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

[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.