Would this experiment disprove Bohmian mechanics?

[bolbteppa]

Also, one of the most shocking things I've seen in physics yet is the Dirac sea explanation of vacuum polarization in B&D volume 1, that's such a shocking explanation for the difference between bare and observed charge, I don't know what to do with it yet...

 

[stevendaryl]

The word "realism" I'd completely abandon from any serious physics discussion. I have never understood what the philosophers precisely mean. In most of the cases they mean "deterministic". Bell's theorem is about what he called "local deterministic theories", and that's how we should label this class of models which are all ruled out by all "Bell tests" done today.

I feel that "determinism" versus "nondeterminism" is not what Bell's theorem is about, and local realism is not about determinism. Determinism is a conclusion, not an assumption. (Well, it can be an assumption, as well, but it doesn't need to be.)

In an EPR-like experiment in which Alice and Bob are measuring spins of different particles, the local realism assumption is that for each measurement:

• The probability that Alice measures spin-up depends on facts about her detector (the orientation $\vec{a}$ and possibly other variables) plus facts about her particle. So it's a function $P_A(\vec{a}, X_A, \lambda)$ of her setting $\vec{a}$, other variables describing her device, $X_A$, and variables describing the particle, $\lambda$.
• Similarly, the probability that Bob measures spin-up is another function: $P_B(\vec{b}, X_B, \lambda)$, which depends on his setting, $\vec{b}$, other facts about his detector, $X_B$, and facts about the particle, $\lambda$.

The EPR perfect anti-correlations (for spin-1/2 pairs) imply that

For all $\vec{a}$, for all $X_A$, for all $X_B$, if Alice gets spin-up with setting $\vec{a}$ (which means that the probability of getting spin-up must be greater than 0), then Bob will definitely not get spin-up at setting $\vec{a}$. This means that for fixed $\lambda$,

• If $P_A(\vec{a}, X_A, \lambda) \gt 0$, then $P_B(\vec{a}, X_B, \lambda) = 0$

Similarly, if Alice gets spin-down with setting $\vec{a}$ (which means that the probability of getting spin-up must be less than 1), then Bob will definitely get spin-up at setting $\vec{a}$. So

• If $P_A(\vec{a}, X_A, \lambda) \lt 1$, then $P_B(\vec{a}, X_B, \lambda) = 1$

Together, these imply that for each value of $\lambda$, and for fixed $\vec{a}$, either

$P_B(\vec{a}, X_B, \lambda) = 0$ for all $X_B$, or $P_B(\vec{a}, X_B, \lambda) = 1$ for all $X_B$. In other words, for each pair $\lambda, \vec{a}$, it is 100% deterministic whether Bob gets spin-up or spin-down. Similarly, Alice's probability must be either 0 or 1 for each pair of setting and $\lambda$.

Determinism follows from perfect correlation/anti-correlation and the assumption (local realism) that a measurement's probability depends only on facts local to the measurement. It doesn't follow from local realism alone. You could have an intrinsically nondeterministic process that would still satisfy some notion of local realism, but it would then not predict perfect correlations/anti-correlations.

 

[richrf]

I very much appreciate this discussion, as it is the primary reason I come to this forum.

A couple of comments: While some physicists and philosophers may wish to refer to BM as deterministic, I think it is appropriate to acknowledge Bohm's viewpoint that it is causal and not completely deterministic (I personally don't know how model can be partially deterministic. It would be an oxymoron).

Also, I believe far to much weight is placed on Relativity. Relativity, in my view, is a solution to the scientific measurement and synchronization problem, and as such does not speak to the fundamental nature of the universe as does QM. This there is no strong reason to assume one will resolve into the other. One can, for example, approach the investigation of the nature of the universe and not be concerned with the problems of measurement from different frames of reference. It only becomes a problem if one one assumes Relativity as ontological, but this is an assumption that can be questioned.

 

[Demystifier]

the non-localizability of relativistic particles

Every photon detector detects "position of the photon", with some resolution $\Delta x$. Since the Compton length of the photon is infinite (because its mass is zero), the resolution $\Delta x$ is obviously much better than naive estimate according to which the resolution of a relativistic particle cannot be better than its Compton length. The catch is that detection of a photon is not a projective measurement in which photon ends up in an eigenstate of the position operator. To describe the detection of photon position, one does not need a photon position operator. Instead, it is a generalized measurement described by the POVM formalism. By the Neumark's theorem, every POVM can be represented as a projective measurement in a larger Hilbert space. Physically, this means that photon detector does not measure the position of the photon itself, but a position of some macroscopic pointer of the measuring apparatus that is coupled to the photon.

 

[bobob]

Not quite. The point of BM if the same point as QM (and the converse is true). It's quite a tautology, as BM is QM. The only valid reason why it is disregarded, is that it is not as powerful as QFT.

No, it's not quantum mechanics unless you disregard the trajectories as meaningles, which is only thing that makes bohmian mechanics, bohmian mechanics. Differences in interpretation should have physical consequences and physical consequences are subject to experiment. Anything that has no physical consequences is meaningless baggage that only serves to obfuscate a theory. Bohmian mechanics is disregarded becasuse the entire program consists of a few people trying to ensure the ontology doesn't predict anything.

 

[bolbteppa]

https://www.jstor.org/stable/20117507 by a prominent Bohm name quoting the Landau passage on paths (on the first previewable page), I would guess from reading on that his desire to study on came down to a belief that Bohm's alternative was legitimate, which would be such a big deal if true.

Also - I wonder does an article on BM that gets non-relativistic spin from group theory alone exist?

