I A skeptic's view on Bohmian Mechanics

[stevendaryl]

Right, that is realism, non-realism what I wrote above, they are incompatible. So?

I can't really extract a meaning from your statement.

 

[A. Neumaier]

You don't think BM and Bell-EPR are closely related?

Only if everything in the foundations is deemed closely related.

Your discussion sheds light neither on BM nor on the possible mutual misunderstandings displayed in the link in post 1, hence doesn't contribute constructively to the thread. It is ok to have one or two posts clarifying some intermediate arguments from another post in the thread, but not a continuing discussion of these unless they are directly related.

 

[RockyMarciano]

I can't really extract a meaning from your statement.

Well, non-realism denies realism, is this clearer?

 

[stevendaryl]

Not really. You can just as easily say Bob's result determines Alice's.

In either time-slicing, the future result is determined once you know the past results.

 

[RockyMarciano]

Only if everything in the foundations is deemed closely related.

Your discussion sheds light neither on BM nor on the possible mutual misunderstandings displayed in the link in post 1, hence doesn't contribute constructively to the thread. It is ok to have one or two posts clarifying some intermediate arguments from another post in the thread, but not a continuing discussion of these unless they are directly related.

Ok, this is certainly not directly related to the challenge in the OP, but then the thread has been off-topic for many more posts that has been on-topic.

 

[stevendaryl]

In compliance with Professor Neumaier's request, I will not discuss EPR in this thread.

 

[A. Neumaier]

then the thread has been off-topic for many more posts that has been on-topic.

Yes. The point where it becomes intolerable is subject to an uncertainty relation, but at some point it is a macroscopically definite observable.

 

[DrChinese]

In either time-slicing, the future result is determined once you know the past results.

I am not contesting that point. I am saying things outside of the time cone have no impact. That is directly the opposite of predictions by non-local interpretations, which say a time cone is not a limitation. I say there aren't any situations in which entanglement appears and effects occur outside of a time cone (or in some cases, 2 or more connected time cones). The time cone, of course, traced by c and no value higher.

 

[A. Neumaier]

That is directly the opposite of predictions by non-local interpretations, which say a time cone is not a limitation.

I'd be interested to know what happens in a relativistic version of Bohmian mechanics. Do the microscopic particle positions respect Einstein causality, or is the latter considered to be a statistical effect?

 

[PeterDonis]

I'd be interested to know what happens in a relativistic version of Bohmian mechanics.

Is there one?

 

[DrChinese]

Is there one?

I don't think so. On the other hand, demystifier is on record saying "... it cannot be said that there exists a well-defined relativistic QM." There's always an out!

http://xxx.lanl.gov/pdf/quant-ph/0609163v2

 

[zonde]

No. Bohmian mechanics is nonrelativistic and non-field, and its dynamics has not even a notion of spacelike separation that would be well-defined.

Are you saying that Bohmian mechanics allow FTL communication (that spacelike separated observables do not commute)?

 

[ShayanJ]

Are you saying that Bohmian mechanics allow FTL communication (that spacelike separated observables do not commute)?

Bohmian mechanics is like quantum mechanics, defined on the absolute space and time of Newton. There is no notion of space-like separated events in Newton's view!

 

[zonde]

This is a definition that simply mixes locality with realism making them indistinguishable while at the same time claiming it has nothing to do with realism and erroneously endorsing it to Bell. It is terribly confused.

Ok, then here are some of Bell's own words:
"It is important to note that to the limited degree that determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of “local causality” or “no action at a distance”. Of course, mere correlation between distant events does not itself imply action at a distance, but only correlation between the signals reaching the two places. These signals, in the idealized example of Bohm, must be sufficient to determine whether the particles would go up or down. For any residual undeterminism could only spoil the perfect correlation. It is remarkably difficult to get this point across, that determinism is not a presupposition of the analysis."

And please try not to use "realism" in QM context unless you mean "not solipsism" because it's very confusing what you mean with it. (is it determinism here? or causality? or particles having spin at all times?)

 

[zonde]

Bohmian mechanics is like quantum mechanics, defined on the absolute space and time of Newton. There is no notion of space-like separated events in Newton's view!

Hmm, we can say that there can be no photon or any massive particle that has trajectory trough both events if they are spacelike separated by definition.

 

[PeterDonis]

we can say that there can be no photon or any massive particle that has trajectory trough both events if they are spacelike separated by definition.

