Is MWI Considered Local in Quantum Mechanics?

[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).

 

[PeterDonis]

I have also found this arxiv preprint giving a branching spacetime analysis of the GHZ theorem:

https://arxiv.org/abs/quant-ph/9510002

 

[PeterDonis]

Moderator's note: If there is interest in further discussion of the Branching Space-Time model, it probably needs to be treated as a separate interpretation from the MWI and be spun off into its own thread.

 

[Morbert]

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).

Decoherent histories formalism is leveraged heavily by Wallace's camp. Specifically, they are interested in the development of the universal wavefunction wrt decoherence bases. (Though they still identify as Everettians as they believe all histories in a set with nonzero weights occur. DH proponents believe only one history in a set occurs). And projectors in sets of decoherent histories mark out causal structures that branching spacetime maths can be applied to.

 

[PeterDonis]

they still identify as Everettians as they believe all histories in a set with nonzero weights occur. DH proponents believe only one history in a set occurs

Hm, ok, so it is kind of a mixture. Interesting.

 

[vanhees71]

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]."

But that's misleading. There is no action at a distance nor acausal influences in contemporary relativistic QFT by construction. The Nobel committee's formulation is of course inaccurate.

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.

To the contrary, I say you cannot violate Einsteinian causality with any experiment that is describable by relativistic local QFT, and Zeilinger's teleportation is perfectly in agreement with standard QED!

2) If you choose to say that entangled particles exhibit correlations stronger than local realism allows, I agree with that. ReplyIf you choose to say that such correlations can occur without long distance entanglement, I would disagree strongly.

"Long-distance entanglement" of course can occur and is observed with all these experiments we discuss here. It's, however, a correlation due to the preparation procedure and not caused by mutual local measurements on each other that violate Einstein locality.

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.)

Of course, the electromagnetic field is a field, i.e., a quantity that is defined on each point in Minkowski space. A photon has not even a position observable and thus it doesn't make sense to say it's a localize "pointlike" object.

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.

But the results of these Nobel-winning experiments precisely are that you can select (even post-select) sub-ensembles where 1&4 are entangled, namely by projecting based on a local measurement on the pair 2&4. As I said many times before, that's just a more sophisticated realization of a teleportation protocol. Read Zeilinger's original papers (around 1997 or so), where this is make very clear.

 

[PeterDonis]

It's, however, a correlation due to the preparation procedure

Only if you include the BSM in the "preparation procedure".

that's just a more sophisticated realization of a teleportation protocol.

And teleportation has all of the same issues, which you can't just handwave away by saying that QFT satisfies your preferred definition of the term "locality". We have had this discussion before. You can't dictate physics by fiat by defining words.

Also please bear in mind the fact, which I have already pointed out in an earlier post, that this is the interpretations forum and disagreements about QM interpretations are ultimately not resolvable. The best that can be done is for all sides to state their positions and give whatever references they can. We're pretty much at that point in this thread.

 

[DrChinese]

1. The Nobel committee's formulation is of course inaccurate.

2. "Long-distance entanglement" of course can occur and is observed with all these experiments we discuss here. It's, however, a correlation due to the preparation procedure and not caused by mutual local measurements on each other that violate Einstein locality.
...

3. But the results of these Nobel-winning experiments precisely are that you can select (even post-select) sub-ensembles where 1&4 are entangled, namely by projecting based on a local[sic this is nonlocal] measurement on the pair 2&4[sic - I'm sure 2& 3 are intended]. As I said many times before, that's just a more sophisticated realization of a teleportation protocol. Read Zeilinger's original papers (around 1997 or so), where this is make very clear.

1. I think your viewpoint speaks for itself here. As I mention, yours is NOT mainstream science - while that of the Nobel committee is mainstream almost by definition. I would even call them slow and deliberate, considering that Bell died before he could be recognized properly by them.

2. The swapping preparation procedure is nonlocal, and you say that in your 3 (whether you meant to or not). The BSM on 2&3 is performed far from the 1 & 4 photons, and can of course even be performed after they are detected with no change of statistics.

3. Yes, swapping and teleportation use the same underlying technique. I use swapping experiments because they allow one to see the underlying nonlocality with more clarity.

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

Really, nothing you are saying here has anything to do with this thread. No point in us belaboring these points here yet again.

 

[vanhees71]

1. I think your viewpoint speaks for itself here. As I mention, yours is NOT mainstream science - while that of the Nobel committee is mainstream almost by definition. I would even call them slow and deliberate, considering that Bell died before he could be recognized properly by them.

