Is MWI Considered Local in Quantum Mechanics?

[DrChinese]

[Moderator's note: Thread spun off from previous discussion due to topic change.]

It should be obvious by now that MWI cannot be local. That doesn't mean MWI cannot represent a
viable interpretation, but the "local" concept should not be attached to it.

 

[PeterDonis]

What definition of "local" are you using?

I ask because "locality" is usually defined in terms of space and time, but the natural space of the MWI is Hilbert space, which is the space in which the unitary dynamics of QM takes place. In at least one sense, any state in Hilbert space that involves more than one particle is obviously not local in space and time unless the particles are all co-located. In that sense the MWI is of course not local, but neither is any interpretation of QM, since they all make use of the same underlying math. So this definition doesn't seem useful for distinguishing between interpretations.

 

[DrChinese]

What definition of "local" are you using?

I ask because "locality" is usually defined in terms of space and time, but the natural space of the MWI is Hilbert space, which is the space in which the unitary dynamics of QM takes place. In at least one sense, any state in Hilbert space that involves more than one particle is obviously not local in space and time unless the particles are all co-located. In that sense the MWI is of course not local, but neither is any interpretation of QM, since they all make use of the same underlying math. So this definition doesn't seem useful for distinguishing between interpretations.

First, thanks for splitting off the thread.

Gosh, definition of locality... How about the idea that nothing - no influence, cause, change of state, or information - can traverse a distance faster than the speed of light. And just to be even more specific, the direction to be traversed must move forward in time and cannot be retrocausal in any manner.

Hilbert space... well, we perform experiments in the spacetime we observe. And it is experimental issues that insure MWI is not local by the above definition. But in fact, this paper dissects the concept of MWI in Hilbert space:

https://arxiv.org/abs/1210.8447

Of course, we have already settled here the fact that generally, quantum nonlocality is accepted as experimental fact. But we did so with the caveat that also is equivalent to saying a Bell Inequality is violated. So with MWI, the question is: how do distant observers manage to witness those Bell Inequality violations without locality being violated? And also explain how perfect correlations can also be managed...

To be fair, it really takes an MWI proponent to explain this properly. I will provide a suitable scenario tomorrow, but the idea is for MWI to explain - in detail, with a specific example - how photons from independent sources that have never existed in a common light cone can become entangled. And also: why those photons and no other photons are entangled.

If you want to take the MWI side, that's fine, but I am not interested in the usual handwaving I see in articles by Deutsch. Carroll and others. I don't object per se to the postulating of multiple worlds (although that has obvious reasons for objection), just the specific idea MWI is local or localized.

 

[PeterDonis]

this paper dissects the concept of MWI in Hilbert space

The criticism in that paper is one I've seen before--basically that in the MWI nothing can happen. I'm sympathetic to that criticism, but it seems to me to be orthogonal, so to speak, from the question of whether the MWI is local.

If you want to take the MWI side

I'm not taking any side. I'm just trying to get clear about how we are defining "locality". I'm also interested in any references anyone may have where physicists argue (in an actual peer-reviewed paper, not a pop science book or article--I agree that the arguments there, even by physicists, are handwaving and off topic here) that the MWI is local, and what definition of "local" they use.

I'm generally not a fan of the MWI, but it is an interpretation that a lot of physicists appear to favor, so I'm interested in understanding what it says, if only to understand better where the physicists that favor it are coming from.

 

[PeterDonis]

How about the idea that nothing - no influence, cause, change of state, or information - can traverse a distance faster than the speed of light. And just to be even more specific, the direction to be traversed must move forward in time and cannot be retrocausal in any manner.

This doesn't really help unless we can pick out in the actual mathematical model exactly what things fall into the category of "influence, cause, change of state, or information". For example, if we count "whatever produces Bell inequality violations" in this category, then of course the experimental evidence of Bell inequality violations is evidence of a violation of locality. But not everyone seems to agree with that.

