A 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.

 

[DrChinese]

a. 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".

b. 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.

a. Again: once someone explains how nonlocal effects are made to happen using purely local mechanisms, I can determine this for myself. But without that, I can't agree with you.

b. All possible results occur, that's exactly the problem! QM precisely predicts a) some results NEVER happen; and b) some results occur far more or far less than I would expect from MWI. Neither of these are ever explained in a detail example.

I have requested a detail explanation of a specific referenced experiment above, and I believe there is a reader who follows MWI closely enough to walk me through the logic of that example. Specifically:

Photons 1 and 4 share no common past and are distant. A equally remote observer can choose to entangle them or not. How is it that if all outcomes are possible, we always see perfect correlations when those photons are measured at the same angle settings? And in fact Photon 1 can be measured BEFORE the remote observer chooses to entangle it with Photon 4, and even before the measurement setting for Photon 4 is selected? (Keeping in mind here that the same mechanism must also produce Bell inequalities when the angle setting are different.)

And of course I am really asking how this is accomplished through some hypothetical local mechanism.

 

[Morbert]

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?

The light cones of the two 2-photon systems span the BSM. To demonstrate action at a distance to a MWI proponent, the BSM that establishes the branches with entanglement would have to be spacelike separated from both 2-photon systems, which are "type-ii" nonlocal systems. Only then would you have an eventual quantum state determined by the state outside its past light cone.

 

[DrChinese]

a. 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.)

b. 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: It's not just the photon: it's everything.

c.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.

d. 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.

a. Global variables sound confusingly nonlocal to me. And the issue we are discussing is whether MWI is local, not the nonlocal elements of other interpretations. We already (mostly) agree that standard QM has nonlocal elements. The nonlocal extent of an entangled system is something even @vanhees71 agrees to.

b. I'm accepting this point as being a tenet of MWI. And this is actually its most appealing point, in my opinion. It would solve a lot of conceptual problems.

c. Whoa, that's completely impossible! Photons 1 and 4 aren't entangled yet! That doesn't occur until our distant observer chooses to perform the swap or not. And that can be done AFTER Photon 1 is already measured, and there has been a splitting into a V> branch and an H> branch. Photon 4 has no connection to Photon 1 whatsoever, any more than it has a connection with any other photon anywhere. There is nothing at this point that gives an indication that they will be entangled in the future.

d. This is my point. It cannot be local because distant events have yet to occur that will change Photon 4's relationship with Photon 1 from Product State to Entangled State. That occurs in the future, and MWI is supposed to strictly reject anything which does not follow Einsteinian causality. (And please, don't ask me to define that as I think everyone understands that term the same way.)

 

[mattt]

It doesn't matter what experiment we are talking about.

The mathematical derivation of the correct results, pertinent to the given experiment, using the mathematics of standard non-relativistic quantum mechanics, is exactly the same (or mathematically equivalent) in all the interpretations of non relativistic Quantum Mechanics.

The only difference is how they translate it into English words.

 

[DrChinese]

a. The light cones of the two 2-photon systems span the BSM.

b. To demonstrate action at a distance to a MWI proponent, the BSM that establishes the branches with entanglement would have to be spacelike separated from both 2-photon systems, which are "type-ii" nonlocal systems. Only then would you have an eventual quantum state determined by the state outside its past light cone.

a. Photons 2 and 3 meet in this particular experiment, true enough. But that is absolutely not a requirement of QM. They do not need to ever meet or exist in a common light cone either. And in fact quantum repeaters rely on that attribute to work. I can supply the references if you are not sure on this point.

b. I don't understand this angle of the argument. Photons 2 and 3 are supposed to be localized, although I concede that Photons 1 & 2 (likewise 3 & 4) can be considered to have overlapping wave functions in spacetime. When the decision is made to entangle Photons 1 & 4, however, there is no time for any change of change to propagate from that location to either Photon 1 or 4 - which you must concede had no prior connection or correlation at all*. So there must be some kind of action at a distance to explain the change in statistics for Photons 1 & 4 from Product State to Entangled State.*From the reference: "A successful entanglement swapping procedure will result in photons 1 and 4 being entangled, although they never interacted with each other. ... We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4."

 

[DrChinese]

It doesn't matter what experiment we are talking about.

The mathematical derivation of the correct results, pertinent to the given experiment, using the mathematics of standard non-relativistic quantum mechanics, is exactly the same (or mathematically equivalent) in all the interpretations of non relativistic Quantum Mechanics.

The only difference is how they translate it into English words.

Well, I don't think that's actually the case. From SEP:

"The causes of our experience are interactions, and in nature there are only local interactions in three spatial dimensions. These interactions can be expressed as couplings to some macroscopic variables of the object described by quantum waves well localized in 3 D -space, which are in a product with the relative variables state of the object (like entangled electrons in atoms)..."

