A skeptic's view on Bohmian Mechanics

[Demystifier]

In mathematical physics one doesn't need to justify the assumptions, only the conclusions.

Sure, but (1.4) is not presented as an assumption. And even if it was, the point is that such an assumption needs a justification for physical reasons, if we want to derive classical statistical mechanics from classical mechanics.

But let us not forget what it has to do with Bohmian mechanics. You object that some aspects of BM are not proved rigorously, and when I point out to you that analogue things are not proved rigorously in classical statistical mechanics, you argue that in classical statistical mechanics that's not a problem. If you hold the opinion that only the former and not the latter is a problem, then you have double standards. If one wants to be fair, one has to admit that either both are problems (of a very similar kind) or both are not problems.

 

[Demystifier]

Call me a local non-realist:

When I tried to make local non-realism logically consistent, I arrived at a kind of solipsism:
http://lanl.arxiv.org/abs/1112.2034

 

[zonde]

You judge too easily.

Please show me where he errs in his widely cited survey article about Bell inequalities and entanglement.

Here:

However, in all derivations two types of elements can be identified

• locality, no-signalling, non-contextuality
• classicality, hidden variables, classical logic, joint distributions, counterfactual definiteness, “realism”

Since Bell’s inequalities are found to be violated in Nature, one of these two assumptions needs to be dropped.

Bell's derivation is not assuming classicality. And Norsen pointed out this to Werner in his comment in that blog discussion (I can find proper references for this reasoning if you need):

Finally, why does this matter? Because your wrong understanding of Bell’s theorem is based on failing to grasp this very argument. You continue to talk as if the upshot of Bell’s theorem is that we have to choose (at least) one of (what you only quite vaguely describe as) “classicality” and “locality” to reject. You have said that you choose to reject “classicality” and retain “locality”. But the “boxes” argument, or equivalently the EPRB argument I’ve recapped above, shows that in fact this is not a viable option at all. Because what you actually mean by “classicality”, when we hold hands and look at the mathematical derivations (of the inequality) that you undoubtedly have in mind, is nothing but the idea of deterministic hidden variables. But then it is immediately obvious that you cannot “save locality” by abandoning these hidden variables: having the hidden variables was the *only way* to account for the perfect correlations (when Alice and Bob both measure along z) without nonlocality! So you simply cannot account for all the QM predictions in a local way without these hidden variables. (That’s what the EPR type arguments show.) Nor can you account for all the QM predictions in a local way *with* these hidden variables! (That’s what Bell showed!) So as it turns out the hidden variables — your “classicality” — is a completely and total red herring. You can only account for the QM predictions with a *nonlocal* theory. That’s what Bell proved. And all of our threories (I mean Bohmian mechanics, OQM, etc… leaving aside MWI which is also nonlocal but in a distractingly different way) exemplify this. You only convince yourself otherwise by equivocating — by claiming your theory is local (but with a new and different meaning, a meaning for which Bohmian mechanics, too, is “local”).

Even when one is not interested in mathematical details about all possible Bell inequalities, the first 9 pages make interesting reading. They contribute new aspects even for those familiar with Bell's work!

Can you explain how he gets $b_1=b_2$ from (12), (13) at page 9?

Though he understands the matter differently than you and the participants of the debate, you shouldn't think that he is naive or blind. He published extensively on the subject!

I do not think that he is naive. However there is that psychological phenomena that people protect their beliefs with communication barriers. If a person's beliefs are inconsistent with scientific approach it can make him blind to valid scientific reasoning.

 

[A. Neumaier]

You object that some aspects of BM are not proved rigorously, and when I point out to you that analogue things are not proved rigorously in classical statistical mechanics

Then you demonstrate by it that Bohmian mechanics doesn't solve the measurement problem since it only replaces it by the corresponding problem in classical mechanics.

If you hold the opinion that only the former and not the latter is a problem, then you have double standards. If one wants to be fair, one has to admit that either both are problems (of a very similar kind) or both are not problems.

