An argument against Bohmian mechanics?

[PeterDonis]

the next sentences of my post where I actually explain what, physically, I say is not observable

No, you don't, because you're not giving the word "realist" any precise mathematical meaning. (At first you didn't give the word "local" any precise mathematical meaning either, but I think it's established now that for you that means "no FTL signaling", which can be precisely defined mathematically.)

 

[PeterDonis]

Is this Bell's explanation in book?

It's in one of his original papers, which are published in Speakable and Unspeakable in Quantum Mechanics. I don't have any links handy to online versions.

 

[zonde]

I'm not sure I understand what you posted but it seems you missed my point, I'm saying that there should be falsifiable content in a theory, in other word the physical claims of a theory should be testable in principle, if a hidden variables theory claims to allow or not allow FTL influences that should be testable or it has no meaning in addition to having hidden variables determining the measurement outcomes.

Yes, there should be falsifiable content predictions in a theory. But I would not say there are claims in the theory, there are predictions and there are assumptions. Assumptions are indirectly tested by checking that reality is consistent with predictions of the theory.
Hidden variables theory without FTL influences obey Bell inequalities. That's prediction that can tell apart two types of hidden variables theories as hidden variables theory with FTL influences can violate Bell inequalities.

 

[Jilang]

Sorry for not responding to this sooner. In the EPR experiment, Alice and Bob each have probability exactly 1/2 of measuring spin-up along whatever direction they choose to measure spins. The mathematical explanation is that neither Alice's nor Bob's particle is in a superposition, but the two-particle composite system is in the state $\frac{1}{\sqrt{2}} (|u\rangle |d\rangle - |d\rangle |u\rangle)$.

I'm not sure if that answers your question...

Is this just not a result of ignorance of which particle of the pair you have and also which pair you have? Two levels of ignorance, so to speak.

 

[RockyMarciano]

No, you don't, because you're not giving the word "realist" any precise mathematical meaning.

Maybe you missed it but I defined several times what I(and many others) call realist, even quoted explicitly the definition from the Nature paper I linked. If you mean that you don't know what the math content of such definition is just say so and I'll provide it, but I would think everyone at this point knows what the math content of classical deterministic theories with hidden parameters is.
I'm still puzzled by your questions. do you read my answers?

 

[stevendaryl]

Is this just not a result of ignorance of which particle of the pair you have and also which pair you have? Two levels of ignorance, so to speak.

I think you can distinguish which particle without destroying the entanglement. If there is an electric field, for instance, the positron will drift in one direction and the electron will drift in the other.

 

[RockyMarciano]

Hidden variables theory without FTL influences obey Bell inequalities. That's prediction that can tell apart two types of hidden variables theories as hidden variables theory with FTL influences can violate Bell inequalities.

The distinction between assumptions and predictions is fine, but you are not applying it here. The assumption of FTL influences being possible or not in hidden variables theories is not a prediction: in the case when it is assumed there are FTL influences like in the Bohmian interpretations, it is not predicted that FTL signaling is possible, do you agree?(see post #141 if you are doubtfult).
And in the case where it is assumed there are no FTL influences (so called "local hidden variables") actually its math content assumes galilean invariance (i. e. is compatible with infinite propagation velocity like in classical deterministic theories like classical mechanics and like NRQM but NRQM is not hidden variables-aka realist, aka classical deterministic and thus its predictions violate Bell inequalities), there is no constant finite speed limit, so it can't actually predict "no FTL signaling" according to its math content. Do you not agree with this?
So what violations of BI tell apart is classical deterministic hidden variables theories from non-hidden variables theories.

 

[RockyMarciano]

@stevendaryl I''m actually also curious if you agree with anything I wrote in my previous post, and if not where you think I'm wrong.

 

[stevendaryl]

@stevendaryl I''m actually also curious if you agree with anything I wrote in my previous post, and if not where you think I'm wrong.

Which one? The one that starts "The distinction between assumptions and predictions is fine..."

 

[PeterDonis]

If you mean that you don't know what the math content of such definition is just say so and I'll provide it

That would be helpful.

