A Is MWI Considered Local in Quantum Mechanics?

[PeterDonis]

The context is made explicit in the introduction.

I understand perfectly well what the authors are using the term "local causality" to mean. I just think they are being either extraordinarily ignorant or disingenuous by ignoring the other usage of that term in the relativistic QFT community while at the same time making a claim about Lorentz covariant quantum models.

 

[jbergman]

On this view, every QM interpretation is a hidden variable interpretation, since QM itself, independent of any interpretation, is a hidden variable theory. Which makes the term "hidden variable" useless, since the whole point of the term was to distinguish between QM interpretations.

I don't agree with this framing of Bell's work. Bell takes the observables associated with QM as being true. He then shows that no local hidden variable theory can reproduce these observables. These hidden variable theories have no dependence to be augmentations of the standard formalism of QM.

 

[PeterDonis]

I don't agree with this framing of Bell's work.

What you quoted from me has nothing whatever to do with Bell's work. It has to do with your claim about what a "hidden variable theory" is. If you think Bell's definition of what a "hidden variable theory" is was the same as yours, I challenge you to give an explicit reference from his work that supports such a claim. For example, a reference which says that Bell thought the MWI was a hidden variable theory.

(Bell certainly thought the de Broglie-Bohm theory was a hidden variable theory, in fact it was his favorite example of one--a nonlocal one--but dBB is not the MWI. In dBB the hidden variables are the unknown and unknowable particle positions, not the wave function, and AFAIK that was exactly how Bell viewed it.)

Bell takes the observables associated with QM as being true. He then shows that no local hidden variable theory can reproduce these observables. These hidden variable theories have no dependence to be augmentations of the standard formalism of QM.

Nonsense. Bell's formulation of "hidden variable theories" modeled the hidden variables as $\lambda$--which are separate from the wave function, the measurement settings, and the observed results. In other words, his hidden variables precisely are "augmentations of the standard formalism of QM".

 

[jbergman]

What you quoted from me has nothing whatever to do with Bell's work. It has to do with your claim about what a "hidden variable theory" is. If you think Bell's definition of what a "hidden variable theory" is was the same as yours, I challenge you to give an explicit reference from his work that supports such a claim. For example, a reference which says that Bell thought the MWI was a hidden variable theory.

(Bell certainly thought the de Broglie-Bohm theory was a hidden variable theory, in fact it was his favorite example of one--a nonlocal one--but dBB is not the MWI. In dBB the hidden variables are the unknown and unknowable particle positions, not the wave function, and AFAIK that was exactly how Bell viewed it.)Nonsense. Bell's formulation of "hidden variable theories" modeled the hidden variables as $\lambda$--which are separate from the wave function, the measurement settings, and the observed results. In other words, his hidden variables precisely are "augmentations of the standard formalism of QM".

Bell himself states very clearly in, The theory of Local Beables, "Quantum Mechanics is not Locally Causal".

 

[PeterDonis]

Bell himself states very clearly in, The theory of Local Beables, "Quantum Mechanics is not Locally Causal".

Sure. What does that have to do with your claim that the wave function is a hidden variable?

 

[jbergman]

Sure. What does that have to do with your claim that the wave function is a hidden variable?

Here is the comment I made that started this discussion,

I disagree. For the purposes of this discussion, locality should be framed in terms of the definitions associated Bell's papers. As such, all theories of QM are non-local. We can just consider the unobservable features of MWI as another form of hidden variables.

It is quite clear that Bell wouldn't consider MWI as a locally causal theory as he states that QM isn't locally causal.

So really the dispute boils down to whether or not you consider the QM wave function hidden or not. This question isn't of great import, though, to the main point, which is that QM is not embeddable in a local causal theory.

However, I stand by my characterization of the quantum state vector as unobservable and "hidden".

However, I acknowledge that this not the typical usage in this context.

