Graduate Would this experiment disprove Bohmian mechanics?

[bolbteppa]

There is no "assumption of no path" anywhere.

Even proponents of BM, such as slide 4 of http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf , are very clearly aware that all of standard QM can be based on the claim that there are no paths (after which you need to set up things to replace CM and this is the 'positive content' of QM as Landau calls it), it literally quotes the Landau reference I keep bringing up:

..an attitude which propagated into more or less every modern textbook:
“It is clear that [the results of the double slit experiment] can in no way be reconciled with the idea that electrons move in paths.
In quantum mechanics there is no such concept as the path of a particle.” [Landau and Lifshitz]
slide 4 - http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf

In BM the Schrodinger equation comes out of thin air, it's completely unjustified... In normal QM it absolutely does not come out of thin air, it is derived, either as e.g. Dirac does it, or as e.g. Landau does based on the HUP claiming no paths exist, Born, and the necessary existence of a quasi-classical limit, it's all in the Landau reference from first principles that even BM proponents reference...

The Schrodinger equation in BM is clearly just stolen from QM and at best (this is very common) hand-wavingly justified by the existence of these historical derivations as if that makes any theoretical sense or with ludicrous things like the de Broglie relation or probability conservation out of thin air - one can even understand why people would go along with BM: 'if you take X as axioms then Y happens', fine, but it's just a game unless one can face up to the immediate issues that normal QM answers so concisely in starting from 'no paths exist'... The Durr references are no basically different to all the other BM references in this respect.

Clearly if you steal an equation derived on the assumption of no paths and then end up with paths you've made such a gigantic error your 'theory' is immediately nonsense, it's so basic...

What de Broglie and later Bohm did was to use the Schrödinger equation and the resulting wave function but they reinterpreted the physical meaning of this wave function completely compared to the mainstream Copenhagen interpretation, which indeed has more problems than it pretends to solve

I am not even going after the many contradictions other people claim arise even when you take BM at face value, that's another huge discussion, my issues with BM are way more basic, the very tools it uses are completely illegitimate to even use if they do not begin by declaring that paths don't exist and this by itself immediately invalidates the whole thing.

 

[bolbteppa]

So let me try to explain your objection against BM in my own words. You like the idea that the theory is based on paths. You just don't like the idea that a theory that is based on paths takes the Schrodinger equation as one it's postulates. You would be more happy if Schrodinger equation was somehow derived, perhaps as some kind of approximation resulting from a more fundamental theory based on paths. Would that be right?

If that's your objection, then I can agree with you that such theory would be much better than BM. And some people are trying to do something like that. Nevertheless, such attempts have not been very successful, so BM seems to be the best we can do at the moment. Perhaps we should not take BM too seriously as the final theory, but I believe that at least it can serve as an inspiration in a search for a better theory.

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

 

[Demystifier]

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

 

[Lord Jestocost]

If we accept the terminology according to which Bell theorem shows that QM is non-separable, and...

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

 

[vanhees71]

My question is this. If we accept the terminology according to which Bell theorem shows that QM is non-separable, and if we accept the QFT-textbook terminology according to which relativistic QFT interactions are local, then what is the correct word to describe BM? Is BM non-local, or is it just non-separable?

Another important point. To understand locality of interactions in quantum theory, you don't need to deal with QFT. Ordinary non-relativistic QM has local interactions if the potential in the $n$-body Schrodinger equation has the form
$$V({\bf x}_1,\ldots, {\bf x}_n)=V_1({\bf x}_1)+\cdots +V_n({\bf x}_n)$$
BM works perfectly for such local interactions in non-relativistic QM and again leads to characteristic Bohmian "non-locality" in entangled states. Again, would you call it non-locality of BM or non-separability of BM?

Or perhaps we need a third word to charactrize BM?

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory. What you call "non-local" in QM or BM should, however, be renamed somehow, but this will be impossible, because the unprecise language with this notion is too common.

"Locality" should be preserved for the notion in relativistic (Q)FTs, and then you should somehow name the "quantum correlations" described by entanglement differently. I think these correlations are what Einstein had in mind what he called it "inseparability" ("Inseperalität" in German). That's why my suggestion is to call it inseparability.