 

[Demystifier]

$\lambda$ is a variable permanently associated with each electron (in Bohmian mechanics, it would be the position of the electron at some reference time, $t_0$).

No. In Bohmian mechanics, $\lambda$ are the positions (at $t_0$) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

In fact, to understand why BM leads to the same measurable predictions as standard QM, the apparatus positions are much more important than the electron position. See
https://arxiv.org/abs/1112.2034

 

[zonde]

No. In Bohmian mechanics, $\lambda$ are the positions (at $t_0$) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

Does $\lambda$ have to include positions for particles of random number generator that will determine if measurement apparatus will be rotated/not rotated right before measurement in order to make correct predictions?

EDIT: Obviously you can't make prediction without output of random number generator. So the question should be if it's possible to make two conditional predictions based on output of RND.

 

[zonde]

The distinction between assumptions and predictions is fine, but you are not applying it here. The assumption of FTL influences being possible or not in hidden variables theories is not a prediction: in the case when it is assumed there are FTL influences like in the Bohmian interpretations, it is not predicted that FTL signaling is possible, do you agree?(see post #141 if you are doubtfult).
And in the case where it is assumed there are no FTL influences (so called "local hidden variables") actually its math content assumes galilean invariance (i. e. is compatible with infinite propagation velocity like in classical deterministic theories like classical mechanics and like NRQM but NRQM is not hidden variables-aka realist, aka classical deterministic and thus its predictions violate Bell inequalities), there is no constant finite speed limit, so it can't actually predict "no FTL signaling" according to its math content. Do you not agree with this?

"no FTL signaling" is not a valid prediction. Valid prediction is that particular phenomena have such and such properties that it can't be used to get FTL signaling.

So what violations of BI tell apart is classical deterministic hidden variables theories from non-hidden variables theories.

I don't see how this follows from what you said.

 

[stevendaryl]

No. In Bohmian mechanics, $\lambda$ are the positions (at $t_0$) of all particles relevant for the experiment. This includes the position of that electron, as well as positions of all particles constituting the measuring apparatus.

Ah! Thanks.

 

[Demystifier]

Does λ have to include positions for particles of random number generator that will determine if measurement apparatus will be rotated/not rotated right before measurement in order to make correct predictions?

Yes, except with the caveat that it is really a pseudo-random number generator.

 

[Gan_HOPE326]

Sorry for jumping in without having read the full 22-pages thread but just excerpts of it, but this is a topic I'm dearly interested in as I find Bohmian mechanics pretty fascinating, if only because it provides a very useful way to visualise otherwise pretty alien concepts. The paper linked from the OP seems to me to fail the way Demystifier pointed out: it relies on expectation values for correlations $x(t)x(0)$, ignoring that this is not what experiments actually measure. If I were to measure $x(0)$ then I'd alter the wavefunction depending on the uncertainty on position given by my apparatus, and any successive time evolution would have to start not with the groundstate but with a function centred around the measured value. Ideally, if I measured it with infinite precision it'd be a delta function, with no knowledge at all about the momentum of the particle. Such a function would of course contain a lot of high-energy modes from the oscillator, therefore the connected Bohmian particle would move, as it happens in mixed states.

I'd also like to point out this paper that I've been working with since it's interesting for me from a computational point of view:

http://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.041013

This "Many Interacting World" interpretation rewrites Bohmian mechanics by doing away with the wavefunction altogether, or rather, using it as a 'regular' field that generates a (functionally pretty complex) force between copies of the same particles across 'worlds'. In this way the problem of the unidirectional effect of the wavefunction on the particle is solved: if we consider all the particle's copies, when A acts on B, B acts on A equally. I'm not really much into exploring the philosophical implications of such an interpretation or whether it counts as 'real', but I think it's a perhaps more easily acceptable way to look at Bohmian mechanics since it makes it much less 'alien' compared to other classical systems.

 

[RockyMarciano]

I don't see how this follows from what you said.

Easy, if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example), even if they have different assumptions about FTL influence, they are equivalent as theories, they could be only considered as different interpretations of the same hidden variables theories that is put in mathematical terms in the Bell inequalities.

