Is MWI Considered Local in Quantum Mechanics?

[DrChinese]

1) I don't think we can reverse the measurements, because "measurement" says that decoherence has occurred...

2) Also, what you would need to recombine to undo the swap operation is Photons 2 & 3; in other words, instead of putting detectors in the two output arms of the BSM beam splitter, you would need to make that the first beam splitter in a Mach-Zehnder interferometer, where the second beam splitter in the interferometer recombines the beams. ...

1) Fine.

2) Recombining them would not (I believe) produce distinguishable outputs as to the source. But I don't think this matters, we'll use your definition as you have it. If it is measured, there is decoherence.

 

[DrChinese]

It's not entirely correct as a description of how MWI works, at least not as @Morbert is interpreting it. See my post #116.

Your #116 is fine too. Of course we are still missing 1 & 4, and that is the $64,000 question.

 

[Morbert]

If Bob is entangled with any of the degrees of freedom involved, then he branches instantaneously when the BSM is done, because the wave function is nonlocal and all entangled subsystems branch when any branching event affects any one of them. Bob entering the future light cone of the BSM (assuming that information about the BSM result is signaled to him at the speed of light) is when the Bob in each branch knows the branch he is in (because he now knows the BSM result), and updates his model accordingly. But Bob updating his model is not the same as Bob branching.

As per usual, assuming Wallace's account of MWI: If Bob is entangled with the relevant degrees of freedom, Alice will use the appropriate relative state to describe Bob, but this doesn't mean a branching event is initiated at Bob's site when Alice performs her BSM. The nonlocal property of entanglement between microscopic degrees of freedom at Alice and Bob can only have determinable effects at the intersection of Alice and Bob's light cones.

Instead, a local branching event is initiated by Bob when he entangles himself with the relevant degrees of freedom, and a separate local branching event is initiated when Alice does the same, and a third event occurs when these two events intersect. It is this third event where the initial entanglement can have an effect. [edit] -removed the "branching" qualifier because it's not the same event as the events initiated by Alice and Bob. It merely notes the point of intersection.

Wallace provides such an account of two spacelike separated measurements on an entangled particle pair in chapter 8.7 of his book, and the picture below is from that account. I have added the names Alice and Bob.

If Bob is not entangled with any of the degrees of freedom involved, then he does branch when the information about the BSM result reaches him: but then what causes his branching is not the BSM itself, but his observation of the light signals carrying the information about the BSM result, which entangles him with the source of the light.

I don't see this as meaningfully different from what I said before so I will drop this "branch" of the conversation for now unless a meaningful difference is made clear.

 

[DrChinese]

1) I discuss the following, using the clear and solid language of HEP physics:

Definition: a relativistic quantum-field theory is called local, if the local observables obey the microcausality condition and the Hamilton density is a local observable-operator. This implies Einstein causality, i.e., that there's no causal connection between space-like separated events.

2) Entangled systems do not have a "non-local extent" but they describe correlations between the outcome of measurements on observables with indetermined properties, that are stronger than possible for a realistic local hidden-variable theory. It seems to me that the notion of "non-locality" in the "quantum-foundations community" usually has this meaning, ...

3) Now you do a (local!) Bell measurement on photons 2 and 3, enabling you to select a subensemble of the above prepared photons in only considering the four photons if photons 2 and 3 have been found to be in the singlet state $|\psi_{23} \rangle$. This happens randomly for each single experiment with a probability of 1/4. The so selected subensemble is then described by the state
$$|\Psi' \rangle=|\psi_{23} \rangle \otimes |\psi_{14} \rangle,$$
i.e., also the pair 14 is entangled. That's "entanglement swapping". It makes use of the fact that there's the strong correlation between photons 1 and 2 as well as the photons 3 and 4. Although each of the single photons is ideally unpolarized, there's the 100% correlation of the polarizations of photons 1 and 2 as well as of photons' 3 and 4, and this enables the selection of a subensemble in which photons 1 and 4 are entangled although these two photons never have been in "causal contact" ...

1) The issue we have with this centers around the usage of the word "causal". As you use the word, there is no causal action at a distance (AAD) possible - and I agree with that usage of the word "causal". This definition is perfectly fine, and I agree that AAD that involves doing something at one spot cannot deterministically ("causally") affect something at a far away location (i.e. outside the relevant light cone).