So what is the definition of "spacelike separated" in Newtonian mechanics? There isn't one--the concept simply does not exist in Newtonian mechanics.

 

[A. Neumaier]

Is there one?

This answer

That's because wave functions, described by relativistic wave equations (such as Dirac or Klein-Gordon equation), do not propagate faster than c.

to the comment

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c.

seems to suggest that there is one. But no reference is given...

 

[atyy]

Well, you said "I agree", so I thought that's what you got from what I said!
Anyway, that's exactly what I wanted to say. The physics community now is divided. The majority of physicists are happy with quantum mechanics and see no problem in it and just want to use it. There are some people who see some problems and want to solve them. These are not only Bohmians. Everyone who does some research on foundational issues is in this camp. So its not that there are problems that only Bohmians see, its just that Bohmians have their own way of looking at these problems. And I really don't see anything different here and that's what confusing me. Why everyone treats Bohmian mechanics so much different than other interpretations? Its not better than others but its not worse too!

Bohmian Mechanics is different from all other interpretations because it removes the weirdness from QM. That's why people don't like it. You can't write any more popsci books about how weird QM is. It's a PR and financial disaster for physics.

 

[atyy]

There is a lot of rigorous statistical mechanics done in mathematical physics. See, e.g., the nice book by Ruelle. The only approximation made there is the thermodynamic limit, replacing numbers like $N=10^{23}$ by infinity. One can then even estimate the relative error made by this replacement, and it is of the order $N^{-1/2}$, hence very tiny. Thus there is no barrier of the kind you seem to suggest. At least rigorously proving the validity of QM to 11 decimal places is in principle feasible.

Does this book explain why a priori probability density in the phase space is uniform? Or is it just an axiom?

I'm not sure what Ruelle's book exactly states, not the present state of the art. However, in general, the rigourous proofs are not sufficient either because the time needed for convergence to reach equilibrium is far longer than what is observed (eg. comments on ergodic theorems at the end of https://ocw.mit.edu/courses/physics...-fall-2013/lecture-notes/MIT8_333F13_Lec7.pdf), or when the convergence to equilibrium is fast enough it is restricted to some special class of dynamical systems (eg. Axiom A type https://en.wikipedia.org/wiki/Axiom_A or http://www.ihes.fr/~ruelle/PUBLICATIONS/[42].pdf) for which there is no proof that that class includes most physical systems.

Interesting comments on Axiom A systems here: https://arxiv.org/abs/1604.07672v1 and http://www.scholarpedia.org/article/Chaotic_hypothesis.

 

[ShayanJ]

it removes the weirdness from QM.

No it doesn't. The weirdness of QM is encapsulated in its violation of Bell-type inequalities. Bell guaranteed that we can't think about the microscopic world using our intuition from the macroscopic world. Any theory that violates Bell-type inequalities still has some of that weirdness and BM is no exception. Its true that in BM particles have definite positions and momenta at all times, but you have the quantum potential with its weird behavior and probably other weird things.

As I said, I myself don't like BM because I like a smart nature that can handle its business without giving that much attention to its details. I really don't like BM to be the actual mechanism behind the nature and I don't think it is. But this is not a physical argument and I won't let this undermine my ability to assess actual physical arguments for and against BM. What I don't like is when some people think that "I don't like it" is actually a physical argument!

 

[atyy]

No it doesn't. The weirdness of QM is encapsulated in its violation of Bell-type inequalities. Bell guaranteed that we can't think about the microscopic world using our intuition from the macroscopic world. Any theory that violates Bell-type inequalities still has some of that weirdness and BM is no exception. Its true that in BM particles have definite positions and momenta at all times, but you have the quantum potential with its weird behavior and probably other weird things.

As I said, I myself don't like BM because I like a smart nature that can handle its business without giving that much attention to its details. I really don't like BM to be the actual mechanism behind the nature and I don't think it is. But this is not a physical argument and I won't let this undermine my ability to assess actual physical arguments for and against BM. What I don't like is when some people think that "I don't like it" is actually a physical argument!

The Bell inequalities say reality is nonlocal. Reality is not weird unless you think nonlocality is weird.

 

[PeterDonis]

Everyone, "weird" and similar adjectives are subjective judgments, not scientific terms. Please keep the discussion on topic.

 

[ShayanJ]

The Bell inequalities say reality is nonlocal. Reality is not weird unless you think nonlocality is weird.