We all know that Bell prohibits local realistic interpretations from agreeing with the predictions of QM. So I am flat out saying that MWI must be nonlocal, precisely because its most important tenet is the realism of the wavefunction.

 

[Morbert]

a. Photons 2 and 3 meet in this particular experiment, true enough. But that is absolutely not a requirement of QM. They do not need to ever meet or exist in a common light cone either. And in fact quantum repeaters rely on that attribute to work. I can supply the references if you are not sure on this point.

Yes, a reference would be useful.

 

[PeterDonis]

All possible results occur, that's exactly the problem!

If you don't accept the MWI, yes, of course it's a problem. But MWI proponents don't see it as a problem, they see it as a solution: the solution to the "mystery" of "collapse of the wave function". If collapse never actually happens--if the actual dynamics is always unitary--things get a lot simpler, according to MWI proponents.

QM precisely predicts a) some results NEVER happen

In cases where this is true--because those results have zero amplitude--the MWI predicts that they don't happen as well--that there is no branch of the wave function that contains them.

and b) some results occur far more or far less than I would expect from MWI

I don't know what you mean here. MWI assigns exactly the amplitudes to each result that appear in the wave function. Those are the same amplitudes that are used to compute the probabilities of the results.

There is (at least for critics of the MWI) a serious issue with how to make sense of probabilities in the MWI, since using the concept of probability appears (at least to critics) to require that each individual measurement only has one result. MWI proponents sometimes agree that this is an issue that needs to be addressed, but they also appear to believe it has been addressed in the literature they have published.

Of course if you are an MWI skeptic, you won't agree with its proponents on claims like the above. But that's not going to be resolved here.

 

[PeterDonis]

Photons 1 and 4 share no common past and are distant. A equally remote observer can choose to entangle them or not. How is it that if all outcomes are possible, we always see perfect correlations when those photons are measured at the same angle settings?

When you say "all outcomes are possible", what do you mean? If you mean all outcomes contained in the wave function are possible, then the MWI agrees with that--and it says they all happen, because they all have branches in the wave function. And, as I have already said, the wave function is what enforces the correlations.

If you mean there are outcomes that are possible that aren't contained in the wave function, what are you basing that on? We are doing QM here, and in QM, the possible outcomes are the ones that are contained in the wave function.

If you are wondering how the MWI explains what happens when the settings are changed--when the distant observer makes the choice to either entangle or not entangle the photons--the MWI answer is that the wave function contains both possibilities for that as well (at least, assuming that some kind of quantum indeterminacy is involved in making the choice). The wave function in the MWI contains everything: the experimenters, the equipment they use, and the processes they use to choose measurement settings. The "settings chosen to entangle the photons" branch of the wave function only includes the possible results that show the required correlations; the "settings chosen not to entangle the photons" branch of the wave function only includes the possible results that don't show those correlations.

 

[PeterDonis]

c. Whoa, that's completely impossible! Photons 1 and 4 aren't entangled yet! That doesn't occur until our distant observer chooses to perform the swap or not.

As I noted in post #44 just now, the distant observer and the possible choices they can make are included in the wave function.

that can be done AFTER Photon 1 is already measured, and there has been a splitting into a V> branch and an H> branch

Since all of the measurements involved commute--and that is a fact of the basic math of QM, independent of any interpretation--the order in which the branching occurs in the MWI doesn't affect the results. It doesn't matter if the photon 1 measurement branching occurs before or after the choice of swap or no swap branching.

To put this another way, branching occurs in Hilbert space, not 3-dimensional space (or 4-dimensional spacetime if we are doing QFT). The events that are connected to branching are localized in 3-dimensional space (or 4-dimensional spacetime if we are doing QFT), but the branching itself is not. (As I have already remarked, I think this is a valid reason not to consider the MWI to be local. But it doesn't change the fact that this is how the MWI explains things.)

It cannot be local because distant events have yet to occur that will change Photon 4's relationship with Photon 1 from Product State to Entangled State. That occurs in the future

See my remarks above.

MWI is supposed to strictly reject anything which does not follow Einsteinian causality.

Do you have a reference where an MWI proponent makes this claim? As far as I know, MWI is an interpretation of QM, not relativity, and says nothing whatever about any particular concept of causality. It only claims to explain the predictions of QM.

 

[DrChinese]

Do you have a reference where an MWI proponent makes this claim? As far as I know, MWI is an interpretation of QM, not relativity, and says nothing whatever about any particular concept of causality. It only claims to explain the predictions of QM.