In other words, one of the inherent questions in a discussion of this type is whether we're actually arguing about physics, or only arguing about words and labels. If you and I both agree on the physics--we both agree on what the results will be of any conceivable experiment we can perform, for example we both agree about Bell inequality violations, entanglement swapping, "retrocausality", etc.--but you say all this is "nonlocal" while I say it's "local", what, exactly, are we disagreeing about? Can we just taboo the words "local" and "nonlocal" and discuss the physics without them? Or will be be leaving out something essential if we do that?

 

[PeterDonis]

one of the inherent questions in a discussion of this type is whether we're actually arguing about physics, or only arguing about words and labels

Btw, I should make it clear that this is not a criticism of you (@DrChinese) for asking the question. If it's a criticism of anything, it's a criticism of the literature that has focused so much attention on terms like "locality" when much, if not most (maybe even all) of that discussion boils down in the end to people using the same word with different meanings and talking past each other.

 

[Demystifier]

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

 

[martinbn]

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

You say that MWI is alocal because the wave function lives in a higher dimensional abstract space. But that is not specific to this interpretation, it is true for all of them. This just introduces a new word for something different!

 

[gentzen]

You say that MWI is alocal because the wave function lives in a higher dimensional abstract space. But that is not specific to this interpretation, it is true for all of them. This just introduces a new word for something different!

But in most other interpretations, there also exists something which lives in normal 3+1 dimensional space. If you deny the existence of that 3+1 dimensional space, or at least the existence of anything living in that space, then the locality notion of that 3+1 dimensional space no longer applies to you.

 

[Demystifier]

You say that MWI is alocal because the wave function lives in a higher dimensional abstract space. But that is not specific to this interpretation, it is true for all of them. This just introduces a new word for something different!

What @gentzen said above.

 

[martinbn]

But in most other interpretations, there also exists something which lives in normal 3+1 dimensional space. If you deny the existence of that 3+1 dimensional space, or at least the existence of anything living in that space, then the locality notion of that 3+1 dimensional space no longer applies to you.

Are you saying that @Demystifier says that in MWI the 4 dimensional space-time doesnt exist or nothing exists in it? My understanding of MWI is that there is no such claim, of course i might just not know enough about MWI.

 

[Demystifier]

Are you saying that @Demystifier says that in MWI the 4 dimensional space-time doesnt exist or nothing exists in it? My understanding of MWI is that there is no such claim, of course i might just not know enough about MWI.

Yes. According to MWI, the wave function is all what exists.

 

[martinbn]

Yes. According to MWI, the wave function is all what exists.

Can you give a reference for that, so i can see exactly what is meant by it?

 

[Demystifier]

Can you give a reference for that, so i can see exactly what is meant by it?

E.g. https://plato.stanford.edu/entries/qm-manyworlds/
which says "Part (i) states that the ontology of the universe is a quantum state, which evolves according to the Schrödinger equation or its relativistic generalization."

 

[martinbn]

E.g. https://plato.stanford.edu/entries/qm-manyworlds/
which says "Part (i) states that the ontology of the universe is a quantum state, which evolves according to the Schrödinger equation or its relativistic generalization."

I am not sure it means what you say it does. For example the very first sentence of the article says

The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own.

To me this says that space and time exist and also many worlds exist. Very far from the statement that only the wave function exists!

 

[gentzen]

I am not sure it means what you say it does. For example the very first sentence of the article says

The Many-Worlds Interpretation (MWI) of quantum mechanics holds that there are many worlds which exist in parallel at the same space and time as our own.

To me this says that space and time exist and also many worlds exist. Very far from the statement that only the wave function exists!

The word exists here is tricky, because MWI uses it with two different meanings. The worlds and space are supposed to exist in the sense of "emergence", but the wave function is posited to exist in a different sense, namely as the fundamental substrate (of everything).

 

[Demystifier]

I am not sure it means what you say it does. For example the very first sentence of the article says

To me this says that space and time exist and also many worlds exist. Very far from the statement that only the wave function exists!