Since when is standard relativistic QFT not "mainstream science"?

2. The swapping preparation procedure is nonlocal, and you say that in your 3 (whether you meant to or not). The BSM on 2&3 is performed far from the 1 & 4 photons, and can of course even be performed after they are detected with no change of statistics.

It's entirely local. The projection is done by a local measurement on photons 2 & 3. The correlations ensuring that then for the so prepared subensemble also photon 1&4 are entangled is due to the initial preparation of the four-photon state. That's mainstream science.

3. Yes, swapping and teleportation use the same underlying technique. I use swapping experiments because they allow one to see the underlying nonlocality with more clarity.

There is no nonlocality, i.e., no violation of Einstein causality. It's inseparability that's described by entanglement of this kind! That may be not "main-stream terminology" but it's main-stream physics!

 

[PeterDonis]

There is no nonlocality, i.e., no violation of Einstein causality.

@vanhees71, we have had the discussion about terminology too many times. Enough is enough. I have now banned you from further posting in this thread.

 

[PeterDonis]

It's entirely local. The projection is done by a local measurement on photons 2 & 3. The correlations ensuring that then for the so prepared subensemble also photon 1&4 are entangled is due to the initial preparation of the four-photon state.

For the record, this has been addressed multiple times already in this thread: the operations you describe are local, but the wave function is not.

 

[DrChinese]

Following up post #79, here is how the MWI describes the version of the entanglement swapping experiment I gave the math for there, where photon 1 is measured before the swap/no swap operation. (I will also consider below the version where both photons are measured before the swap/no swap operation.)

(I should note once again that in post #79 and here, I have switched the entangled states I am talking about so that they are the singlet state, i.e., $HV - VH$, since that is the one that seems to be used most often in these experiments.)

1. The branching for the photon 1 measurement is of course simple: we end up with two worlds, one in which photon 1 is H (and photon 4 is V), the other with photon 1 V (and photon 4 H).

2. Now we look at the swap operation. (The no swap operation, as noted already, is just the identity, which does not induce any branching.) I said in an earlier post that the only branching induced by the swap/no swap decision is "swap" vs. "no swap"; that means that the state I wrote in post #79 as $U_S \Psi_{1A}$, i.e., the state in the "swap" branch, should not have any further branching. And indeed it doesn't: we still have just two branches, corresponding to the two branches induced by the photon 1 measurement as described above. All that has happened is that the photon 2 and 3 degrees of freedom have undergone the unitary operation described for $U_S$ in post #79.

3. The final branching is now the photon 4 measurement, which, as we can see from post #79, also produces no further branching in the "swap" branch. In other words, the two "worlds" in the "swap" branch already have the correct photon 4 states for the expected entanglement with photon 1, and no others. So once again, the wave function enforces the correlations, just as the MWI says.

We could do a similar analysis for the case where photon 4 is measured, then the swap/no swap decision occurs, then photon 1 is measured. The result would be the same. So, to summarize, we have analyzed three cases of time ordering, with results as follows:

Case 1: swap/no swap, then photon 1 & 4 measured: "swap" and "no swap" branches, then two further branches in the "swap" branch (since 1 & 4 are entangled so only the correlated results have amplitudes), and four further branches in the "no swap" branch (since 1 & 4 are uncorrelated in this branch so all four possible combinations have amplitudes).

Case 2/3: measure 1 (or 4), then swap/no swap, then measure 4 (or 1): two branches at the first measurement, then each branch gets two further branches ("swap" and "no swap"), then no further branching in the "swap" branch (since the swap operation has rotated the photon 2 & 3 branches in just the right way to enforce the right correlations between photons 1 & 4). We haven't explicitly analyzed the "no swap" branch for this case, but the result is that we get a further two-branch split so that there are four final branches that have "no swap" results. And, since everything commutes, the two "swap" branches are the same (in terms of their wave functions) as the two "swap" branches in Case 1 above, and the four "no swap" branches are the same as the four "no swap" branches in Case 1 above. The order of the branching is different, but the final resulting branches are the same.

That leaves one more case:

Case 4: measure both 1 and 4, then swap/no swap. Here we get four total branches from the two measurements. The "no swap" branch induced by the swap/no swap decision is now trivial: it's the same four branches that are the final result in the "no swap" cases above. (The "no swap" operation is just the identity, as noted above, so this should come as no surprise.) But what about the "swap" branch?

