I QFT made Bohmian mechanics a non-starter: missed opportunities?

[gentzen]

He is a polite guy, this is why he doesn't directly tell anybody to shut up. But it seems to me that this is what he means.

It doesn't see like that to me.

My own perception is rather along the lines of what I expressed in the following comments:

Maybe more fundamental, I would have found it nice to clarify A. Neumaier's view on Ensembles in quantum field theory. I don't even understand why he thought that you have to "repeatedly prepare a quantum field extending over all of spacetime" in order to use an ensemble interpretation of QFT. But if already the fact that an ensemble interpretation is not universally applicable is never acknowledged, not even in simple examples, then this makes it difficult for me to dive into such subtle issues.

If you always say "it is simple," or "I don't understand your problem," or "...", then this might be harmless as long as your conversation partner is right anyway and doesn't need your input. But you get him into trouble in the occasional cases where he is wrong, and would have benefitted from you input to see this for himself.

So with respect to BM, the relevant question for me seems to be whether you or other Bohmians could have benefitted from his input. (I will try to "invent" such a possible scenario below, just for fun.)

Well, a big part of my choice of the minimal statistical interpretation, which is very similar to a flavor of Copenhagen, which neither assumes a collapse (which cannot occur for causality reasons and it's not needed at all to use the quantum formalism to compare what's predicted concerning physical observables and what's found when measured)

My impression is that neither Ballentine nor Einstein would agree that the minimal statistical interpretation is a flavor of Copenhagen.

nor a quantum-classical cut (for which there is not the slightest evidence; rather the classical behavior of macroscopic objects is well-understood as an effective description of coarse-grained macroscopically relevant observables), is Occam's razor.

My impression is that you don't understand Bohr's position at all, and "accidentally" side with Heisenberg's position with respect to the cut. But from the perspective of the minimal statistical interpretation, only Bohr's position seems to be valid.
I guess your basic problem is that you don't understand why you have to first fix a context before applying statistics. Many scientists in the "softer sciences" ran into the practical consequences of this misunderstanding. The currently favored solution is to preregister (i.e. fix a context for) studies that would risk to get into trouble with this.

In the case of BM first of all there's no need to calculate the Bohmian trajectories, because it's not needed to confront the theory with experiment.

Maybe the situation is rather the opposite, and BM could actually benefit from input of skeptics like you. If you compute the complete evolution of the whole wavefunction anyway, then the trajectories of BM cannot really give you additional experimentally relevant information. But maybe there is another way to look at BM, where the trajectories are really helpful? What if you compute more than a single trajectory, and really sample from the ensemble of trajectories? The trajectories now tell you which part of the wavefunction you have to compute, and which parts you can ignore. Because now your predictions are really based on the trajectories alone, and no longer on a MWI-like wavefunction.

 

[vanhees71]

My impression is that neither Ballentine nor Einstein would agree that the minimal statistical interpretation is a flavor of Copenhagen.

May be. I thought the key issue with the Copenhagen flavors is just to take the probabilistic meaning of the quantum state in addition to the other postulates, and that's common to all Copenhagen flavors. Then there are as many Copenhagen interpretations as there are early quantum physicists under sufficient influence of Bohr and Heisenberg...

My impression is that you don't understand Bohr's position at all, and "accidentally" side with Heisenberg's position with respect to the cut. But from the perspective of the minimal statistical interpretation, only Bohr's position seems to be valid.

What precisely IS Bohr's position? All I read by him is just some philosophical gibberish. There's no concrete math, and without this you can't clarify the meaning of the words. Where does he think this quantum-classical cut should be? How is this consolidated by experiment?

 

[gentzen]

What precisely IS Bohr's position? All I read by him is just some philosophical gibberish. There's no concrete math, and without this you can't clarify the meaning of the words. Where does he think this quantum-classical cut should be? How is this consolidated by experiment?

Bohr's position is that you have to describe your experiment before you can apply QM, and you have to describe your experiment (i.e. what you actually do in your laboratory) in terms of classical physics (edit: or rather classical concepts), because that is the description that can be communicated.