But no one in the general physics community is saying otherwise! What is being asserted is that there is a kind of AAD - called "quantum nonlocality" or just "nonlocality" in which indeterministic (random) effects propagate superluminally. I won't quote experiments, but simply quote the 2022 Nobel committee: "...[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 [i.e. outside a light cone]."

So if you define such indeterministic AAD to violate "Einsteinian causality" (as I do), fine. If you choose to say it violates something else (so you can maintain "Einsteinian causality"), that's fine - use whatever term you like for what is being violated by experimentally demonstrated indeterministic AAD. 2) If you choose to say that entangled particles exhibit correlations stronger than local realism allows, I agree with that. If you choose to say that such correlations can occur without long distance entanglement, I would disagree strongly.

The most common viewpoint for entanglement of 2 photons is that they DO have spatiotemporal extent. And in fact such a system is defined as one biphoton. (Which violates conventional locality by definition.)3) We have already well settled the fact that there are no subensembles of (1&2)x(3&4) in which 1&4 share any entanglement (or correlations) whatsoever. From our swapping example: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4." But sure, go ahead and ignore the results of Nobel winning experiments.

 

[PeterDonis]

Of course we are still missing 1 & 4

Once you've worked through the rest of my earlier posts that I referenced, my take on that should be clear.

 

[PeterDonis]

Wallace provides such an account of two spacelike separated measurements on an entangled particle pair in chapter 8.7 of his book

His book is pop science as far as I know, which means it is not a valid reference here. If his book contains references to peer-reviewed papers of his that expound the same viewpoint, then references to those papers would be very helpful.

a branching event is initiated by Bob when he entangles himself with the relevant degrees of freedom

And if this is what causes Bob to branch, then, as I said before, he wasn't entangled with any relevant degrees of freedom before that event, which means Bob is irrelevant to the questions we are actually discussing, questions like: if the swap/no swap choice is made by the experimenter at the BSM that operates on Photons 2 & 3, when do Photons 1 & 4 branch into "swap" and "no swap" branches? Photons 1 & 4 are entangled with 2 & 3 prior to the swap/no swap decision, so Bob is not analogous to them and nothing Wallace or anyone else says about Bob is relevant to them. Or, if Photon 1 is measured before the swap/no swap decision is made, when does Photon 2 branch? Photon 2 is entangled with Photon 1, so anything said about Bob is irrelevant. And so on.

I'm not aware of any peer-reviewed paper, by Wallace or anyone else, that addresses the case where Bob is entangled with the degrees of freedom that Alice operates on. But if you have a reference to one, by all means post it.

 

[gentzen]

His book is pop science as far as I know

I highly doubt that his book can be classified as "pop science". From a review:

While Albert [1988] was afraid to scare the reader with the concept of a spin and complicated his book by simulating it with colors, Wallace uses positive operator valued measures (POVMs), C-star algebras, Borel measure, decoherence functional, decision-theoretic representation theorems and many other concepts that most physics graduates never encountered. The reader is assumed to have a significant philosophical background too, so the book is fully accessible only to those few who can, like Wallace, have Ph.D. both in physics and philosophy.

Of course, it is not a textbook, and not peer reviewed either. So I am not disputing that it is not a valid reference here. But if you really want to claim that it is pop science, I would like to see a reference for your definition of pop science.

 

[PeterDonis]

if you really want to claim that it is pop science, I would like to see a reference for your definition of pop science.

Pop science is anything that's not a textbook or peer reviewed paper. Yes, of course the quality of such works varies widely. But the point is that whatever the author claims in the book is not constrained by having to pass peer review by other experts. That's what makes it pop science: the author can get away with claims that they would not be able to get away with in a peer-reviewed work, because there are no other experts in the loop to challenge them.

 

[gentzen]

Pop science is anything that's not a textbook or peer reviewed paper.

I was more looking for a published reference, like this definition from wikipedia

Popular science (also called pop-science or popsci) is an interpretation of science intended for a general audience. While science journalism focuses on recent scientific developments, popular science is more broad ranging. It may be written by professional science journalists or by scientists themselves. It is presented in many forms, including books, film and television documentaries, magazine articles, and web pages.

or a listing of its common characteristics, like (from the same article)

Some usual features of popular science productions include:

• Entertainment value or personal relevance to the audience
• Emphasis on uniqueness and radicalness
• Exploring ideas overlooked by specialists or falling outside of established disciplines
• Generalized, simplified science concepts
• Presented for an audience with little or no science background, hence explaining general concepts more thoroughly
• Synthesis of new ideas that cross multiple fields and offer new applications in other academic specialties
• Use of metaphors and analogies to explain difficult or abstract scientific concepts

That definition distinguishes between "science journalism" and "pop science", even so both fall under your definition of being neither a textbook, nor peer reviewed. Also note that a monograph is not necessarily a textbook (even so some people may disagree). In fact, Wallace's book can be seen as a pretty normal monograph in philosophy.