You should distinguish things which exist in the fundamental sense (wave function in MWI) from things which exist in the emergent sense (3-dimensional space in MWI).

This is somewhat analogous to a chemist who says that only atoms exist (in the fundamental sense), but does not deny that water exists (in the emergent sense).

EDIT: Now I saw that @gentzen said the same.

 

[martinbn]

The word exists here is tricky, because MWI uses it with two different meanings. The worlds and space are supposed to exist in the sense of "emergence", but the wave function is posited to exist in a different sense, namely as the fundamental substrate (of everything).

You should distinguish things which exist in the fundamental sense (wave function in MWI) from things which exist in the emergent sense (3-dimensional space in MWI).

This is somewhat analogous to a chemist who says that only atoms exist (in the fundamental sense), but does not deny that water exists (in the emergent sense).

EDIT: Now I saw that @gentzen said the same.

But your argument says only the wave function exists. Whether the other things are fundamental in the theory or emergent doenst matter. If they exist, your argument is invalid.

With your analogy the sea is not wet it is not non-wet, it is a-wet. Because water dosnt exist.

 

[Demystifier]

But your argument says only the wave function exists. Whether the other things are fundamental in the theory or emergent doenst matter. If they exist, your argument is invalid.

No, in my argument I talk about existence in the fundamental sense. Even if I don't say that explicitly, it should be implicit from the context. As long as all interpretations of QM make the same measurable predictions, the issue whether some interpretation of QM is local or non-local or alocal makes sense only from the fundamental point of view.

 

[gentzen]

But your argument says only the wave function exists. Whether the other things are fundamental in the theory or emergent doenst matter. If they exist, your argument is invalid.

With your analogy the sea is not wet it is not non-wet, it is a-wet. Because water dosnt exist.

Being wet is an emergent property too (just like the existence of water), hence Demystifier's argument woud be invalid for water.

So if we stay purely on the emergent level, then space-time and non-signaling locality do emerge in MWI. But non-signaling locality is also a property of the Copenhagen interpretation. But with respect to wave function collapse, MWI is neither local nor non-local. If you insist that wave function collapse too emerges, then it is just as non-local as the Copenhagen interpretation in this respect. If you insist that the wave function is fundamental and doesn't collapse, then Demystifier's argument applies. In no case can you get more locality from MWI than you could also get from the Copenhagen interpretation.

 

[gentzen]

In no case can you get more locality from MWI than you could also get from the Copenhagen interpretation.

Well, maybe you can get a bit more, if go on some intermediate level between fundamental wavefunction and emergent classical reality. In a certain sense, Lev Vaidman aims for such a level. But he has neither convinced his other MWI proponents so far, nor Demystifier or other MWI skeptics. In fact, Demystifier (and other Bohmians) are "pissed-off" by that part of Lev Vaidman's position. In his SEP article, he was careful to just explain the concensus view, and didn't mix in his personal ideas.

 

[Demystifier]

But with respect to wave function collapse, MWI is neither local nor non-local.

Exactly. It is not non-local because there is no fundamental collapse in MWI, but it is also not local because wave function is not a local object (not defined at a 3-space position).

 

[Morbert]

David Wallace looks at two concepts of locality in his MWI book "The Emergent Multiverse": i) Local as satisfying no action at a distance, and ii) local as in separable.

He says MWI is local in the sense of i) because the quantum state in some region depends only on the quantum state of some cross-section of the past light cone of that region. He says MWI is nonlocal in the sense of ii) because extended regions of the state can contain information that cannot be associated with subregions of that region. He notes that classical theories can be nonlocal in the sense of ii) as well (though for a different reason), and gives the Aharonov–Bohm effect in electromagnetism as an example.

 

[PeterDonis]

You should distinguish things which exist in the fundamental sense (wave function in MWI) from things which exist in the emergent sense (3-dimensional space in MWI).

How is 3-dimensional space fundamental rather than emergent in other interpretations?