I think Bell's assumptions are a good description of what we'd call non-weird. Its not something subjective, Newtonian mechanics is not weird. But relativity is, and any theory that violates Bell-type inequalities is. Weird means non-intuitive and strange to our common sense and our intuition and common sense come from years of living as macroscopic beings dealing with other macroscopic beings and always moving much slower than light w.r.t. each other.
So for me, the fact that you can somehow rewire your mind so that you call relativity, non-locality, etc. intuitive and appealing to common sense doesn't mean that they're not weird. They're weird for a macroscopic being moving much slower than light.
I should mention that I have no problem with relativity and I really love it and have succeeded in developing an intuition for it but as I said that's not natural for a human being.

 

[PeterDonis]

I think Bell's assumptions are a good description of what we'd call non-weird.

Yes, but it's still your opinion and not something that's amenable to scientific testing. So, as I said, it's off topic. This thread is supposed to be about scientific aspects of Bohmian mechanics, not who does or does not think it is "weird". Please bear that in mind.

 

[atyy]

So I would ask any Bohmian why there is a limit - in a nonlocal theory - to entanglement which exactly matches the limits given by c. You never see 2 entangled particles unless they were in contact (limited by c) with some other system that gave rise to the entanglement. I would think that non-local mechanism would give rise to entanglement of all kinds of other things where c is not a limiting factor, if it is also the "out" that explains quantum non-locality. (And yes I know BM is supposed to be equivalent to QM, but this question still seems open to me.)

This part is put in by hand, but it is not restricted to Bohmian Mechanics, and we can restrict ourselves to Copenhagen QM. If we take the Wilsonian view of QFT (in the Copenhagen interpretation), then QED should be thought of as conceptually arising from a non-relativistic quantum mechanical system such as lattice QED. There are also other ways in which relativistic QED can arise from a non-relativistic lattice theory with different degrees of freedom than just a discretization of QED. In these systems, technically, FTL is permitted. In practice they are not. These are governed by Lieb Robinson bounds: https://arxiv.org/abs/0808.2495.

Within BM, in addition to emergent relativity via a Lieb-Robinson bound, the other assumption that is important is quantum equilibrium. In particular cases, this can be justified analogously to how equilibrium statistical mechanics can arise from Newtonian mechanics.

The two key ideas are:
1. Quantum equilibrium allows BM to approximate non-relativistic QM as closely as needed.
2. Lieb Robinson bounds allow non-relativistic QM to approximate relativistic QM as closely as needed.

Taken together these are at the physics level of rigour (but the Lieb-Robinson bound has been made very rigourous), and the major flaw in this argument is that even at the physics level of rigour the argument does not yet seem to go through for chiral fermions interacting with non-abelian gauge fields. I believe it is fine for QED and quantum gravity.

 

[A. Neumaier]

what Ruelle's book exactly states, not the present state of the art.

Its an old book, thus it definitely doesn't tell the state of the art. But in math, old books don't become obsolete, truth is truth at all times.
Most results, however, are not based on the ergodic theorem, so what you write is not so relevant.

 

[A. Neumaier]

What I don't like is when some people think that "I don't like it" is actually a physical argument!

Why did you then complain when I argued that physicists make choices based on with what they can feel happy? It is not a physics argument but an argument why one is prepared to consider certain assumptions or arguments as fruitful. Fruitful is also a subjective aspect, but very important in the development of science!

 

[atyy]

Its an old book, thus it definitely doesn't tell the state of the art. But in math, old books don't become obsolete, truth is truth at all times.
Most results, however, are not based on the ergodic theorem, so what you write is not so relevant.

You are clearly not familiar with the work you cite! Ruelle's resulst are axiom A results!

 

[Demystifier]

If by real you mean EPR real, they are not.

So, if I understood you correctly, the first spin is EPR real (because it is measured by Alice), the second spin is also EPR real (because it is measued by Bob), but both spins together are not EPR real (because nobody observed both spins). Is that what you are saying?

 

[Demystifier]

So my point is that non-realism has nothing to do with saying "nothing exists". It only has to do with saying: "no initial configuration determines the observed outcome."

I think this should be called non-determinism.

We live in a subjective universe, and how we choose to observe actively shapes the reality we see.

This is non-realism. But I never understood why so many people think that non-determinism and non-realism is the same.