The fact that distant measurements commute is either a) simply a restatement of the idea that QM does not respect the usual Einsteinian locality/causality (i.e. quantum nonlocality is evident), or b) there are locality constraints at play (what you imply). For our discussion though, it is meaningless. QM predictions for entangled statistics are based on a future distant context. There are no experiments that demonstrate otherwise. The statements "A causes B" and "B causes A" cannot be distinguished in these as it would in a classical model. Arguing otherwise is circular reasoning.

As to the reference request: I already provided that in post #41: The causes of our experience are interactions, and in nature there are only local interactions in three spatial dimensions. These interactions can be expressed as couplings to some macroscopic variables of the object described by quantum waves well localized in 3 D -space, which are in a product with the relative variables state of the object (like entangled electrons in atoms)..." That is an absolute statement of the direction of causality being one way only.

And again I point out that a) I am the only person here providing references; and b) this thread is about someone who is a believer in MWI trying to explain how MWI operates without nonlocality. I would appreciate someone explaining how Alice observes Photon 1, splitting things into an H> branch and a V> branch, and then point out: where does the branching occur that places distant Photon 4's H> result into the same branch as Photon 1's H> result (likewise pairing the V> side) in each and every instance - without any element of Photon 1 or Photon 2 ever being near to Photon 4 (and Photon 3 never being close to Photon 2 while it is also close to Photon 4).

I say MWI is nonlocal, and experiments as referenced prove it. The Nobel committee commented about this and other related works recently: "[Anton Zeilinger's] research group has demonstrated a phenomenon called quantum teleportation, which makes it possible to move a quantum state from one particle to one at a distance." That would be action at a distance, which is what I keep saying is generally accepted science. Is the Nobel committee wrong? Does anyone seriously think they have never heard of MWI? Or are they just using loose lingo?

Apparently every MWI adherent claims these experiments are easily explained, yet I cannot find a comprehensible explanation anywhere. It's all hand waving, with no reasonable attempts to explain Bell/swapping/GHZ/etc. (I have read works by Deutsch and Vaidman and found them sorely lacking). I have provided a straightforward example from an important paper, and would appreciate someone taking some time to discuss that example without quibbling over every word.

@PeterDonis, I will gladly continue to discuss with you as long as you are willing to put in the time, but so far you have refused to make an actual statement related to the experiment I cited. Why split hairs over words when my example is right there to discuss? If you think MWI does not specify it follows Einsteinian causality, then say so unambiguously - and perhaps YOU could provide a reference for that. It is clear to me it claims to follow traditional notions of locality and causality, and goes so far to claim it is local realistic. No need for me to cite or prove that, because if someone comes along and says it doesn't, then my questions are answered.

 

[PeterDonis]

The fact that distant measurements commute is either a) simply a restatement of the idea that QM does not respect the usual Einsteinian locality/causality (i.e. quantum nonlocality is evident), or b) there are locality constraints at play (what you imply).

I'm not sure I understand. If the measurements are spacelike separated, we would expect them to commute, even on classical grounds.

The mysterious part, from a classical point of view, is how such measurements can commute even when they are timelike or null separated. But "distant" is not a word I would use to describe the measurements that situation. I would describe it as a situation where, classically, we would expect causal ordering, but quantum mechanics doesn't give us that. The measurements in question could just as well take place at the same spatial location; QM doesn't require that they be spatially distant.

QM predictions for entangled statistics are based on a future distant context.

They are based on an overall context that can include measurements that are in the causal future of other measurements, but still, as noted above, commute (where classically we would expect them not to).

As to the reference request: I already provided that in post #41: The causes of our experience are interactions, and in nature there are only local interactions in three spatial dimensions. These interactions can be expressed as couplings to some macroscopic variables of the object described by quantum waves well localized in 3 D -space, which are in a product with the relative variables state of the object (like entangled electrons in atoms)..." That is an absolute statement of the direction of causality being one way only.

I'm afraid I don't agree. It is a statement of how "interactions" work in QM. In itself it is not a statement of any particular notion of causality. It certainly is not a claim that the MWI requires "Einsteinian causality".

"Interactions" is not the same thing as "entanglement". In more technical language, "interactions" refers to terms in the Hamiltonian, not properties of the quantum state. Interaction terms in the Hamiltonian are as the quote describes them. But if they are acting on entangled degrees of freedom, in QM they can do things that make no sense classically, like end up producing correlations that violate the Bell inequalities between particles that have never interacted, and indeed don't even have to have ever existed at the same time.

this thread is about someone who is a believer in MWI trying to explain how MWI operates without nonlocality.

If you think this refers to me, I don't see where you are getting it from. I have never claimed that MWI operates without nonlocality. If we define "nonlocality" as "Bell inequality violations", then obviously MWI must accept nonlocality, just as any QM interpretation must. (I have not even claimed to be a "believer in MWI".)