 

[bolbteppa]

Also, I believe far to much weight is placed on Relativity. Relativity, in my view, is a solution to the scientific measurement and synchronization problem, and as such does not speak to the fundamental nature of the universe as does QM. This there is no strong reason to assume one will resolve into the other. One can, for example, approach the investigation of the nature of the universe and not be concerned with the problems of measurement from different frames of reference. It only becomes a problem if one one assumes Relativity as ontological, but this is an assumption that can be questioned.

Relativistic quantum theory is one of the most successful theories of all time, BM by the claims of Bohm's motivation for setting it up alone should actually be more successful in describing it.

 

[Boing3000]

No, it's not quantum mechanics unless you disregard the trajectories as meaningles, which is only thing that makes bohmian mechanics, bohmian mechanics.

There is nothing in standard QM about trajectories. That's why BM is QM and more (pilot wave/trajectories)

Differences in interpretation should have physical consequences and physical consequences are subject to experiment.

That would definitely be an fine additional feature, but that feature don't come from "interpreting" but new math that can be used to make new computation/prediction.

Anything that has no physical consequences is meaningless baggage that only serves to obfuscate a theory.

That's obviously false. Any theories that make the same predictions are equivalent. There may be an infinite number a them, we'll never know. We use the simpler to tackle the problem at hand.
"additional baggage" is not meaningless if it solves one of the obvious problem in the theory (measurement problem). It fixes the theory.
"additional baggage" is not meaningless if it remove/explain the stochastic nature of the theory, when this theory cannot even explain what randomness come from, nor what it randomness is.

Bohmian mechanics is disregarded becasuse the entire program consists of a few people trying to ensure the ontology doesn't predict anything.

You have no idea why it is disregarded and this varies a lot. The reasons given are based on scientific opinion (even wrong ones)
BM is no more about ontology than QFT is about the ontology of fields than "bare" QM is about the ontology of "we'll never know, so please shut-up" or "God have the ledger and play dice with you .. fool".

People that disregard too many things are just too keen on wearing binders.

 

[vanhees71]

There is a really interesting subtlety here, my understanding is that while a position-space single particle first-quantized wave function for a photon is impossible by their arguments, a momentum-space first-quantized wave function however is not only completely fine, even more insanely - only free particle momentum-space wave functions are inherently measurable in QFT in general and measuring interactions in RQT are just as meaningless as paths are in non-rel QM - as he says in the first 3 pages (previewable on amazon) here: https://www.amazon.com/dp/0750633719/?tag=pfamazon01-20

As to the first volume of B&D, the historic stuff at the beginning I still wonder about it, but once he gets to scatting he uses multi-particle wave functions so I think it's actually totally fine, and in fact a bit quicker to get things like Compton scattering, and the bits of volume 2 I've read so far are shockingly good.

That's true. A "photon" or "particle" is defined by asymptotic free states. You don't need necessarily momentum eigenstates (which are "improper eigenstates" anyway, because they are not square integrable but distributions), it can be any free single-particle state (like a wave packet).

I'd not recommend to study BD Vol. 2 although it's indeed still good for some topics (often even better than newer books), but it's really a bit outdated now (particularly the part about renormalization). I'd recommend as a introductory book

M. D. Schwartz, QFT and the Standard Model, Cambridge University Press (2014)

and then for an in-depth study

S. Weinberg, The QT of Fields (3 Vols.), Cambridge University Press (1995...)

and

A. Duncan, The conceptual framework of QFT, Oxford University Press (2012)

 

[vanhees71]

Why? Simon Gröblacher et al. state it quite simply in "An experimental test of non-local realism" (https://arxiv.org/abs/0704.2529v2):

"Physical realism suggests that the results of observations are a consequence of properties carried by physical systems."

Well, it's hard to repair the damage done by Heisenberg and Bohr. It's repaired only slowly since Bell's groundbreaking work and with progress in what's called "quantum information".

 

[Demystifier]

Bohmian mechanics is disregarded becasuse the entire program consists of a few people trying to ensure the ontology doesn't predict anything.

The Bohmian ontology predicts probabilities of measurement outcomes. Of course, standard QM without any ontology at all also predicts the same probabilities of the same measurement outcomes. So what's the point of introducing ontology?

Without ontology it looks as if measurement outcomes do not exist unless someone observes them. It looks as if the Moon is not there when nobody observes it. Most physicists find it incoherent, or at least too difficult, to think that the Moon is really not there when nobody observes it. Hence they need some ontology, at least as a thinking tool (see my signature). BM is a theory that explicitly adds such a thinking tool to the standard minimal QM.

But that's not all. In standard QM, the Born rule is an axiom. In BM the Born rule can be derived from another axiom, the axiom that particles have deterministic trajectories specified by BM. This another axiom, however, is not necessarily better than the first axiom, so this does not necessarily make BM better than standard QM. The true reason why BM is better than standard QM is explained in the paragraph above.

 

[stevendaryl]

In standard QM, the Born rule is an axiom. In BM the Born rule can be derived from another axiom, the axiom that particles have deterministic trajectories specified by BM. This another axiom, however, is not necessarily better than the first axiom, so this does not necessarily make BM better than standard QM. The true reason why BM is better than standard QM is explained in the paragraph above.

Isn't it an additional assumption that the initial positions of particles is chosen according to a probability distribution that agrees with $|\psi|^2$?

 

[Lord Jestocost]

Well, it's hard to repair the damage done by Heisenberg and Bohr.

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?

 

[Demystifier]

Isn't it an additional assumption that the initial positions of particles is chosen according to a probability distribution that agrees with $|\psi|^2$?

Not really. It can be explained from the continuity equation, in the same sense in which probability in classical statistical mechanics can be explained from the Liouville equation.

 

[stevendaryl]

Not really. It can be explained from the continuity equation, in the same sense in which probability in classical statistical mechanics can be explained from the Liouville equation.

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?

 

[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 Schrodinger 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.