 

[PeterDonis]

a monograph is not necessarily a textbook (even so some people may disagree)

A monograph is kind of a gray area; they aren't typically (as far as I know) peer-reviewed, but they are constrained more by existing research.

Wallace's book can be seen as a pretty normal monograph in philosophy.

Possibly, but that doesn't mean it would also be considered a pretty normal monograph in physics.

 

[Morbert]

And if this is what causes Bob to branch, then, as I said before, he wasn't entangled with any relevant degrees of freedom before that event

You did not say this before. You supposed that he was entangled with the relevant degrees of freedom before Alice's BSM, not his own interactions that induced his entanglement.

which means Bob is irrelevant to the questions we are actually discussing, questions like: if the swap/no swap choice is made by the experimenter at the BSM that operates on Photons 2 & 3, when do Photons 1 & 4 branch into "swap" and "no swap" branches? Photons 1 & 4 are entangled with 2 & 3 prior to the swap/no swap decision, so Bob is not analogous to them and nothing Wallace or anyone else says about Bob is relevant to them. Or, if Photon 1 is measured before the swap/no swap decision is made, when does Photon 2 branch? Photon 2 is entangled with Photon 1, so anything said about Bob is irrelevant. And so on.

Bob is relevant to the questions we are discussing because observer-dependence is an interesting angle to explore.

 

[PeterDonis]

You did not say this before.

Yes, I did:

If Bob is not entangled with any of the degrees of freedom involved, then he does branch when the information about the BSM result reaches him: but then what causes his branching is not the BSM itself, but his observation of the light signals carrying the information about the BSM result, which entangles him with the source of the light. And in this case, Bob is not analogous to, for example, the other photons in the experiment, because those photons are entangled with the degrees of freedom involved in the BSM.

 

[PeterDonis]

You supposed that he was entangled with the relevant degrees of freedom before Alice's BSM

That was one of two possibilities that I described. But I also described the other.

 

[Morbert]

Yes, I did:

That was one of two possibilities that I described. But I also described the other.

You are not following your own train of thought. You confused the former scenario for the latter.

 

[PeterDonis]

Bob is relevant to the questions we are discussing because observer-dependence is an interesting angle to explore.

Then you need to formulate a scenario that includes all of the measurements that @DrChinese specified, not just the BSM, and includes whatever kind of observer dependence you want to explore. What you have given so far does not do that.

 

[PeterDonis]

You are not following your own train of thought. You confused the former scenario for the latter.

Where did I do that? I don't see any such confusion in any of my posts, or in anything you quoted from my posts.

 

[Morbert]

Where did I do that? I don't see any such confusion in any of my posts, or in anything you quoted from my posts.

You said
"And if this is what causes Bob to branch, then, as I said before, he wasn't entangled with any relevant degrees of freedom before that event" which is not true, as he would have been entangled with any relevant degrees of freedom before the event, namely the BSM by Alice.

 

[Morbert]

Then you need to formulate a scenario that includes all of the measurements that @DrChinese specified, not just the BSM, and includes whatever kind of observer dependence you want to explore. What you have given so far does not do that.

My post was fine.

 

[PeterDonis]

You said
"And if this is what causes Bob to branch, then, as I said before, he wasn't entangled with any relevant degrees of freedom before that event" which is not true, as he would have been entangled with any relevant degrees of freedom before the event, namely the BSM by Alice.

You're the one who is missing the train of thought. Let's go back and start again.

There are two logical possibilities: either Bob is entangled with any relevant degrees of freedom before the event, or he isn't.

If he is entangled, then what causes him to branch is Alice making the BSM. Bob's branching happens instantaneously, because branching happens to the wave function, not in spacetime, and Bob, being entangled, is part of the wave function that all branches instantaneously when the BSM is done.

Therefore, if what causes Bob to branch is the light signals from the BSM reaching him, then, by simple contraposition, Bob wasn't entangled with any relevant degrees of freedom before the light signals reached him--because if he had been, he would have branched instantaneously when the BSM happened, not when the light signals from it reached him.