 

[Lord Jestocost]

...
What precisely IS Bohr's position? .....

The following could perhaps clarify few things. N.P. Landsman in “Between classical and quantum”, chapter 3.2 “Object and apparatus: the Heisenberg cut” (https://arxiv.org/abs/quant-ph/0506082):

“Describing quantum physics in terms of classical concepts sounds like an impossible and even selfcontradictory task (cf. Heisenberg, 1958). For one, it precludes a completely quantum-mechanical description of the world: ‘However far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms.’ But at the same time it precludes a purely classical description of the world, for underneath classical physics one has quantum theory.66 The fascination of Bohr’s philosophy of quantum mechanics lies precisely in his brilliant resolution of this apparently paradoxical situation.

The first step of this resolution that he and Heisenberg proposed is to divide the system whose description is sought into two parts: one, the object, is to be described quantum-mechanically, whereas the other, the apparatus, is treated as if it were classical. Despite innumerable claims to the contrary in the literature (i.e. to the effect that Bohr held that a separate realm of Nature was intrinsically classical), there is no doubt that both Bohr and Heisenberg believed in the fundamental and universal nature of quantum mechanics, and saw the classical description of the apparatus as a purely epistemological move without any counterpart in ontology, expressing the fact that a given quantum system is being used as a measuring device.67 For example: ‘The construction and the functioning of all apparatus like diaphragms and shutters, serving to define geometry and timing of the experimental arrangements, or photographic plates used for recording the localization of atomic objects, will depend on properties of materials which are themselves essentially determined by the quantum of action’ (Bohr, 1948), as well as: ‘We are free to make the cut only within a region where the quantum mechanical description of the process concerned is effectively equivalent with the classical description’ (Bohr, 1935).68” [Bold by LJ]

 

[vanhees71]

Of course, I have to describe the experiment I want to analyze, but why should I be forced to do this in terms of classical physics. Most of the experiments done which lead to last year's physics Nobel prize are not even describable without QT!

https://physicsworld.com/a/the-bohr-paradox/

 

[gentzen]

Of course, I have to describe the experiment I want to analyze, but why should I be forced to do this in terms of classical physics.

Because to describe the experiment, you should describe what the experimenters actually do, not how you interpret what they do in terms of your theory.

 

[vanhees71]

To describe an experiment you also need theory to be able to talk about what's done, and if the experiment tests predictions of QT, it's impossible to describe it entirely with classical physics. E.g., when quantum opticians use entangled photon pairs from parametric down-conversion, you cannot describe this entirely in terms of classical physics since Fock states of photons are entirely quantum, and there entanglement cannot be described in any way by classical physics.

 

[gentzen]

To describe an experiment you also need theory to be able to talk about what's done, and if the experiment tests predictions of QT, it's impossible to describe it entirely with classical physics.

You are focusing too much on classical physics, and not enough on classical concepts. You should ask yourself which sort of quantum concepts you could use in addition to purely classical concepts to describe what is being done by experimenters. For example, is it unproblematic to talk about the ground-state of some simple atom, ion, or molecule? What about some specific excited state, or some equilibrium thermal state?

In the end, you need stuff which can be reliably described and reproduced. At least, if the results of your experiment consists mostly of statistics.

 

[Demystifier]

You are focusing too much on classical physics, and not enough on classical concepts.

Focusing more on concepts and less on physics is against everything what @vanhees71 stands for.

 

[Ken G]

Ironically, I think the key to Bohr's "cut" is along the lines of what @vanhees71 has also been saying, that the essential features of any scientific theory must be observables. Poincare covariance is not observable, wavefunctions and Foch states are not observable, quantum fields are not observable, etc. The irony is that although @vanhees71 criticizes Bohr for being too philosophical, it seems to me all Bohr is doing is recognizing the elephant in the room of the logical inconsistencies we have pointed out above (about conflating observables and theoretical constructs as if they were the same thing). Bohr is saying that we have a fundamental paradox to navigate, the ontologies of physics are based on unobservable concepts, while the epistemology of observational science is based on objective tests. Hence in quantum mechanics, the "cut" is essentially the cut between ontology and epistemology, the two pieces of everything we learn in physics that we pretend fit together seamlessly. But they do not fit together seamlessly, and this is essentially the role of interpretations, to create a milieu that allows contact between these things that do not actually touch.