I never claimed that classical statistical mechanics has no foundational problems; indeed it has more or less the same problems as quantum mechanics, though they get far less attention than the latter. A nice book reviewing the problems and partial solutions of classical statistical mechanics is L. Sklar, Physics and Chance, Cambridge 1993.

The problem of justifying that a classical measurement apparatus actually measures a classical microscopic observable is of the same level of difficulty as the problem of justifying that a quantum measurement apparatus actually measures a quantum microscopic observable. Both questions involve hard statistical mechanics.

 

[A. Neumaier]

Bell's derivation is not assuming classicality.

Bell's arguments are purely classical (i.e., based on a deterministic model). That's the whole point of hidden variables.

 

[A. Neumaier]

Can you explain how he gets $b_1=b_2$ from (12), (13) at page 9?

He describes it as Bob's guess. Not as a rigorous deduction.

 

[zonde]

Bell's arguments are purely classical (i.e., based on a deterministic model). That's the whole point of hidden variables.

This so called "classicality" is inferred (not assumed) from locality and prediction of perfect correlations.

 

[A. Neumaier]

If a person's beliefs are inconsistent with scientific approach it can make him blind to valid scientific reasoning.

Yes, and this is amply shown by both sides of the debate. Mind reading and misunderstandings abound.

 

[Demystifier]

Then you demonstrate by it that Bohmian mechanics doesn't solve the measurement problem since it only replaces it by the corresponding problem in classical mechanics.

Sure, BM doesn't solve the measurement problem rigorously. But that's true for almost any macroscopic phenomena, that our fundamental microscopic theories cannot explain them rigorously.

 

[zonde]

Yes, and this is amply shown by both sides of the debate.

Where does it shows in the arguments of Norsen?

 

[A. Neumaier]

Where does it shows in the arguments of Norsen?

This is off topic here, so I answered in a new thread.

 

[RockyMarciano]

Here:

Bell's derivation is not assuming classicality. And Norsen pointed out this to Werner in his comment in that blog discussion (I can find proper references for this reasoning if you need):

Norsen is wrong. QFT is an example of how you can reject hidden variables classicality and preserve locality in the form of microcausality, in a perfectly sound mathematical and physical way.

 

[RockyMarciano]

When I tried to make local non-realism logically consistent, I arrived at a kind of solipsism:
http://lanl.arxiv.org/abs/1112.2034

But that is because you don't seem to distinguish "philosophical realism" from "physical realism" i.e. classicality, as used in the context of EPR. they don't have anything to do with each other.

 

[stevendaryl]

But that is because you don't seem to distinguish "philosophical realism" from "physical realism" i.e. classicality, as used in the context of EPR. they don't have anything to do with each other.

What do you mean by those two terms?

 

[Demystifier]

you don't seem to distinguish "philosophical realism" from "physical realism"

Please, explain the difference!

 

[RockyMarciano]

What do you mean by those two terms?

Please, explain the difference!

The difference is very important and can be read in the literature on EPR and even in some QM books that have more extended space dedicated to this issue than the usual more concentrated with calculations and the Schrodinger equation.

Philosophical realism just asserts the existence of an external reality outside the mind. This is a very general principle and only a pure solipsist could deny it. Every scientist is realist in this sense, otherwise it wouldn't have any object of study or of observation.
Further distinctions can be made is this general form of assertion: metaphysical, gnoseological(and within this one:extreme, Kantian and Aristotelian,Platonic). But the essential point is that none of these has anything to do with the EPR realism or classicality which is a form of deterministic realism.
A definition of this last one is the assertion that if the value of a physical magnitude can be predicted with certainty, without perturbing the physical system, then there is an element of physical reality(in the sense of being determined spatially and temporally independent of any measurement) corresponding to this predicted physical magnitude, in other words the results of possible measurements are predetermined in time and space.

Are you guys seriously saying that this last realism(the one used in EPR and Bell'sm theorem discussions) is equivalent to the first that just denies solipsism as non-scientific?

