htm

 

[Demystifier]

If there is an "aether" in any sense, it's most probably not a naive one as thought in the 19th century!

I certainly agree on that.

 

[Demystifier]

For the relativistic treatment of the Doppler effect for arbitrary waves, including he special case of light in vacuo, see
http://www.mathpages.com/rr/s2-04/2-04.htm

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

 

[Demystifier]

I don't comment on ... speculations in this forum.

If a new theory does not produce a new prediction, then it's irrelevant for science. If a new theory does produce a new prediction, then it's a speculation that nobody takes seriously. Unless, for some sociological reasons, the theory becomes "popular".

 

[atyy]

Honestly, this is really unbelievable - if special relativity was "emergent" from Galilean classical mechanics, it would contradict the most basic claim of Galilean relativity about interactions being instantaneous which is mandatory in Galilean relativity (c.f. vol. 1 Mechanics sec. 5), there is absolutely no way special relativity can be emergent from Galilean relativity without contradicting Galilean relativity (c.f. vol 1. Mechanics sec. 5 and vol. 2 Classical Theory of Fields sec 1), there's a reason why Einstein is so famous - he fundamentally changed all of classical mechanics with special relativity, it's literally wrong to say SR is "emergent" from Galilean relativity on the most basic grounds.

Well, this is a bit farfetched since with overwhelming evidence the correct space-time description is relativistic rather than Newtonian. So the fundamental description of matter should be relativistic rather than Newtonian.

https://arxiv.org/abs/1106.4501
"The sense in which AdS/CFT duality illustrates the possibility of emergent relativity, and the special role of strong coupling, are briefly discussed."

 

[Demystifier]

https://arxiv.org/abs/1106.4501

I like the beginning:
"Every child knows that things which are further away are really just smaller. It is only grown-ups who think this an illusion. After all, a distant object looks smaller in every detail, in principle all the way down to its atomic structure. And yet, the grown-ups point out, the Bohr radius is a constant of Nature.
But perhaps it is the grown-ups who are under the illusion. Physics may indeed play out on a flat screen, with an illusion of “depth” created by shrinking or expanding mutable 2D “atoms”, conspiring to fake 3D atoms of fixed size but varying distance from us."

 

[atyy]

I don't understand what you mean concerning relativistic QFT. Of course, there are mathematical formal problems. What I'm talking about is the physical theory applied to real-world observations, and that's the Standard Model using a renormalized perturbative approach and appropriate resummations to make predictions about real-world observations that are of astonishing precision. Despite the fact that everybody in the HEP community looks for "physics beyond the standard model" as if were the holy grail, there's no established result to this effect. So standard relativistic QFT and the Standard Model are very successful theories, at least FAPP. However, there seems not to be a convincing ontological addition a la BM for non-relativistic QM that can help with the ontological quibbles some philosophers and even some physicists still have with minimally interpreted QFT.

There are ideas, for example, that lattice gauge theory can provide a non-perturbative formulation that gives rise to relativistic quantum field theory as a low energy effective theory.

https://arxiv.org/abs/hep-lat/0211036, Stefano Capitani, Lattice Perturbation Theory
"In principle all known perturbative results of continuum QED and QCD can also be reproduced using a lattice regularization instead of the more popular ones." [I think this is not strictly true, even at the physics level of rigour, because of the chiral fermion problem.]

http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf, Gerard 't Hooft, The Conceptual Basis of Quantum Field Theory
"Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

 

[vanhees71]

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

Sigh. It clearly makes the important point that for light, and only for light, in vacuo the Doppler effect depends only on the relative velocity between source and observer, while for sound it depends in addition on the (local) four-velocity of the medium. A medium always introduces a physically distinguished (local) frame of reference, namely its rest frame, while "the vacuum" doesn't provide such a disinguished frame, i.e., the vacuum is Poincare invariant.

 

[vanhees71]

There are ideas, for example, that lattice gauge theory can provide a non-perturbative formulation that gives rise to relativistic quantum field theory as a low energy effective theory.

https://arxiv.org/abs/hep-lat/0211036, Stefano Capitani, Lattice Perturbation Theory
"In principle all known perturbative results of continuum QED and QCD can also be reproduced using a lattice regularization instead of the more popular ones." [I think this is not strictly true, even at the physics level of rigour, because of the chiral fermion problem.]

http://www.staff.science.uu.nl/~hooft101/lectures/basisqft.pdf, Gerard 't Hooft, The Conceptual Basis of Quantum Field Theory
"Often, authors forget to mention the first, very important, step in this logical procedure: replace the classical field theory one wishes to quantize by a strictly finite theory. Assuming that physical structures smaller than a certain size will not be important for our considerations, we replace the continuum of three-dimensional space by a discrete but dense lattice of points."

Well, the regularization you use is irrelevant for this debate, as long as you get a Poincare invariant continuum limit.

 

[stevendaryl]

As far as I can see it explicitly says that, in the Doppler effect, there is no substantial difference between sound and light.

The relativistic Doppler effect can be thought of as a combination of the nonrelativistic Doppler effect plus the time dilation of the moving sender. Motion through a medium doesn't normally affect the rate of clocks, so I don't see why it should have the time dilation effect.

On the other hand, you could imagine a "sound clock" with a sound echoing back and forth between two rigid walls. If the walls are in motion and are oriented perpendicular to that motion, it will experience a kind of time dilation with the speed of light replaced by the speed of sound.