In essence, BM allows the observables, or more correctly the behaviors of the observers, to penetrate into the ontologies by seeking classical interpretations of those ontologies. Everett's prescription is the opposite, the abstract ontologies of the wavefunctions are allowed to penetrate into the behaviors of the observers (who thusly become unable to observe the entire landscape of the universe they are interacting with). And the Bohr "cut" allows us to avoid interpenetration by either domain, essentially "punting" on the need to describe the contact. These are all just ways of handling a paradox that has always been right in front of our faces, even before quantum mechanics: we test our theories with observations, but we do not observe the elements of the theories, nor do we have any theories that describe the behaviors of the testers. This loophole is never closed, it is merely ignored. Quantum mechanics is the place where it is more difficult to ignore, but it was always there.

 

[haushofer]

In the case of BM first of all there's no need to calculate the Bohmian trajectories, because it's not needed to confront the theory with experiment. All our colleagues measure are cross sections and related quantities.

Critics of heliocentrism: In calculating trajectories of planets in our sky you don't need to invoke heliocentrism to confront theory with observation. All astronomers on earth measure with their telescopes are positions on the hemisphere.

 

[gentzen]

Ironically, I think the key to Bohr's "cut" is along the lines of what @vanhees71 has also been saying, that the essential features of any scientific theory must be observables.

Well, there are also actions in addition to observables in control theory, and intervertions in statistical studies. In fact, one of the main differences between the ancient greek precursor of science and the modern scientific method are precisely the controlled experiments enabled by the systematic use of interventions.

The irony is that although @vanhees71 criticizes Bohr for being too philosophical, ... Hence in quantum mechanics, the "cut" is essentially the cut between ontology and epistemology, the two pieces of everything we learn in physics that we pretend fit together seamlessly. But they do not fit together seamlessly, and this is essentially the role of interpretations, to create a milieu that allows contact between these things that do not actually touch.

The irony is that you get very philosophical here, to the point where I can no longer see why vanhees71 should be willing to try to understand what you are saying. In case all you wanted to do is preaching to the choir, well done, your comment is full of brilliant and lovely reflections. But in case you wanted to communicate with vanhees71, I am not convinced of your approach.

 

[Ken G]

Well, there are also actions in addition to observables in control theory, and intervertions in statistical studies. In fact, one of the main differences between the ancient greek precursor of science and the modern scientific method are precisely the controlled experiments enabled by the systematic use of interventions.

I agree, if we are to take into account everything that is on the plate of the scientist, we cannot blithely label a bunch of outcomes as "observations" without some care given to the behaviors that are necessary in order to count them as such. That's why I said it was really behaviors of people moreso than just observables.

The irony is that you get very philosophical here, to the point where I can no longer see why vanhees71 should be willing to try to understand what you are saying. In case all you wanted to do is preaching to the choir, well done, your comment is full of brilliant and lovely reflections. But in case you wanted to communicate with vanhees71, I am not convinced of your approach.

The idea is to convince @vanhees71 that his approach somewhat simplifies the actual requirements of doing science. We can all agree that the scientific method is the defining character of that discipline, and as such it involves a confrontation between theoretical prediction and observational test. The former is generated by manipulating ontologies, and the latter by manipulating epistemologies. At issue is the confrontation itself, which involves crossing a kind of "cut" where an apple is held up next to an orange and some sort of comparison is made. An attempt to formalize that comparison was carried out by Bayes, for example, and other attempts have also been made (say, a frequentist perspective), and the various subjective elements of these formalizations mirror the process of creating interpretations of theories.

One simply cannot deny there is a need to add this kind of scaffolding to the process of testing predictions, it is just that we generally sweep such attempts under the rug and pretend that it is all very straightforward. Then we look at specific examples, like choosing MOND or dark matter to explain galactic dynamics (or, say, heliocentric vs. geocentric solar system models), and we see it is not so straightforward and may generate ongoing debates that can never be resolved beyond all doubt or skepticism. Nor do they need to be, because science is an ongoing process by its very nature.