 

[DrChinese]

Btw, I should make it clear that this is not a criticism of you (@DrChinese) for asking the question. If it's a criticism of anything, it's a criticism of the literature that has focused so much attention on terms like "locality" when much, if not most (maybe even all) of that discussion boils down in the end to people using the same word with different meanings and talking past each other.

We've had this discussion before, true, and you seem to feel there is more ambiguity in the term "local" and "locality" than most authors.

a) If I can send signals faster than c (which is impossible as we know it), that violates locality.
b) If 2 entangled particles exert a mutual influence on each other when they occupy a region of space, that violates locality.
c) If a measurement on one of 2 entangled particles causes a remote change to its distant partner, that violates locality - even if the change itself has a random character which cannot be controlled sufficiently to send any useful information.
d) If I can teleport a quantum state from one quantum system to another sufficiently distant, that violates locality.
e) If I can remotely change a quantum state sufficiently distant, that violates locality.

On the other hand: if there is a local mechanism which can explain any of the criteria above, then that criterion should be struck. I don't think we need to worry about a) as there is no point of disagreement on this. The others may or may not be issues, depending on the MWI perspective. Obviously, there are experiments which demonstrate d) and e). Of course, it is not unusual for proponents of an interpretation to simply deny the validity of experiments which appear to go against their preference.

I think a reasonable experimental reference is:

High-fidelity entanglement swapping with fully independent sources
https://arxiv.org/abs/0809.3991
Rainer Kaltenbaek, Robert Prevedel, Markus Aspelmeyer, Anton Zeilinger
"Entanglement swapping allows to establish entanglement between independent particles that never interacted nor share any common past. ..."

I'd like someone to explain how this specifically works under MWI without invoking any kind of nonlocal action or global variables. And if the answer is to deny the published paper, well, that doesn't really explain anything in my book.

I'm perfectly good with starting out photons 1/2/3/4 having some kind of spreading wave function. I am also good with the idea that a polarization measurement of photon 1 (say) splits things into 2 versions (worlds, universes, histories, wavefunctions, wave states or whatever we want to call it). In one world, the Photon 1 polarization is now H> and in the other world it is V>. According to one source on MWI: "The wavefunction obeys the empirically derived standard linear deterministic wave equations at all times. The observer plays no special role in the theory and, consequently, there is no collapse of the wavefunction."

Presumably, if MWI is local (or localized or whatever you might call it): during their short life span, photons 1 & 4 never come close to each other. They are not synchronized (entangled) with each other initially. The swapping operation on photons 2 & 3 can occur distant to both 1 and 4. So how do 1 & 4 become entangled when they are far from each other (and far from 2&3 as well) ? In other words, at what point should we expect to see worlds in which the 1 & 4 photons are showing entangled outcomes? And at what point did their "deterministic wave equations" overlap or interact with each other in a manner that allows them to be synchronized?

Thanks,

-DrC

PS Keep in mind, I don't know how it really works in any interpretation, other than I believe there is a nonlocal component of some kind involved that explains one or more of the criteria I presented.

 

[PeterDonis]

Obviously, there are experiments which demonstrate d) and e).

For d), yes, quantum teleportation has been demonstrated.

For e), no, "remotely change a quantum state" is not something we can directly observe. We don't directly observe quantum states. We only directly observe measurement results. Similar remarks apply to your b) and c): those involve things that aren't directly observable ("exert a mutual influence" and "remote change"). Some interpretations contain things like "mutual influence" and "remote change" as a way of explaining things like Bell inequality violations, but I'm not sure the MWI is one of them. (Bohmian would be the most obvious example of such things, since the quantum potential updates instantaneously.)

 

[DrChinese]

David Wallace looks at two concepts of locality in his MWI book "The Emergent Multiverse": i) Local as satisfying no action at a distance, and ii) local as in separable.