 

[vanhees71]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

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.

 

[Demystifier]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

The first half of the Bell's theorem is indeed an inequality which only talks about local classical theories. But there is also the second half, which shows that quantum mechanics violates the inequality from the first half.

 

[Demystifier]

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory.

That of course is wrong. Newtonian mechanics (which is more general concept than Newton gravity) can have both local and non-local forces. The Newton gravity is of course non-local, but potential of the form I have written in the post above is local, i.e. does not involve action at a distance.

 

[vanhees71]

Local forces are only if you have an external field, i.e., if $\vec{F}=\vec{F}(t,\vec{x}(t))$. Interactions must be instantaneous due to the Lex Tertia. That's the very point why the most simple way to realize causality in relativity is to use fields to describe interactions, i.e., you can obey momentum conservation without action at a distance since the fields are dynamical quantities carrying energy, momentum, etc.

 

[bolbteppa]

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

If I had to choose two books I would pick Landau and Dirac, of these two I would pick Landau - it's amazing that Bell translated it and becomes one of the main BM proponents

The whole Landau-Peierls Bohr-Rosenfeld relativistic quantum theory debacle is fascinating, c.f. volume 4 section 1 also, its this kind of craziness that made me look at BM properly, I can't imagine how BM could ever deal with these kinds of things (even if it made sense non-relativistically).

 

[Demystifier]

Local forces are only if you have an external field, i.e., if $\vec{F}=\vec{F}(t,\vec{x}(t))$.

That's in perfect agreement with what I said about local forces in non-relativistic Newtonian mechanics.

 

[vanhees71]

That's the big question. I'd be converted completely to BM as soon as it could be sensibly used for relativistic QFT. My feeling is, it won't be about particle trajectories but field equations with an "infinite tower" of equations a la the Schwinger-Dyson equations in standard QFT.

BTW I don't know, whether I ever have understood anything of Bohr's writings. I mean original papers by Bohr. I cannot make sense of his reply to the infamous EPR paper with the same title.

The Peierls argument concerning the non-localizability of relativistic particles, however has a heuristic point, clearly telling every beginner in relativistic QT not to waste time with socalled "relativistic QM", which is even more difficult and even less well-defined than relativistic QFT. In other words, start with relativistic QFT right away. In the "extreme relativistic" case, i.e., massless quanta (e.g., photons) you cannot even define a position observable to begin with. So any attempt to use first-quantization pictures for relativistic QT are a priori flawed, and indeed the best theory Dirac could come up with within a heuristical start with first quantization was his hole-theoretical formulation of QED, which is finally equivalent to the QFT formulation of QED, which is the only way QED should be taught in the 21st century. So forget Bjorken/Drell vol. I. Vol. II is better but also outdated (although some things are very well treated compared to some more sloppy treatments in more modern textbooks, e.g., the LSZ reduction formula).

 

[vanhees71]

That's in perfect agreement with what I said about local forces in non-relativistic Newtonian mechanics.

Yes, but they are always an approximation. The really fundamental systems in Newtonian mechanics are however closed systems of interacting particles obeying the Third Law, and thus are action-at-a-distance models.

 

[bolbteppa]

The Peierls argument concerning the non-localizability of relativistic particles, however has a heuristic point, clearly telling every beginner in relativistic QT not to waste time with socalled "relativistic QM", which is even more difficult and even less well-defined than relativistic QFT. In other words, start with relativistic QFT right away. In the "extreme relativistic" case, i.e., massless quanta (e.g., photons) you cannot even define a position observable to begin with. So any attempt to use first-quantization pictures for relativistic QT are a priori flawed, and indeed the best theory Dirac could come up with within a heuristical start with first quantization was his hole-theoretical formulation of QED, which is finally equivalent to the QFT formulation of QED, which is the only way QED should be taught in the 21st century. So forget Bjorken/Drell vol. I. Vol. II is better but also outdated (although some things are very well treated compared to some more sloppy treatments in more modern textbooks, e.g., the LSZ reduction formula).

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.

 

[Lord Jestocost]

The word "realism" I'd completely abandon from any serious physics discussion.

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."

 

[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?