 

[vanhees71]

I agree, if we are to take into account everything that is on the plate of the scientist, we cannot blithely label a bunch of outcomes as "observations" without some care given to the behaviors that are necessary in order to count them as such. That's why I said it was really behaviors of people moreso than just observables.

The idea is to convince @vanhees71 that his approach somewhat simplifies the actual requirements of doing science. We can all agree that the scientific method is the defining character of that discipline, and as such it involves a confrontation between theoretical prediction and observational test. The former is generated by manipulating ontologies, and the latter by manipulating epistemologies. At issue is the confrontation itself, which involves crossing a kind of "cut" where an apple is held up next to an orange and some sort of comparison is made. An attempt to formalize that comparison was carried out by Bayes, for example, and other attempts have also been made (say, a frequentist perspective), and the various subjective elements of these formalizations mirror the process of creating interpretations of theories.

Theoretical predictions are not due to some philosophical isms or "logies" but the use of math to evaluate what the theory predicts for a given experiment. Nobody cares about "epistemologies" vs. "ontologies". It's just a matter of how well the theorist can mathematically describe what's measured by a given experimental setup or the other way, how the experimentalist can test a given prediction of the theorists by constructing an adequate measurement. Both are creative acts rather than some nebulous philosophical speculation.

One simply cannot deny there is a need to add this kind of scaffolding to the process of testing predictions, it is just that we generally sweep such attempts under the rug and pretend that it is all very straightforward. Then we look at specific examples, like choosing MOND or dark matter to explain galactic dynamics (or, say, heliocentric vs. geocentric solar system models), and we see it is not so straightforward and may generate ongoing debates that can never be resolved beyond all doubt or skepticism. Nor do they need to be, because science is an ongoing process by its very nature.

Well, there are some tensions in the cosmological standard model ($\Lambda\text{CDM}$ model), and it's not yet clear, whether there really is "dark matter" (in the sense that there are yet unknown "dark-matter particles" and maybe yet unknown interactions, all called "physics beyond the Standard Model of particle physics") or if the description of the gravitational interaction by GR has to be modified. Given the high-precision confirmation of GR and the somewhat shaky grounds of MOND, I'd not think that MOND is a convincing solution of these problems. Of course, science is always "an ongoing process by its very Nature", and that's why philosophical "isms" are rather obstacles to the progress of science.

 

[Demystifier]

Of course, science is always "an ongoing process by its very Nature", and that's why philosophical "isms" are rather obstacles to the progress of science.

It's an obstacle only for scientists who spend too much time on this subforum.

If there was no us who constantly put "ism" obstacles in front of you, you would probably have quantized gravity by now.

Now seriously. Philosophy is not an obstacle to the progress of science. In principle, scientists do what they do independently of philosophers, nobody forces scientists to listen what philosophers have to say. Indeed, most scientists simply ignore philosophers and do pure science instead. However, some scientists are not able to simply ignore it. Some scientists are deeply disturbed and irritated by philosophers, and it is this psychological state of being disturbed and irritated that constitutes an obstacle for those scientists. So the problem is not the philosophers, they just do their job, which is philosophy. The problem is how some scientists cope with it. They should learn to focus their mind on things they really care about, and ignore the stuff that makes them disturbed and irritated, be it philosophy, string theory, particle physics (for some cond-mat physicists), politics, or whatever.

 

[Demystifier]

"Bohm's language destroys the symmetry between position and velocity,"

I never understood why is that a problem. In classical physics, most of the languages (Newton, Lagrange, ...) do the same, and nobody complains that it's a problem. Even in quantum physics, the Lagrangian path integral formulation destroys the symmetry between position and velocity, and again nobody complains.

 

[vanhees71]

It's an obstacle only for scientists who spend too much time on this subforum.

If there was no us who constantly put "ism" obstacles in front of you, you would probably have quantized gravity by now.