He says MWI is local in the sense of i) because the quantum state in some region depends only on the quantum state of some cross-section of the past light cone of that region. He says MWI is nonlocal in the sense of ii) because extended regions of the state can contain information that cannot be associated with subregions of that region. He notes that classical theories can be nonlocal in the sense of ii) as well (though for a different reason), and gives the Aharonov–Bohm effect in electromagnetism as an example.

i) But there are experiments in which photons become entangled that have never existed in a common past light cone. See my #25.

ii) Not sure how this statement even is supposed to make sense. OK, if there are nonlocal extended regions with information that is not present in subregions, how do remote photons 1 & 4 get entangled?

 

[DrChinese]

i) For d), yes, quantum teleportation has been demonstrated.

ii) For e), no, "remotely change a quantum state" is not something we can directly observe. We don't directly observe quantum states. We only directly observe measurement results.

iii) Similar remarks apply to your b) and c): those involve things that aren't directly observable ("exert a mutual influence" and "remote change"). Some interpretations contain things like "mutual influence" and "remote change" as a way of explaining things like Bell inequality violations, but I'm not sure the MWI is one of them. (Bohmian would be the most obvious example of such things, since the quantum potential updates instantaneously.)

i) Check.

ii) As to e), it is really difficult to get around the experiment I referenced as doing that. As I have asserted previously (of course you reject it): Photon 1 & 4 change states and therefore their observed statistics change. Yes, you need to make a straightforward deduction to conclude the changed statistics are a predicted result of the swap. I mean, really, what else could that be a result of except the swap (which is also remote).

iii) I didn't say b) and c) are proven. I just said that if those criteria were demonstrated, then MWI (or any interpretation for that matter) would be nonlocal.

 

[PeterDonis]

I'd like someone to explain how this specifically works under MWI without invoking any kind of nonlocal action or global variables.

I'm not sure that would be possible as you state it here--the wave function would play a role similar to a "global variable", since it contains entangled degrees of freedom which can be widely separated in 3-dimensional space. (But, as has already been noted, that is true of any interpretation since they all use the same underlying math, which contains the wave function playing that same role.)

The first thing one would have to do to describe any experiment using the MWI would be to get rid of anything that says or implies that measurements have single results or that wave functions collapse. For example:

a polarization measurement of photon 1 (say) splits things into 2 versions (worlds, universes, histories, wavefunctions, wave states or whatever we want to call it). In one world, the Photon 1 polarization is now H> and in the other world it is V>.

It's not just the photon: it's everything. The "world" ("branch of the entangled wave function" would be a better term) in which the photon 1 polarization is $\ket{H}$ also has the polarization measuring device registering "H", the human brains that perceive the device's readout believing that the result was "H", etc., and similarly pari passu for the branch in which the photon 1 polarization is $\ket{V}$. If photons 1 and 4 end up entangled, so their polarizations must be equal if measured along the same direction, then the branch in which the photon 1 polarization is $\ket{H}$, with all that goes with it, will also have the photon 4 polarization being $\ket{H}$< with all that goes with it (which will now include all the information that gets exchanged between experimenters who communicate with each other regarding the two results). And similarly pari passu for the branch in which the photon 1 and 4 polarizations are $\ket{V}$.

If you ask what makes it so that everything matches up correctly in each branch, that's simple: those are the only possibilities that exist in the wave function. There is no branch of the wave function in which both photons 1 and 4 are measured along the same direction but their polarizations aren't the same. That is what it means to say that photons 1 and 4 are entangled in the parallel polarization state.

Whether all this counts as "local" is a different question. No "nonlocal influence" has to go between the photons during the measurements to enforce the correct correlations between the measurement results, because that is already enforced by the wave function itself, as above. But the wave function itself is a function on Hilbert space, not 3-dimensional space, and, as has already been noted, it contains entangled degrees of freedom that can be widely separated in 3-dimensional space, so it's hard to see how it can be considered "local" in 3-dimensional space.

MWI proponents, at least judging from the literature, might not agree with all of the above. But, as has also been noted, to those who are skeptical of the MWI the arguments of its proponents seem like handwaving. So there is probably not going to be any real resolution of issues like this unless and until we find some way to go beyond just different intepretations of existing QM and make these different viewpoints into actual alternative theories that make different experimental predictions that can then be tested.