 

[Demystifier]

A definition of this last one is the assertion that if the value of a physical magnitude can be predicted with certainty, without perturbing the physical system, then there is an element of physical reality(in the sense of being determined spatially and temporally independent of any measurement) corresponding to this predicted physical magnitude, in other words the results of possible measurements are predetermined in time and space.

OK, this defines what is physical realism, being the same as EPR realism. What is not clear, however, what then is physical non-realism? Where exactly should one put a "not" word in the explanation above to define non-realism?

 

[stevendaryl]

Philosophical realism just asserts the existence of an external reality outside the mind...
Further distinctions can be made is this general form of assertion: metaphysical, gnoseological(and within this one:extreme, Kantian and Aristotelian,Platonic). But the essential point is that none of these has anything to do with the EPR realism or classicality which is a form of deterministic realism.
A definition of this last one is the assertion that if the value of a physical magnitude can be predicted with certainty, without perturbing the physical system, then there is an element of physical reality... corresponding to this predicted physical magnitude, in other words the results of possible measurements are predetermined in time and space.

Well, I think that Einstein and Bell would disagree that the second definition has nothing to do with the first.

 

[zonde]

Norsen is wrong. QFT is an example of how you can reject hidden variables classicality and preserve locality in the form of microcausality, in a perfectly sound mathematical and physical way.

No, Norsen addressed this issue in the last sentence that I quoted. In QFT contexts "locality" is defined differently and is not the same as Bell's assumed "locality".
Norsen (bold mine):
"You only convince yourself otherwise by equivocating — by claiming your theory is local (but with a new and different meaning, a meaning for which Bohmian mechanics, too, is “local”)."

 

[RockyMarciano]

OK, this defines what is physical realism, being the same as EPR realism. What is not clear, however, what then is physical non-realism? Where exactly should one put a "not" word in the explanation above to define non-realism?

Non-realism is obviously dropping EPR Realism, which is not quite the same as declaring oneself solipsist(as you seem to incorrectly imply), and is perfectly physical as QFT shows.

 

[RockyMarciano]

Well, I think that Einstein and Bell would disagree that the second definition has nothing to do with the first.

I'm not sure about Bell, but I agree Einstein had some concerns there. But it is the general consense that he was not right about this particular issue in relation with QM. He had strongly assumed that the only possible reality was classical reality and saw no other possibility. Had he lived to learn about Bell's theorem and actual EPR experiments and QFT he might have changed his mind.

 

[Demystifier]

Non-realism is obviously dropping EPR Realism, which is not quite the same as declaring oneself solipsist(as you seem to incorrectly imply), and is perfectly physical as QFT shows.

My point is that EPR realism can be dropped in many different ways. Solipsism is one way, but there are also others. What is the "right" way?

As one possible meaning, let me copy-paste from my presentation at a conference:

1.2 Making sense of local non-reality

- One interpretation of Bell theorem: local non-reality
- Physics is local, but there is no reality.

- Does it mean that nothing really exists?
- That would be a nonsense!

Here is what it should really mean:

- Physics is not a theory of everything.
- Something of course exists, but that’s not the subject of physics.
- Physics is not about reality of nature,
it is only about what we can say about nature.
- In physics we should only talk about measurable stuff.
- It’s important to talk also about non-measurable stuff,
but just because it’s important is not a reason to call it physics.

Bell theorem ⇒ reality is non-local
- logically correct, but that is not physics

QM ⇒ signal locality
- that is measurable, so that is physics

In short, “local non-reality” should mean:
- Reality is non-local.
- Physics is about the measurable, which is local.

- In that form, local non-reality does not necessarily
need to be accepted, but at least can be reasonably debated.

 

[stevendaryl]

I'm not sure about Bell, but I agree Einstein had some concerns there. But it is the general consense that he was not right about this particular issue in relation with QM.