Let's look again at the math: we apply the photon 1 and 4 measurement operators (which just put bars over those photon kets) to the state $\Psi_0$. What do we get? We get this:

$$
M_1 M_4 \Psi_0 = \bar{H}_1 V_2 H_3 \bar{V}_4 - \bar{V}_1 H_2 H_3 \bar{V}_4 - \bar{H}_1 V_2 V_3 \bar{H}_4 + \bar{V}_1 H_2 V_3 \bar{H}_4
$$

If we then apply $U_S$ to this, we see something that might seem strange: the middle two terms in the above, the ones where the photon 2 & 3 kets are the same, get annihilated. ($U_S$ applied to those combinations of photon 2 & 3 states gives zero, as shown in post #79.) What does this mean?

What it means is that, in those branches of the wave function $M_1 M_4 \Psi_0$, i.e., for "worlds" in which the photon 1 & 4 measurement results are already recorded to be inconsistent with entanglement, the swap operation cannot take place.

This is addressing your post #81:

1. I assume you mean photons 1 & 2 - and not 1 & 4. At the time of the measurement of photon 1, there is no association of the 1 & 2 system with any other system in the universe. In fact, there is no requirement 3 & 4 yet even exist.

2. The branching between your swap and no swap is both partially accurate and excessively over-simplified at the same time. I'll explain.

If a swap occurs, it is only because the 2 and 3 photons were indistinguishable. If no swap occurs, it is only because the 2 and 3 photons were distinguishable. Indistinguishability is a physical requirement if MWI is to give us the same experimental results as predicted by QM. (And note that we are assuming there are to be relative coincident clicks within the specified time window for Photons 1 & 4 in all cases we consider.) Do you see the problem here? Nothing happening is in fact a fork of some kind, if we say the other fork is a swap.

3. In the experiment, we are only considering cases of 4 fold coincidences. That's true, swap or no swap. So assuming the no swap case is creating by delaying Photon 3 by 30 ns and the window is 13 ns wide, we end up with something like a. and b. below. Note that the times I give are adjusted for path length, except Photon 3's length adjustment does not consider the extra 30 ns delay that may or may not be added by the experimenter.

(Arrival times in ns, where 0 is the first measured.)
a. Successful swap example, all detections within 13 ns window:
Photon 1=0
Photon 2=2
Photon 3=6 (no delay by the experimenter)
Photon 4=3

b. No swap example, one BSM detection is outside the 13 ns window (because the experimenter chose "no swap"):
Photon 1=6
Photon 2=0
Photon 3=32 (a 30 ns delay was performed)
Photon 4=5

Now, all of the detections are made by 8 APD type detectors after each photon passes through 1 of 4 polarizing beam splitters (PBS). There are actually 4 variable orientations for the PBSs, yielding an H> or V> for their direction. (For simplicity's sake, we consider the 2 & 3 permutations in which one of the two identifiable Bell states appear. For our purposes, it really doesn't matter which ones as we assume the experimenter can see this and and will report accordingly. Let's call one a +swap and the other a -swap, where a +swap means 1 & 4 will be correlated and a -swap means 1 & 4 will be anti-correlated. Of course, we can still have Nswap which is the no swap case.) There will always be a click at 2 of the 4 BSM detectors (ideal case of course). And if they are within the time window, there will be a +swap or a -swap. Hopefully, we are in agreement to here.

So here is where we need help from the MWI proponent. The Nswap must mean the 2&3 photons did not swap because they did not overlap sufficiently closely in the beam splitter (BS). The +swap and -swap cases result from suitable overlap followed by polarization measurements on 2 & 3 which indicate which type resulted.

So what we know, IF there is a swap: there were 2 branches created by measurement of photon 1 (H> or V>) and that doubled when the swap was detected as + or -.

Photons 1&2&3:
H>+swap>
H>-swap>
V>+swap>
V>-swap>

Plus a doubling to 8 branches, if we now add photon 4 and measure it at the same angle as photon 1:

Photons 1&2&3&4, branches with a swap:
H>+swap>H>
H>-swap>H> X
V>+swap>H> X
V>-swap>H>
H>+swap>V> X
H>-swap>V>
V>+swap>V>
V>-swap>V> X

But 4 of those 8 cases (marked X) can NEVER occur (ideal case). How can the distant photon 4 "know" which photon 1 outcome it must be matched to? If MWI were local and deterministic, the outcome of the photon 4 measurement is independent of the swap being +swap or -swap. And in fact, the outcome of the photon 4 measurement is independent of the swap not occurring at all (the Nswap case), which happens whenever the experimenter so chooses.