 

[PeterDonis]

As to e), it is really difficult to get around the experiment I referenced as doing that.

No, it isn't. I just explained in post #29 how the MWI accounts for the correlations without any "influence" having to travel between the photons during the measurements: the correlations are enforced by the wave function. Of course, as I noted, that still doesn't make the MWI "local", since it's hard to see how the wave function can be "local" in 3-dimensional space. But it does provide a way to account for the correlations without "remote influence".

 

[PeterDonis]

I didn't say b) and c) are proven. I just said that if those criteria were demonstrated, then MWI (or any interpretation for that matter) would be nonlocal.

MWI doesn't even contain anything like what is described in b) or c), so those items are simply irrelevant if we're talking about evaluating the MWI. Other interpretations (for example, I mentioned Bohmian in that earlier post) might contains things like that, but the MWI doesn't.

 

[Demystifier]

How is 3-dimensional space fundamental rather than emergent in other interpretations?

I'm talking about the non-relativistic theory. For example in the "standard" interpretation, the fundamental things are measurement outcomes, which happen in 3-space (not in Hilbert space or 3N-space of N particles).

 

[PeterDonis]

I'm talking about the non-relativistic theory.

Yes, to be clear, I wasn't asking about 3-dimensional space vs. 4-dimensional spacetime. I was asking about 3-dimensional space (or 4-dimensional spacetime in the relativistic theory) vs. Hilbert space.

 

[DrChinese]

MWI doesn't even contain anything like what is described in b) or c), so those items are simply irrelevant if we're talking about evaluating the MWI. Other interpretations (for example, I mentioned Bohmian in that earlier post) might contains things like that, but the MWI doesn't.

*You* were the one who asked for an expanded version of what locality is, which can also be answered by describing what nonlocality is. So I answer that as completely as I thought reasonable, and I did not claim these do or don't apply to MWI. I seek that answer.

Regardless, I certainly don't agree that b) and/or c) might not be an issue for MWI. That's what I am trying to find out. MWI proponents argue there is no nonlocal element to the interpretation, and I say one or more of criteria a-e are actually present. I can't find out which because most expositions on MWI simply hand-wave away Bell. From https://www.hedweb.com/manworld.htm#faq

"Q32
Does the EPR experiment prohibit locality?
What about Bell's Inequality?

[Long calculation attempting to explain why there are perfect EPR correlations, but nothing explaining even the most basic elements of Bell. Read it yourself, but it basically skips the key objections to theories claiming to be local realistic - or, as is stated in the next paragraph, local deterministic.-DrC]

To recap. Many-worlds is local and deterministic. Local measurements split local systems (including observers) in a subjectively random fashion; distant systems are only split when the causally transmitted effects of the local interactions reach them. We have not assumed any non-local FTL effects, yet we have reproduced the standard predictions of QM.

So where did Bell and Eberhard go wrong? They thought that all theories that reproduced the standard predictions must be non-local. It has been pointed out by both Albert [A] and Cramer [C] (who both support different interpretations of QM) that Bell and Eberhard had implicity assumed that every possible measurement - even if not performed - would have yielded a single definite result. This assumption is called contra-factual definiteness or CFD.

What Bell and Eberhard really proved was that every quantum theory must either violate locality or CFD. Many-worlds with its multiplicity of results in different worlds violates CFD, of course, and thus can be local.

Thus many-worlds is the only local quantum theory in accord with the standard predictions of QM and, so far, with experiment."

Pure gibberish. Obviously, the smoking gun here is that a nonlocal context - the measurement choices of Alice and distant Bob - are the only things needed to calculate the quantum prediction. That is true even when the photons being measured have no common past, and it is true when the measurement settings of Alice and Bob are changed midflight in a fashion in which no information about Alice's setting can reach Bob (and vice versa).

So no, I don't rule out b) and c) at all.

 

[PeterDonis]

I certainly don't agree that b) and/or c) might not be an issue for MWI.

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.