Well, I'm not sure that this is the obstacle in my case ;-).

Now seriously. Philosophy is not an obstacle to the progress of science. In principle, scientists do what they do independently of philosophers, nobody forces scientists to listen what philosophers have to say. Indeed, most scientists simply ignore philosophers and do pure science instead. However, some scientists are not able to simply ignore it. Some scientists are deeply disturbed and irritated by philosophers, and it is this psychological state of being disturbed and irritated that constitutes an obstacle for those scientists. So the problem is not the philosophers, they just do their job, which is philosophy. The problem is how some scientists cope with it. They should learn to focus their mind on things they really care about, and ignore the stuff that makes them disturbed and irritated, be it philosophy, string theory, particle physics (for some cond-mat physicists), politics, or whatever.

I think we all are in the danger to be caught in our world views. The most prominent example is Einstein, who could not accept the irreducible randomness of Nature, revealed by QT. For the last 30 years of his life he looked for a phantom, inventing a lot of general classical field theories with no success (paralleled by Schrödinger).

Philosophers of science tend to event pseudo-problems which are simply not there like the "measurement problem" or the "ontology of elementary particles".

 

[WernerQH]

Not being able to perceive a problem can be a handicap. For the afflicted it appears to be a benefit.

 

[A. Neumaier]

I think we all are in the danger to be caught in our world views.

Did you ever consider that you might be caught in your own world view?

 

[vanhees71]

Of course, that's why I said "we all".

 

[Demystifier]

I think we all are in the danger to be caught in our world views. The most prominent example is Einstein, who could not accept the irreducible randomness of Nature, revealed by QT. For the last 30 years of his life he looked for a phantom, inventing a lot of general classical field theories with no success (paralleled by Schrödinger).

Our world views is what motivates us. Without any world views at all we would probably not be scientists at all. Bell also did not accept irreducible randomness of Nature, and that lead him to the famous Bell theorem. If Einstein did not have the world view he had, would he ever made his great discoveries (that made him famous) in the first place?

 

[vanhees71]

Yes, but otherwise Bell's writings on the foundations of QM are utmost confusing, inventing new words with very vague meaning. At the end everything was clarified by the experiments, and standard QT was consolidated at amazing significance. There's no need for funny new words substituting "observables", "experiments", "measurments".

The young Einstein was very much down to earth and a paradigmatic example for a "no-nonsense physicist", i.e., his ideas were founded in a profound knowledge about the phenomenology and an amazing ability to extract the important bare essence of them to get the idea for his famous theories. E.g., he boiled down the problem with electrodynamics not being Galilei invariant to the fact that if you consider Newton's 1st law (independence of the natural laws of the choice of an inertial frame and the existence of an inertial frame in the first) the problem was that if Maxwell's equations are invariant under changes from one to another inertial frame then the (phase) velocity of em. waves must be independent of the motion of the light source wrt. any inertial frame, and this lead him to the reinterpretation of Lorentz transformations as the symmetry transformations for changing from one inertial frame to another as defining a new description of space and time. The math was there, btw, already in the 1890ies (Woldemar Voigt) and in Lorentz's and Poincare's works, but the essence of the physics, solidly based on phenomenology of electromagnetics is due to Einstein.

The same holds true for his work on the foundations of thermodynamics and its relation to (classical) statistical mechanics. The key idea again was very simple: If there is atomistic structure of matter and the macroscopic phenomenology is due to the coarse-grained description of these particle-like constituents of matter a la Boltzmann, there must be observable fluctuations. This lead him to his famous paper on Brownian motion and the dissipation-fluctuation theorem and many more (critical opalescence, blueness of the sky, etc.) and the determination of the Avogadro number.

The same happened with his greatest discovery, general relativity, where he realized that the essence of the gravitational interaction is the weak equivalence principle, which he took as the heuristical principle to formulate a relativistic theory of the gravitational interaction. Again it was based on very solid empirical facts. There was some confusion on the way due to mathematical obstacles. I'm also not sure, whether is overadmiration of Mach was helpful or rather an obstacle.