Photons 1&2&3&4, combined swap/no swap branches:
H>+swap>H>
H>-swap>H> X
V>+swap>H> X
V>-swap>H>
H>+swap>V> X
H>-swap>V>
V>+swap>V>
V>-swap>V> X
H>Nswap>H>
H>Nswap>V>
V>Nswap>H>
V>Nswap>V>

Clearly, the correct outcomes for Photon 4 depend mightily on the branching that occurs elsewhere. It's outcome could not have been a result of propagation of a wavefunction change evolving such that it respects c. And saying that the disallowed combinations have a weight of 0 while the allowed combinations have a weighting of 1 doesn't change the question.

 

[PeterDonis]

1. I assume you mean photons 1 & 2 - and not 1 & 4.

I was referring to the state after a swap has occurred (if it occurs). Before the swap, I agree that photons 1 & 2 are entangled and there is no relationship between photons 1 & 4.

Nothing happening is in fact a fork of some kind, if we say the other fork is a swap.

I agree in general that "nothing happening" can be a decoherent branch.

However, in the case of the swap/no swap, we have distinguishable states of the detectors in the output arms of the BSM, so there is no "nothing happening" option in which no macroscopic change occurs at all. If a swap occurs, one photon is detected in each output arm of the BSM. If no swap occurs, then either there is a detection in only one output arm and not the other, or there is no detection in either output arm. All of these are macroscopically distinguishable changes, since we also have a narrow time window for the detections, if any, to occur.

As for the "no swap" decision by the experimenter creating distinguishability by forcing photons 2 & 3 to arrive at sufficiently different times at the BSM, I agree that that is being done, and it is included in what I was calling the "BSM" or "swap/no swap decision" operator. You can of course make a finer-grained time-based analysis of what is going on there, but it doesn't change anything about the MWI description I gave.

here is where we need help from the MWI proponent. The Nswap must mean the 2&3 photons did not swap because they did not overlap sufficiently closely in the beam splitter (BS). The +swap and -swap cases result from suitable overlap followed by polarization measurements on 2 & 3 which indicate which type resulted.

Yes. That was the basis of my analysis.

The only real change you are introducing here is that in the "no swap" case, you are allowing either the photon 1 or the photon 4 detection to be between the photon 2 and photon 3 detections. My MWI analysis did not specifically include that case. However, since this can only occur in the "no swap" branch, it actually doesn't affect the MWI description, because in the "no swap" case the unitary operator on the photon 2 & 3 states is just the identity, so it doesn't matter at what point in time we apply it; it doesn't change the wave function at all!

The rest of your description is hard for me to follow (in fact it is almost unreadable because of formatting). But I have already thoroughly described the actual branching process in previous posts. If you think my description is wrong (I'm not sure you actually do--see comments at the end of this post about "nonlocal"), I would much rather that you either quote specific statements from those posts that you either disagree with or cannot understand, or at the very least adopt the same notation (and use LaTeX for it) that I did in my posts, to describe what you think the branching is, if it's not the same as what I said in my posts.

That said, I can comment on a few things:

4 of those 8 cases (marked X) can NEVER occur (ideal case).

Yes, that's the point!

How can the distant photon 4 "know" which photon 1 outcome it must be matched to?

Because the other possibilities are eliminated as never occurring--see above. (But note that I am not claiming that this process, in its entirety, is local--see below.)

If MWI were local and deterministic, the outcome of the photon 4 measurement is independent of the swap being +swap or -swap.

Please note that I have not claimed that the MWI is "local and deterministic". In fact, as I have posted previously, I think that while the unitary operators involved are local (they only operate on degrees of freedom at their spatial location--for example, the BSM only operates on the photon 2 & 3 degrees of freedom), the wave function is not local (because it includes entangled degrees of freedom that are spatially separated). And since the unitary operators operate on the wave function, we have "local" plus "nonlocal" gives "nonlocal". So based on that I would say that the MWI is nonlocal and deterministic. Maybe that is a sufficient answer to the original question of this thread.

 

[DrChinese]

1. I was referring to the state after a swap has occurred (if it occurs). Before the swap, I agree that photons 1 & 2 are entangled and there is no relationship between photons 1 & 4.