I would put Bell in the same camp as Einstein in this regard. And I don't agree that there is a consensus that Einstein was wrong. He was certainly wrong about local hidden variables--tests of Bell's inequality show that there are no such variables. As to whether the lack of local hidden variables implies nonrealism or nonlocality, there isn't a consensus.

 

[RockyMarciano]

No, Norsen addressed this issue in the last sentence that I quoted. In QFT contexts "locality" is defined differently and is not the same as Bell's assumed "locality".
Norsen (bold mine):
"You only convince yourself otherwise by equivocating — by claiming your theory is local (but with a new and different meaning, a meaning for which Bohmian mechanics, too, is “local”)."

Bohmian mechanics cannot be local in the way QFT is as BM is indistingushable from NRQM, so that is already showing Norsen assertions are at odds whith what most people know.
You could try and define what is the definition of locality(separated from classicality) that Bell assumed.

 

[RockyMarciano]

My point is that EPR realism can be dropped in many different ways. Solipsism is one way, but there are also others.

Glad you say this, I had the impression that you equated non-realism in the Bell context wih denying external reality. Solipsism is not a valid way for any scientist.

What is the "right" way?

Well', I'd say QFT is in the right path, but there are of course many things to solve.

 

[Demystifier]

I had the impression that you equated non-realism in the Bell context wih denying external reality.

Any comments on the extended version of my post #57?

 

[RockyMarciano]

I would put Bell in the same camp as Einstein in this regard. And I don't agree that there is a consensus that Einstein was wrong. He was certainly wrong about local hidden variables--tests of Bell's inequality show that there are no such variables. As to whether the lack of local hidden variables implies nonrealism or nonlocality, there isn't a consensus.

I guess I'm one of the lucky ones that has already reached a conclusion in the choice between nonrealism and nonlocality just by discarding any theory that contemplates FTL communication. It was not that hard, I'd say most physicists agree that predictive acausal nonlocality(that is nonlocality not just as a non-falsifiable ontology allowing "FTL influences" which adds nothing to a theory) is not compatible with science, which is causal(or at the very least microcausal like QFT shows) by definition.

 

[RockyMarciano]

As one possible meaning, let me copy-paste from my presentation at a conference:

1.2 Making sense of local non-reality

- One interpretation of Bell theorem: local non-reality
- Physics is local, but there is no reality.

- Does it mean that nothing really exists?
- That would be a nonsense!

Here is what it should really mean:

- Physics is not a theory of everything.
- Something of course exists, but that’s not the subject of physics.
- Physics is not about reality of nature,
it is only about what we can say about nature.
- In physics we should only talk about measurable stuff.
- It’s important to talk also about non-measurable stuff,
but just because it’s important is not a reason to call it physics.

Bell theorem ⇒ reality is non-local
- logically correct, but that is not physics

QM ⇒ signal locality
- that is measurable, so that is physics

In short, “local non-reality” should mean:
- Reality is non-local.
- Physics is about the measurable, which is local.

- In that form, local non-reality does not necessarily
need to be accepted, but at least can be reasonably debated.

I dislike the use of the word "reality" here because even if an effort is made in your reasoning to separate non-realism from solipsism it still assumes that reality is classical, and I also dislike the distinction between reality and physics that is added by you, as if reality wasn't precisely what is measurable in principle.
Non-realism, that I prefer to call non-classicality in the vein of the Werner text quoted by DrChinese can be reasonably debated just by defining reality as "measurable stuff", that is all is needed in QFT for instance.

 

[stevendaryl]

Here's the way that I understood Einstein's notion of realism. He thought of the world as a succession of physical states, where the current state determines the possible future states. Note that there is no assumption of determinism here, because this notion of realism is (to me) consistent with nondeterminism. Nondeterminism would just mean that there are many possible future states consistent with the current state.

(Relativity would generalize this, in the sense that given the history of the world, there are infinitely many ways to "slice" that history into a succession of states. Any laws of physics saying which future states follow from which current states would have to work for all possible ways of slicing.)