It's a bit different with his idea of "light quanta", and he was very critical against his own work in this respect, and indeed the naive "localized massless-point-particle picture" is utterly wrong, and he was dissatisfied with his own but unfortunately also with the modern description in terms of QED (Jordan+Born 1925/26, Dirac 1927 but also even after 1948, when the renormalization issue had been understood).

 

[gentzen]

I never understood why is that a problem. In classical physics, most of the languages (Newton, Lagrange, ...) do the same, and nobody complains that it's a problem. Even in quantum physics, the Lagrangian path integral formulation destroys the symmetry between position and velocity, and again nobody complains.

But BM is based on Hamiltonian mechanics, where this symmetry follows from the invariance under (linear) canonical transformations. Those canonical transformations are symmetries of undamped systems, symmetries of coupled oscillations, maybe not even harmonic oscillations, but undamped.

And it is a feature of BM that urges you to react. And many people did react: Antony Vallentini reacted by believing in the fundamental reality of those particles and their positions, Sabine Hossenfelder reacted by the dubious claim that any other observable too could play the role of positions in BM, some MWI proponents reacted by claiming that BM would be MWI in constant state of denial, ...

My own reaction is the suspicion is that it acts like a boundary condition with respect to symmetry breaking, and that the primacy of position is related to the "fact" that spatial boundary conditions are somehow unavoidable, while time or energy related bounday conditions are (or at least "feel") more optional.

 

[Demystifier]

Philosophers of science tend to event pseudo-problems which are simply not there like the "measurement problem" or the "ontology of elementary particles".

There is no such thing as pseudo-problem. Any problem is a real problem, if and only if someone subjectively perceives it as a problem. More importantly, dealing with a problem that only few people perceive as a problem may lead to a solution that many perceive as a progress. For example, thinking about the "measurement problem" lead to the theory of decoherence, and to the discovery of weak measurement. The progress in science is often induced by philosophy, whether you like it or not.

 

[Demystifier]

But BM is based on Hamiltonian mechanics

No it isn't. Perhaps you wanted to say that it is based on Hamilton-Jacobi mechanics? The Hamilton-Jacobi mechanics (unlike Hamilton mechanics) also breaks symmetry between positions and velocities. The fact that BM is not Hamilton mechanics plays an important role in understanding quantum statistical mechanics from a Bohmian perspective, in my recent https://arxiv.org/abs/2308.10500 .

 

[vanhees71]

I think all this was not induced by philosophy but by real physical problems, i.e., how to understand/interpret results of real-world measurements in terms of QT. The key of all these achievements is not some fictitious measurement problem but simply Born's rule, i.e., the probabilistic interpretation of the quantum state. The measurement problem was thus solved by Born's footnote in 1926 (it had even to be corrected in print that of course not $\psi(t,\vec{x})$ but $|\psi(t,\vec{x})|^2$ is the probability density for the position of the particle).

 

[Demystifier]

I think all this was not induced by philosophy but by real physical problems

It was induced by both.

 

[gentzen]

No it isn't. Perhaps you wanted to say that it is based on Hamilton-Jacobi mechanics? The Hamilton-Jacobi mechanics (unlike Hamilton mechanics) also breaks symmetry between positions and velocities.

I didn't know this. I will try to update my knowledge before continuing this discussion.

 

[vanhees71]

No it isn't. Perhaps you wanted to say that it is based on Hamilton-Jacobi mechanics? The Hamilton-Jacobi mechanics (unlike Hamilton mechanics) also breaks symmetry between positions and velocities. The fact that BM is not Hamilton mechanics plays an important role in understanding quantum statistical mechanics from a Bohmian perspective, in my recent https://arxiv.org/abs/2308.10500 .

In standard quantum mechanics the closed thing to phase-space physics is the one-particle density matrix in Wigner representation, but this Wigner function is NOT yet a valid phase-space distribution function, because it's real but not positive semi-definite. That's only a sufficiently coarse-grained quantity, and through the coarse graining you get macroscopic, classical behavior out of QT (including of course decoherence). No need for Bohmian magic at all!