If the specification of the scenario that you intended is that Bob was entangled with relevant degrees of freedom before the event, that just means that Bob receiving the light signals cannot be what causes Bob to branch, by the reasoning I have just given. So if you are claiming both that Bob was entangled and that what causes him to branch is the light signals reaching him, then you are simply being inconsistent. You have to pick one or the other. You can't have both.

My post was fine.

Not for what I asked for. See above.

 

[Morbert]

If he is entangled, then what causes him to branch is Alice making the BSM.

The above statement is what is being challenged by Wallace's account of branching. I.e. Whether or not it is possible that Bob is entangled with the relevant degrees of freedom and also doesn't undergo instantaneous branching induced by Alice making the BSM. Your contraposition only follows if the above statement survives the challenge.

Bob's branching happens instantaneously, because branching happens to the wave function, not in spacetime.

Wallace discusses spacetime branching, and references authors like Nuel Belnap and Guido Bacciagaluppi, and I will need some time to see which references are relevant. (Though a preliminary scan suggests Bacciagaluppi is most relevant, and I will share when I can confirm this). Ultimately The relation between branching and the wave function is more subtle than the above quote.

 

[PeterDonis]

The above statement is what is being challenged by Wallace's account of branching.

Then I would want to see the math. Because my understanding is that there is no math that says this. Wallace is just asserting it as his unsupported opinion. That's why, if there is a peer-reviewed paper that expounds Wallace's claims here, I would like a reference to it, because such a paper would have to include math if there is any.

 

[PeterDonis]

I will need some time to see which references are relevant.

That's fine.

 

[Morbert]

Then I would want to see the math. Because my understanding is that there is no math that says this. Wallace is just asserting it as his unsupported opinion. That's why, if there is a peer-reviewed paper that expounds Wallace's claims here, I would like a reference to it, because such a paper would have to include math if there is any.

It's an interpretation presented by Guido Bacciagaluppi here, presented somewhat as an aside by Vaidman here, defended by Vaidman here. Similarly, this paper shows that what you call branching can be interpreted as relational change by looking at a joint measurement by Alice and Bob on an entangled microscopic system.

Note that it is a as much matter of interpretation of mathematics as it is mathematics itself. It is an Everettian interpretation of quantum theories emphasising macroscopic events amplifying microscopic events. It is often contrasted with "global branching" in literature which is an interpretation more akin to what you implied (see Vaidman's self-locating uncertainty paper above, page 16 and 17). With that said, there is a formal mathematical structure to Wallace's branching, cited by Wallace and Bacciagaluppi.

 

[PeterDonis]

It's an interpretation presented by Guido Bacciagaluppi here, presented somewhat as an aside by Vaidman here, defended by Vaidman here. Similarly, this paper shows that what you call branching can be interpreted as relational change by looking at a joint measurement by Alice and Bob on an entangled microscopic system.

Note that it is a as much matter of interpretation of mathematics as it is mathematics itself. It is an Everettian interpretation of quantum theories emphasising macroscopic events amplifying microscopic events. It is often contrasted with "global branching" in literature which is an interpretation more akin to what you implied (see Vaidman's self-locating uncertainty paper above, page 16 and 17). With that said, there is a formal mathematical structure to Wallace's branching, cited by Wallace and Bacciagaluppi.

I'll read these in more detail when I have time, but on a first quick read through, of all these references, the only one that looks like it could possibly address the issue is the last one--the book on "Branching Space-Times". And even that will only be the case if there is some actual math about how to handle branching space-times.

There is no such math in any of the other references. There is hand-waving, like the talk of "leaves of spacetime" in the first paper, but no actual math to support any such thing--and without actual math, hand-waving is useless. (There is of course math in the papers, but it's just the usual math of wave functions that we have already discussed in this thread, and in that math there is no spreading of branching at light speed, for reasons I have already explained. To the extent these papers are claiming that that math can support a claim of branching at light speed, I simply disagree: it doesn't.) Even the reference to algebraic QFT in the first paper does not help, because there are no "leaves of spacetime" in QFT: there is one spacetime, at each point of which one thing happens. QFT can calculate probabilities for different possible things happening at some point in spacetime, but there is nothing in it that can represent multiple things actually happening at one point in spacetime, which is what "leaves of spacetime" would require.