 

[PeterDonis]

Here is the comment I made that started this discussion

That post was in response to @gentzen, not to me. Your post in response to me was:

I think that is too narrow of an interpretation. IMO, the wave function should be considered hidden, hence, it's state is a hidden variable.

And I disagreed with that:

On this view, every QM interpretation is a hidden variable interpretation, since QM itself, independent of any interpretation, is a hidden variable theory. Which makes the term "hidden variable" useless, since the whole point of the term was to distinguish between QM interpretations.

And then you went off on a tangent about Bell's work. Your claim that the wave function should count as a "hidden variable" has nothing to do with Bell's work.

So really the dispute boils down to whether or not you consider the QM wave function hidden or not.

Yes, and I said no, for the reason I gave in the post of mine that I quoted above. If you want to respond to that argument, by all means do so. But the argument I made has nothing to do with Bell's work. It's a simple argument about whether you want the term "hidden variable" to be useful in distinguishing between QM interpretations, or not.

This question isn't of great import, though, to the main point, which is that QM is not embeddable in a local causal theory.

I have not disagreed with that at all, for the definition of "local causal" that you are using (in which a "local causal" theory would not be able to violate the Bell inequalities). As I commented in response to @Morbert, though, I think one needs to be clear that this definition of "local causality" is not the same as the one that is used by the relativistic QFT community; to that community, relativistic QFT is "locally causal", because spacelike separated operators commute.

I stand by my characterization of the quantum state vector as unobservable and "hidden".

It's not a direct observable, no, although quantum tomography can in principle pin it down to any desired degree of accuracy given enough repetitions of a particular preparation procedure.

"Hidden" in the sense of "hidden variable interpretation" would, as I said, make that term useless, since by this definition every QM interpretation is a "hidden variable interpretation" since QM itself is a "hidden variable theory". If you want to use such a definition, I can't stop you, but I don't see the point.

 

[kered rettop]

They're "not an issue" only because the MWI does not contain anything corresponding to what they describe. There are no "mutual influences" or "remote changes" in the MWI. That's because there aren't any in the wave function, and in the MWI, the wave function is all there is.

None of this means the MWI does not have to account for the experimental results. Of course it does, just as any QM interpretation does. It just doesn't do it by appealing to "mutual influences" or "remote changes". It does it by, first, saying that the wave function is all there is; second, saying that there is no collapse, so all of the possibilities contained in the wave function actually exist (meaning that measurements don't have single results--all possible results happen); and third, saying that the wave function is what enforces the correlations such as are observed in Bell inequality violations, entanglement swapping, etc.

Is it not true that the unentangled state is a superposition of Bell states and that entanglement swapping doesn't so much impose entanglement as separate the Bell states (using the tags obtained from the idler photons at D1 and D4)?

 

[kered rettop]

"Hidden" in the sense of "hidden variable interpretation" would, as I said, make that term useless, since by this definition every QM interpretation is a "hidden variable interpretation" since QM itself is a "hidden variable theory". If you want to use such a definition, I can't stop you, but I don't see the point.

I thought "hidden variables" meant "hidden variables added to standard QM". So I'm thinking that you don't need to play devil's advocate, amusing though it may be for us spectators. The definition is simply wrong.

 

[PeterDonis]

Is it not true that the unentangled state is a superposition of Bell states

I don't know what you mean by "the unentangled state". The initially prepared state has photons 1 and 2 entangled, and photons 3 and 4 entangled. After the entanglement swap, photons 1 & 4 are entangled and photons 2 & 3 are entangled. All of the entangled states involved are Bell states (in the simplest version, which is the one I analyzed in detail with math, they are all singlet states). The full 4-photon states are products of two entangled Bell states, not superpositions.

the idler photons

There are no "idler photons" in the experiments discussed.

 

[kered rettop]

There are no "idler photons" in the experiments discussed.

Oops.

 

[syed]

In my view, MWI is neither local nor non-local. It is alocal. See https://arxiv.org/abs/1703.08341

Just wanted to say: great article!