 

[Demystifier]

In standard quantum mechanics the closed thing to phase-space physics is the one-particle density matrix in Wigner representation, but this Wigner function is NOT yet a valid phase-space distribution function, because it's real but not positive semi-definite.

There is also the Husimi distribution, defined in terms of coherent states. It is positive definite in the phase space, but (there is always a but) its marginalization over position (or momentum) does not lead to the usual distribution in momentum (or position) space. Nevertheless, there is a well defined measurement procedure that leads to the Husimi distribution, roughly this is what one gets when one attempts to measure position and momentum simultaneously. In this sense Husimi distribution is more physical than the Wigner one, but for some reason it is less well known.

 

[martinbn]

... Pauli's criticism that "Bohm's language destroys the symmetry between position and velocity,"...

Is there a symmetry that BM does not destroy?

 

[martinbn]

I never understood why is that a problem. In classical physics, most of the languages (Newton, Lagrange, ...) do the same, and nobody complains that it's a problem. Even in quantum physics, the Lagrangian path integral formulation destroys the symmetry between position and velocity, and again nobody complains.

You don't understand it because it is philosophy, which does not conform with your philosophy.

 

[gentzen]

Is there a symmetry that BM does not destroy?

I guess BM is still invariant under linear canonical transformations that don't mix conjugate variables. But you are right, even this is an interesting question, how it actually preserves the invariance in that case. I guess it preserves it in the same sense like "most of the languages (Newton, Lagrange, ...)" preserve the symmetry between position and velocity, namely that all you need to do is give up an overly literal interpretation of its language.

 

[martinbn]

I guess BM is still invariant under linear canonical transformations that don't mix conjugate variables. But you are right, even this is an interesting question, how it actually preserves the invariance in that case. I guess it preserves it in the same sense like "most of the languages (Newton, Lagrange, ...)" preserve the symmetry between position and velocity, namely that all you need to do is give up an overly literal interpretation of its language.

I meant it more generally. For example, bohmians believe that there is a preferred frame (undetectable in any way of course), so the symmetry between rest and motion is destroyed.

 

[Demystifier]

Is there a symmetry that BM does not destroy?

Translation symmetry, rotation symmetry, the usual discrete symmetries, ...

 

[Demystifier]

so the symmetry between rest and motion is destroyed.

This is actually a good point. In classical mechanics, acceleration is absolute, while velocity and position are relative. In Bohmian mechanics, even velocity is absolute, while only position is relative.

 

[vanhees71]

Without the slightest evidence for this being true!

 

[gentzen]

For example, bohmians believe that there is a preferred frame

Without the slightest evidence for this being true!

You both seem to have a very strong tendency to "reify" mathematical concepts, or at least the tendency to belief that bohmians would "reify" their mathematical concepts.
N David Mermin is very skeptical of that tendency, especially with respect to MWI proponents.

Am I right that you accuse bohmians of having metaphysical prejudices, because you belief that they mistake their mathematical concept for the true physical reality?

 

[Demystifier]

Without the slightest evidence for this being true!

Define "true". It is true in the same sense in which it is true that EM potential in the Coulomb gauge is not Lorentz invariant. Those who can't think of Bohmian trajectories as something "real" may still think of them as something analogous to gauge potentials.

 

[Demystifier]

bohmians believe that there is a preferred frame (undetectable in any way of course)

The only thing that Bohmians a priori believe, without actual evidence, is that nature can be described mathematically even in situations when it is not measured. Everything else, like nonlocality, trajectories, violation of certain symmetries, preferred frame, etc. are a posteriori properties of specific mathematical models that satisfy the a priori belief above in a way compatible with observations. There are Lorentz-covariant Bohm-like models without a preferred frame, there are even local Bohm-like models, but such models are less popular because they seem more contrived and complicated.

 

[martinbn]

Translation symmetry, rotation symmetry, the usual discrete symmetries, ...

Is that true? In what sense are they present? Consider a spherically symmetric source and detector. In QM this is truly symmetric. In BM the particle has a trajectory from the source to a point on the sphere of the detector. That is not spherically symmetric. It only looks like it because the trajectory is undetectable and over a large number of trials the results have agree with QM, so one says that the initial data is symmetric.