The only framework I'm aware of that contemplates assigning amplitudes to different "versions" of spacetime is quantum gravity--there the different "versions" are different curvatures due to different distributions of stress-energy, but the same framework could be used to represent different things happening at some event due to quantum uncertainty, and possibly some version of that could represent multiple things happening due to quantum uncertainty. But quantum gravity isn't mentioned in any of the references, as far as I could tell on a first reading.

 

[PeterDonis]

Note that it is a as much matter of interpretation of mathematics as it is mathematics itself. It is an Everettian interpretation of quantum theories emphasising macroscopic events amplifying microscopic events.

I understand that these papers claim that the math in question can justify a claim of branching spreading at the speed of light. But, as I said in my previous post, I think their claim is false. Talk of "macroscopic events amplifying microscopic events", and that process being "local" in spacetime, is all very well, but I've already addressed that earlier in this thread: yes, the operators that represent that process in the math are local--they only act on quantum degrees of freedom that are at their spatial location--but the wave function is not local--it includes entangled quantum degrees of freedom that are spatially separated. And branching happens to the wave function, not just to certain localized degrees of freedom: any degrees of freedom that are entangled with a localized degree of freedom that gets acted on by an operator that causes branching, will branch, because they have to--they're all together in the wave function. You can't separate them and say that only one branches when the operator acts, and the other doesn't branch until a light travel time later. They all branch together. That's what the math says. Arguments to the contrary based on that math are just hand-waving with no justification. That's why I have said there needs to be different math to justify a claim of branching spreading at the speed of light.

 

[Morbert]

(There is of course math in the papers, but it's just the usual math of wave functions that we have already discussed in this thread, and in that math there is no spreading of branching at light speed, for reasons I have already explained. To the extent these papers are claiming that that math can support a claim of branching at light speed, I simply disagree: it doesn't.)
[...]
yes, the operators that represent that process in the math are local--they only act on quantum degrees of freedom that are at their spatial location--but the wave function is not local--it includes entangled quantum degrees of freedom that are spatially separated. And branching happens to the wave function, not just to certain localized degrees of freedom [...] Arguments to the contrary based on that math are just hand-waving with no justification. That's why I have said there needs to be different math to justify a claim of branching spreading at the speed of light.

Given some expansion of the global state into macrosocopically distinct terms (worlds), Wallace et al interpret macroscopic properties of subsystems that are unchanged across different terms as unbranched, as evidenced by the appropriate traces, even though each term in the expansion of the global state is macroscopically distinct. I.e. Even if a global state is changed by local operations, the properties instantiated by that state exhibit a local branching structure. I do not see how this is hand-waving. If there is vagueness, there is vagueness on all sides, as I have come across plenty of literature attempting to clarify the physical meaning of the global state in an Everettian context. Simply noting that the changing global state is nonseparable and being done with it is just as hand-waving.

 

[PeterDonis]

Wallace et al interpret macroscopic properties of subsystems that are unchanged across different terms as unbranched

In other words, he discards all information about entanglement. That does seem to me to be hand-waving, since without entanglement you can't account for the correlations.

Simply noting that the changing global state is nonseparable and being done with it is just as hand-waving.

No, it isn't, it is taking the MWI exactly at its word: the MWI says the wave function is reality, so a nonseparable wave function means a nonseparable reality according to the MWI.

We are probably at the point where we're not going to resolve anything further here, since we are talking about a QM interpretation and QM interpretation disputes are not resolvable if it gets to the point of differing opinions. There is no way to experimentally test the matter. This is the kind of case that the guidelines for this subforum talk about. Relevant references are given in the thread and any reader can read them and make up their own mind.

 

[Morbert]

We are probably at the point where we're not going to resolve anything further here, since we are talking about a QM interpretation and QM interpretation disputes are not resolvable if it gets to the point of differing opinions.

Ok. For the record, I am not a MWI proponent insofar as I think it is an incomplete project.

 

[PeterDonis]

For the record, I am not a MWI proponent

Neither am I. But this thread is about the MWI, so whether we're proponents or not, we should try to understnd as best we can what it says. It might well be that there are different versions of the MWI in the literature, so that even its proponents don't all agree on what it says. (It would not be the only QM interpretation that is like that.)

 

[PeterDonis]

I have found a review of the "Branching Space-Times" book online here:

https://ndpr.nd.edu/reviews/branching-space-times-theory-and-applications/

From the review, it looks like a sort of mixture of consistent histories and the MWI. Unfortunately, the review does not describe any actual math in the book (although the description of some chapters suggests that there might be some).