The point of Einstein's "elements of reality" is this: Suppose the world is in some state $S_1$ where you know with certainty the value of some future measurement; you know that measurement $M$ will result in $r$. Then if we make the non-solipsistic assumption that this prediction is revealing something about the world (as opposed to just being a prediction about future states of your own brain), then it seems that what we can conclude is that a future state $S_2$ is not possible if in state $S_2$ measurement $M$ has a different result than $r$. In that case, the "element of reality" can be defined explicitly:

For any state $S$, let $F(M,S)$ be the set of possible results of measurement $M$ in some possible future of $S$. The fact that $r \in F(M,S)$ is a fact about state $S$. It's an "element of reality".

So to me, Einstein's criterion for "elements of reality" just follows from the assumption that there exists a physical state, and the non-solipsistic view that the predictions of physics reveal something about the world.

So what does it mean to reject Einstein's realism? It seems to me that it means either solipsism, or it means rejecting the idea that there are physical states.

 

[stevendaryl]

I dislike the use of the word "reality" here because even if an effort is made in your reasoning to separate non-realism from solipsism it still assumes that reality is classical

What does it mean for reality to be classical or not?

 

[ShayanJ]

So what does it mean to reject Einstein's realism? It seems to me that it means either solipsism, or it means rejecting the idea that there are physical states.

But from your description, it seems to me that rejecting Einstein's realism means accepting contextuality which isn't discussed as frequently as realism or locality, although it seems to be the more important concept.

EDIT: It may seem that accepting that there is no state is the same as accepting contextuality. But I don't think so. Contextuality can mean that the state should always take into account the observer. Its even compatible with the existence of an underlying non-contextual theory.

 

[zonde]

Bohmian mechanics cannot be local in the way QFT is as BM is indistingushable from NRQM, so that is already showing Norsen assertions are at odds whith what most people know.

Locality in QFT is defined as spacelike separated observables commute. Bohmian mechanics is local in that sense.

You could try and define what is the definition of locality(separated from classicality) that Bell assumed.

J.S. Bell's Concept of Local Causality

 

[stevendaryl]

But from your description, it seems to me that rejecting Einstein's realism means accepting contextuality which isn't discussed as frequently as realism or locality, although it seems to be the more important concept.

I don't see how contextuality changes anything. According to Wikipedia (https://en.wikipedia.org/wiki/Quantum_contextuality), contextuality means

...the measurement result of a quantum observable depends on the specific experimental setup being used to measure that observable

I don't see how that affects the discussion of realism. In my description, nowhere did I assume noncontextuality.

As I understand it, noncontextuality would allow us to say: "The particle has spin up along axis $\hat{a}$", while contextuality would only allow us to say: "With such-and-such setup for measuring spin along axis $\hat{a}$, I got spin-up". That distinction is probably important, but I don't see how it affects the discussion of realism. Instead of the element of reality being the spin of the particle, the element of reality would be the future result of a measurement of the spin using such-and-such setup. It makes the elements of reality more complicated, but conceptually, I don't understand what difference it makes.

 

[ShayanJ]

For any state S, let F(M,S) be the set of possible results of measurement M in some possible future of S. The fact that r∈F(M,S) is a fact about state S. It's an "element of reality".

This notion of reality seems too fundamental for physics to be abandoned and its general enough to include QM too, even in the Copenhagen interpretation. So I think this is not Bell's notion of reality because he was trying to compare the classical laws of physics with the quantum laws of physics.(I mean laws that have the same familiar nature as the classical intuitive laws that we know, vs. the unintuitive laws with the same nature as QM.)

 

[Demystifier]

defining reality as "measurable stuff"

Measurable or measured? Spin is measurable, but is it real before it is actually measured?

Furthermore, suppose that we have entangled EPR pair of particles with spin. Suppose that spin of one particle is measured by Alice, and spin of another particle is measured by Bob. Suppose that Alice and Bob do not compare the results of their measurements. In this case, are both spins real? If yes, are the results of those measurements correlated? If yes again, is the correlation real?