The same situation happens with the different interpretations of QM, all being the same theory even if their assumptions are contradictory.
So the value of experiments violating the BI can be interpreted as rejecting deterministic hidden variable theories, and I say only theories, because for instance interpretations of QM are of course not affected as long as they don't claim themselves to be independent theories.

 

[RockyMarciano]

Which one? The one that starts "The distinction between assumptions and predictions is fine..."

I think my point is clearer in #437.

 

[PeterDonis]

if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example), even if they have different assumptions about FTL influence, they are equivalent as theories

Huh? On your definition of "local", there is no such thing as a "nonlocal hidden variable theory", because all of them agree that FTL signaling is impossible. So what you should be saying here is simply that by your definition, there are no nonlocal hidden variable theories, period. You should not be saying anything about the predictions that nonlocal hidden variable theories make, because by your definition there are no such theories.

On Bell's definition of "nonlocal", where it means "violates the Bell inequalities", then it is meaningful to talk about the predictions of nonlocal hidden variable theories. But by definition, those are distinguishable as theories from local hidden variable theories, since the latter satisfy the Bell inequalities. The fact that both agree that FTL signaling is impossible does not make them equivalent as theories, since the Bell inequalities can be tested experimentally.

 

[RockyMarciano]

Huh? On your definition of "local", there is no such thing as a "nonlocal hidden variable theory", because all of them agree that FTL signaling is impossible. So what you should be saying here is simply that by your definition, there are no nonlocal hidden variable theories, period. You should not be saying anything about the predictions that nonlocal hidden variable theories make, because by your definition there are no such theories.

But I explained how my definition of local(and of nonlocal) has no empirical content when applied to hidden varaible theories. If I gave predictive value to "local" you would be right. But I showed how it doesn't have predictive value. Otherwise it should be easy to show how local or non local hiddenvariables predict FTL signaling/no signaling. The nonlocal case is clear enough, do you think local hidden variables predict "no FTL signaling"? Then violation of the inequalities should convince you FTL signaling is possible. Does it?

On Bell's definition of "nonlocal", where it means "violates the Bell inequalities", then it is meaningful to talk about the predictions of nonlocal hidden variable theories. But by definition, those are distinguishable as theories from local hidden variable theories, since the latter satisfy the Bell inequalities. The fact that both agree that FTL signaling is impossible does not make them equivalent as theories, since the Bell inequalities can be tested experimentally.

I agree if one defines nonlocal as "violates the Bell inequalities", but this cause all kind of confusion, even more if as I said it can be shown that for hidden variable theories local/nonlocal can be seen as different interpretations of the same hidden variable theory(much as it happens with QM interpretations). Then the test of the inequalities gives a clear way to reject hidden variables altogether.

 

[PeterDonis]

I explained how my definition of local(and of nonlocal) has no empirical content

Which makes no sense to me since FTL signaling is something that is straightforward to test for. So testing whether a theory's predictions are "local" (no FTL signaling) or "nonlocal" (allows FTL signaling) is straightforward. And by that definition, all theories we currently know of are local. There are no nonlocal theories.

when applied to hidden varaible theories

I don't see how this matters at all. There are no nonlocal hidden variable theories by your definition, but there are no nonlocal non-hidden-variable theories by your definition either. (At least, none that have not been ruled out by experiment.) Hidden variables are simply irrelevant to local/nonlocal by your definition.

I showed how it doesn't have predictive value

You did no such thing. You did the opposite, by defining "local" and "nonlocal" in terms of FTL signaling, which obviously has direct predictive value since it can be directly tested.

Otherwise it should be easy to show how local or non local hiddenvariables predict FTL signaling/no signaling.

You don't even appear to understand your own definition. Once again: by your definition, there are no nonlocal theories. Hidden variable/no hidden variable is irrelevant. You can't even "show" anything about what "nonlocal hidden variables" predict until you have a theory to use to do the predicting. There isn't one.

Of course there are hidden variable theories that predict violations of the Bell inequalities, but you have explicitly said that is not the definition of "nonlocal" you want to use. And yet you keep talking as if there are "nonlocal" theories that we can discuss. There aren't.

for hidden variable theories local/nonlocal can be seen as different interpretations of the same hidden variable theory

Are you reading what you write? You are saying here, if we use your definition of "local" and "nonlocal", that theories that predict no FTL signaling, and theories that predict FTL signaling is allowed, "can be seen as different interpretations of the same hidden variable theory". That is obviously self-contradictory since the predictions differ for a direct observable.