 

[martinbn]

You both seem to have a very strong tendency to "reify" mathematical concepts, or at least the tendency to belief that bohmians would "reify" their mathematical concepts.
N David Mermin is very skeptical of that tendency, especially with respect to MWI proponents.

Am I right that you accuse bohmians of having metaphysical prejudices, because you belief that they mistake their mathematical concept for the true physical reality?

Yes, but not in this discussion.

 

[martinbn]

The only thing that Bohmians a priori believe, without actual evidence, is that nature can be described mathematically even in situations when it is not measured.

You say this, but it is not true. Because QM has that property and yet bohmians are unhappy with it.

Everything else, like nonlocality, trajectories, violation of certain symmetries, preferred frame, etc. are a posteriori properties of specific mathematical models that satisfy the a priori belief above in a way compatible with observations. There are Lorentz-covariant Bohm-like models without a preferred frame, there are even local Bohm-like models, but such models are less popular because they seem more contrived and complicated.

You have given references for those, but so far I haven't seen one that does anything more than wishful thinking.

 

[Demystifier]

In BM the particle has a trajectory from the source to a point on the sphere of the detector. That is not spherically symmetric.

In physics symmetry refers to the laws (equations of motion), not to particular solutions.

 

[Demystifier]

You say this, but it is not true. Because QM has that property and yet bohmians are unhappy with it.

No, standard QM does not describe nature in the absence of measurement. Neither in a probabilistic sense (because the Born rule in arbitrary basis is only valid when an observable is measured, it cannot be universally valid due to the contextuality theorems), nor in a deterministic sense (Schrodinger equation is deterministic, but standard QM insists that nature is not deterministic).

Indeed, adherents of standard QM often emphasize that a physical theory should not describe nature in the absence of measurement, because any such description would necessarily be metaphysical. This fact (that standard QM does not describe nature in the absence of measurement) they see as a strength of standard QM, not as its weakness.

 

[Demystifier]

You have given references for those, but so far I haven't seen one that does anything more than wishful thinking.

Can you be more precise? What exactly is missing in these models to be more than "wishful thinking"?

 

[vanhees71]

Define "true". It is true in the same sense in which it is true that EM potential in the Coulomb gauge is not Lorentz invariant. Those who can't think of Bohmian trajectories as something "real" may still think of them as something analogous to gauge potentials.

They are not observable, and so are the electromagnetic potentials, no matter in which gauge you work. That's a mathematical fact, independent of any interpretation.

 

[Demystifier]

They are not observable, and so are the electromagnetic potentials, no matter in which gauge you work. That's a mathematical fact, independent of any interpretation.

You mean empirical fact, not "mathematical". And yes, Bohmians of course agree that trajectories are not observable. But the point is that even unobservable things have a role in theoretical physics, gauge potentials are an obvious example. Once we agree that unobservable things can have some role in physics, we can discuss what exactly is the role of the trajectories.

 

[Quantum Waver]

Indeed, adherents of standard QM often emphasize that a physical theory should not describe nature in the absence of measurement, because any such description would necessarily be metaphysical.

Isn't the point of measurement to figure out what nature is doing all the time? What makes a measurement special such that nature would behave differently? The standard CI inspired approach is deeply dissatisfying. Is there another scientific field that has this approach to measurement, other than psychology or sociology?

 

[vanhees71]

You mean empirical fact, not "mathematical". And yes, Bohmians of course agree that trajectories are not observable. But the point is that even unobservable things have a role in theoretical physics, gauge potentials are an obvious example. Once we agree that unobservable things can have some role in physics, we can discuss what exactly is the role of the trajectories.

No it's a mathematical fact, because gauge invariance means redundance, i.e., the same physical situation is described by different gauge potentials, and thus the gauge potential cannot be local observables already in the classical theory. At the QFT level in addition the gauge potentials do not obey the microcausality constraint and thus again cannot represent local observables. At least for these mathematical reasons the assumption that the em. potentials would represent observables, makes no sense. That's independent of any interpretation.