What I am trying to do in this thread is to make it clear what the MWI actually says and doesn't say. I am not trying to argue that the MWI is local or that it is not. But being clear about what the MWI says and doesn't say seems to me to be an essential prerequisite to even trying to evaluate whether or not the MWI is local.

I would appreciate someone explaining how Alice observes Photon 1, splitting things into an H> branch and a V> branch, and then point out: where does the branching occur that places distant Photon 4's H> result into the same branch as Photon 1's H> result (likewise pairing the V> side) in each and every instance - without any element of Photon 1 or Photon 2 ever being near to Photon 4 (and Photon 3 never being close to Photon 2 while it is also close to Photon 4).

I have already answered this question. And I have repeatedly referred you to my answer when you have repeated this question in previous posts. I don't know why you keep ignoring what I have already said.

so far you have refused to make an actual statement related to the experiment I cited

I disagree. I have made one, and I have repeatedly referred you to it. In the interest of facilitating discussion, I'll repeat the gist of it once more: the wave function enforces the correlations. The wave function already contains all the correlations you describe. That is how the MWI explains them.

If you want me to go into more detail in actually writing down how the wave function does that, that's fine, I can take a stab at it. But it would be nice if you would at least acknowledge that I have given the above answer, multiple times now.

 

[DrChinese]

And just in case anyone thinks I am mischaracterizing something about MWI, this is from Vaidman in Plato:

a) The MWI is a deterministic theory for a physical Universe and it explains why a world appears to be indeterministic for human observers. ... The quantum state of the Universe at one time specifies the quantum state at all times.

b) The MWI does not have action at a distance.

c) The most celebrated example of nonlocality of quantum mechanics given by Bell’s theorem in the context of the Einstein-Podolsky-Rosen argument cannot get off the ground in the framework of the MWI because it requires a single outcome of a quantum experiment.

---------------

My comments:

a) Deterministic here means there is only forward in time causality. I would also say this is a claim of realism

b) No action at a distance here means it is local and there is no nonlocality. This is refuted by any swapping or teleportation experiment, see my post above with this from the Nobel committee: ""[Anton Zeilinger's] research group has demonstrated a phenomenon called quantum teleportation, which makes it possible to move a quantum state from one particle to one at a distance.""

c) Bell Theorem requiring "a single outcome from a quantum experiment" is not even true, but regardless: If this isn't hand-waving, I don't know what hand-waving is. It is typical of local realism proponents to invent "tacit" or "hidden" assumptions in Bell and then deny them - and end discussion there (as Vaidman has).

Bell's theorem requires only that an observer in any branch see a single outcome from a quantum experiment. There is no requirement that there are no other branches containing other observers. )Bell was certainly familiar with Everett's thesis and certainly never thought his theorem didn't apply to MWI. If you are interested, you can read about some of Bell's shifting ideas about things like Everett, Bohm and GRW here.)

 

[PeterDonis]

Deterministic here means there is only forward in time causality.

No, it doesn't. Deterministic laws can be evolved backward in time just as easily as forward. The quote you give even says so: it says the quantum state at one time specifies the quantum state at all times, not just all future times. If we could know the full quantum state of the entire universe now, according to the MWI, we would know it for all times, including all the way back to the Big Bang.

No action at a distance here means it is local and there is no nonlocality.

I would want to see a lot more detail about what Vaidman actually means by "action at a distance" before accepting any such claim (and I'll read through the article you reference again to see if I can find such detail). If, for example, you think Vaidman is claiming that the MWI does not predict Bell inequality violations, then I would expect Vaidman himself to object, since the MWI is an interpretation of QM and QM itself, independent of any interpretation, predicts Bell inequality violations.

Bell Theorem requiring "a single outcome from a quantum experiment" is not even true

I'll need to read through the article again to evaluate this as well.

I note, btw, that Zeh, in the paper you reference, appears both to be an MWI proponent (since he says he believes the Schrodinger equation is always valid) and to have no trouble accepting that the MWI is nonlocal. I also note that in the paper, he mentions David Deutsch's version of the MWI and contrasts it with his own. I would be interested in any other comments he has on the writings of the other MWI proponents you have referred to.

 

[PeterDonis]

No action at a distance here means it is local and there is no nonlocality.

I would want to see a lot more detail about what Vaidman actually means by "action at a distance" before accepting any such claim

And it didn't take me long to find, since it's in the same paragraph of the article as the quote that you, @DrChinese, gave in post #48. Here are the last three sentences of that paragraph, which you failed to quote:

Although the MWI removes the most bothersome aspect of nonlocality, action at a distance, the other aspect of quantum nonlocality, the nonseparability of remote objects manifested in entanglement, is still there. A“world” is a nonlocal concept. This explains why we observe nonlocal correlations in a particular world.

So based on this, I definitely do not agree with the claim quoted at the top of this post.