 

[RockyMarciano]

A condition to understand what I wrote is the following: I've made a clear and reasoned distinction between the definitions "doesn't/does allow FTL communication" as assumptions(not predictions) in a theory in which they can't be verified by construction of the theory, and the definitions in other contexts where they can be given a testable meaning easily. Of course for anyone not being able to grasp this distinction or that ignores the arguments I gave for it will find incomprehensible what I wrote.

 

[RockyMarciano]

Example:Bohmian mechanics assumes, but doesn't predict "FTL communication". If it predicted it , it woulnd't be an interpretation of QM.

 

[PeterDonis]

the definitions "doesn't/does allow FTL communication" as assumption in a theory in which they can't be verified by construction of the theory

And this definition means nothing to me, because I don't care about it. I care about the testable definition, since that's the one that has obvious physical meaning. Basically you're making up your own definition of something and then arguing that it's not verifiable. You may be right, but so what?

 

[RockyMarciano]

And this definition means nothing to me, because I don't care about it. I care about the testable definition, since that's the one that has obvious physical meaning. Basically you're making up your own definition of something and then arguing that it's not verifiable. You may be right, but so what?

I justified why I consider local/nonlocal not to have predicitive value in a hidden variables theory(if you think it does have tell me how and you may convince me). I think it helps to clarify how experiments showing violations of Bell's inequalities should be interpreted. Similarly different interpretations of QM with a lot of assumptions with no predictive value, some of them quite outrageous serve for some to clarify the meaning of QM wheter one cares for those weird assumptions or not.

 

[PeterDonis]

I justified why I consider local/nonlocal not to have predicitive value in a hidden variables theory

I'm sorry, I can't even understand why anyone should care about your definitions so what you think of as a justification I see as meaningless.

 

[RockyMarciano]

Hmm, I think you are not seeing the difference between assumptions and predictions. In any case my definitions are taken from the paper I linked. It's simply that they don't have predictive value in the context of deterministic hidden variables theories. Take Galilean relativity, even if compatible with no constant finite speed, it doesn't actually predict FTL signaling, but it also assumes local action as separability of inertial frames and yet it doesn't predict "no FTL signaling" either.

 

[PeterDonis]

I think you are not seeing the difference between assumptions and predictions.

I think you are insisting on using words in a very unusual and idiosyncratic way, and then wondering why what you say doesn't make sense to others.

Take Galilean relativity, even if compatible with no constant finite speed, it doesn't actually predict FTL signaling, but it also assumes local action as separability of inertial frames and yet it doesn't predict "no FTL signaling" either.

I don't understand what all this means, except for "no constant finite speed". The way I would describe Galilean relativity, as opposed to SR, is that Galilean relativity allows instantaneous causality--two events can be causally connected regardless of their separation in space as compared to their separation in time (the latter can even be zero). But Galilean relativity is perfectly compatible with light having a finite speed; it just won't be a finite invariant speed, it will vary depending on the observer's state of motion relative to the source.

 

[zonde]

Easy, if neither local nor nonlocal hidden variables theories are capable of producing verifiable predictions about FTL signaling(do you agree with this?, if not give some example),

I agree.

even if they have different assumptions about FTL influence, they are equivalent as theories, they could be only considered as different interpretations of the same hidden variables theories that is put in mathematical terms in the Bell inequalities.

Two theories do not have to produce different predictions for any test. Different theories can agree about some prediction but disagree about other predictions. Bell inequality violations can be experimentally tested and that's enough to say that they are different theories rather than just interpretations.

 

[RockyMarciano]

I agree.

Two theories do not have to produce different predictions for any test. Different theories can agree about some prediction but disagree about other predictions. Bell inequality violations can be experimentally tested and that's enough to say that they are different theories rather than just interpretations.

They don't have to do it for any test, but I'm only referring to one specific test, the one that bears on the distinction local/nonlocal. So of course the experimental test of BI's violations is enough to tell apart deterministic hidden variables theories from non-deterministic(nonhidden variables) theories and that's what it does. In many books and papers they call this telling apart local and nonlocal theories(like in the example you linked), because they use "local" to mean deterministic hidden variables which causes further confusion.

One very clear example of the confusion is that Bohmian mechanics is an interpretation that is deterministic hidden variables but as a theory it must follow QM predictions that are non-deterministic as confirmed by experiment, so it is actually a non-deterministic non-hidden variables theory with deterministic hidden variables interpretation. The word "schizofrenic" mentioned in previous posts could define this situation.

 

[RockyMarciano]

I think you are insisting on using words in a very unusual and idiosyncratic way, and then wondering why what you say doesn't make sense to others.

In fact I'm insisting on something you are also insisting on(although paradoxically you also insist on saying you don't care when someone attempts to do it) , namely disentangling(npi) the confusing content of ordinary language from what the mathematical and physical content of experiments and Bell's theorem actually imply. And believe me it is not an easy task.

I don't understand what all this means, except for "no constant finite speed". The way I would describe Galilean relativity, as opposed to SR, is that Galilean relativity allows instantaneous causality--two events can be causally connected regardless of their separation in space as compared to their separation in time (the latter can even be zero). But Galilean relativity is perfectly compatible with light having a finite speed; it just won't be a finite invariant speed, it will vary depending on the observer's state of motion relative to the source.

Great, the way you would describe it is basically showing that you did understand what I meant(or that you knew it all along). Since Galilean relativity is perfectly compatible with finite(just not invariant) and infinite speeds it cannot predict observable consequences with respec to FTL signaling being allowed or forbidden. Theories mathematically based on Galilean relativity and without further postulates with predictive content like classical mechanics don't violate the BI. Of course things change if they incorporate additional postulates with predictive content, like the Born rule in QM, in which case they violate the BI.

 

[PeterDonis]

Galilean relativity is perfectly compatible with finite(just not invariant) and infinite speeds

This is true, but so what?

it cannot predict observable consequences with respec to FTL signaling being allowed or forbidden.

Once again I have no idea what you mean. You appear to be using "FTL signaling" to mean something different now, but I don't know what it is.

 

[RockyMarciano]

This is true, but so what?

Once again I have no idea what you mean. You appear to be using "FTL signaling" to mean something different now, but I don't know what it is.

I mean that a deterministic theory like classical Newtonian physics that respects the BI, and is usually interpreted as being compatible with local action(no FTL influence), since measurements at one spatial region don't perturb measurements made at a different spatial region , can also be characterized as nonlocal when one considers for instance Newtonian gravity "action at a distance" instantaneous gravitational effects. That looks clearly like both contradicting assumptions have no predictive value and are just interpretational consequences of its mathematical construction as deterministic theory, and experimental violations of the BI only discard deterministic theories regardless of if one interprets them as local or nonlocal.
Honestly, you may agree or disagree with this, but if you don't understand it either it is hard not to suspect ill intent.

 

[PeterDonis]

measurements at one spatial region don't perturb measurements made at a different spatial region

In Newtonian mechanics, they do. For example, moving a mass at any location instantaneously changes the gravitational field everywhere in the universe, which can instantaneously affect measurements at any distance whatever.

In other words, I understand how Newtonian gravity can be characterized as "nonlocal"; what I don't understand is how it can be characterized as "local".

 

[RockyMarciano]

In Newtonian mechanics, they do. For example, moving a mass at any location instantaneously changes the gravitational field everywhere in the universe, which can instantaneously affect measurements at any distance whatever.

In other words, I understand how Newtonian gravity can be characterized as "nonlocal"; what I don't understand is how it can be characterized as "local".

Because the gravitational action at a distance is not observable by any actual possible measurement of that distant place where it supposedly exerted its influence and therefore there is no way to use it to send information FTL. In other words the deterministic construction of the theory admits both contradictory assumptions, neither the local nor the nonlocal assumptions have observational predictive content. Both are just ordinary language characterizations that exploit a mathematical ambiguity in classical determinist theories.