2. However, in the case of the swap/no swap, we have distinguishable states of the detectors in the output arms of the BSM, so there is no "nothing happening" option in which no macroscopic change occurs at all. If a swap occurs, one photon is detected in each output arm of the BSM. If no swap occurs, then either there is a detection in only one output arm and not the other, or there is no detection in either output arm. All of these are macroscopically distinguishable changes, since we also have a narrow time window for the detections, if any, to occur.

As for the "no swap" decision by the experimenter creating distinguishability by forcing photons 2 & 3 to arrive at sufficiently different times at the BSM, I agree that that is being done, and it is included in what I was calling the "BSM" or "swap/no swap decision" operator. You can of course make a finer-grained time-based analysis of what is going on there, but it doesn't change anything about the MWI description I gave.

3. Yes. That was the basis of my analysis.

The only real change you are introducing here is that in the "no swap" case, you are allowing either the photon 1 or the photon 4 detection to be between the photon 2 and photon 3 detections. My MWI analysis did not specifically include that case. However, since this can only occur in the "no swap" branch, it actually doesn't affect the MWI description, because in the "no swap" case the unitary operator on the photon 2 & 3 states is just the identity, so it doesn't matter at what point in time we apply it; it doesn't change the wave function at all!

4. The rest of your description is hard for me to follow (in fact it is almost unreadable because of formatting). ... I would much rather that you either quote specific statements from those posts that you either disagree with or cannot understand, or at the very least adopt the same notation (and use LaTeX for it) that I did in my posts, to describe what you think the branching is, if it's not the same as what I said in my posts.

5. Yes, that's the point!

Because the other possibilities are eliminated as never occurring--see above. (But note that I am not claiming that this process, in its entirety, is local--see below.)6. Please note that I have not claimed that the MWI is "local and deterministic". In fact, as I have posted previously, I think that while the unitary operators involved are local (they only operate on degrees of freedom at their spatial location--for example, the BSM only operates on the photon 2 & 3 degrees of freedom), the wave function is not local (because it includes entangled degrees of freedom that are spatially separated). And since the unitary operators operate on the wave function, we have "local" plus "nonlocal" gives "nonlocal".

7. So based on that I would say that the MWI is nonlocal and deterministic. Maybe that is a sufficient answer to the original question of this thread.

1. Fine.2. We are in agreement about the 2 & 3 detector clicks.

But there is one little stone left unturned. Indistinguishability is an absolute requirement of a swap. It is, by definition, not reversible (else there would be distinguishability remaining in at least one degree of freedom). Any irreversible process must lead to branching, right? And must be a physical process as well, wouldn't you agree (if it is in fact irreversible)? And this irreversible process can't itself depend on subsequent detector clicks... as those clicks just inform us whether we ended up with |ψ+| or |ψ-| (when 2 nearly simultaneous clicks occur at the BSM).

The detector clicks can occur as much later than the "indistinguishability event" occurs as we would like. The path length from the BS to the PBS can be any length, and the additional path length from the PBS to the detector can be any length. But the event itself must occur at the BS.

[Keep in mind that this process of indistinguishability is mysterious to me. I have never seen a good explanation of this in any paper or interpretation - I just know how the "theoretical" rule is applied in experiments. And I believe it is clearly a physical process (not an update of knowledge or a filtering process) - else inserting a delay (to distinguish photon 2 from photon 3) shouldn't matter. But this is the stuff for another thread...]3. All good.4. Sorry, I thought my presentation would be clear enough. |ψ+| is the same as +swap, |ψ-| is the same as -swap for photons 2&3.

I don't think it is really any different than yours, the difference is that I am trying to differentiate the branching according to a specific time line (and of course I realize that order shouldn't matter, but that is the point we are examining since MWI claims a deterministic description in which order might matter). The first when Photon 1 is measured, the second as Photons 2 & 3 are measured, and the last as Photon 4 is measured.

a. We started with a product state of 2 entangled states:
|12ψ->|34ψ->

b. After measurement of photon 1, we have 2 branches:
|1H2V>|34ψ->
|1V2H>|34ψ->

c. After measurement of photons 2&3, we have 4 branches (ignoring Bell states that can't be identified) that can occur and 4 that cannot:
|1H>|23ψ-|4V>
|1H>|23ψ+|4H>
|1V>|23ψ-|4H>
|1V>|23ψ+|4V>
|1H>|23ψ-|4H> X
|1H>|23ψ+|4V> X
|1V>|23ψ-|4V> X
|1V>|23ψ+|4H> X

d. Note that the counterfactual 4> cases are presented, I realize that an MWI proponent would deny these exist. You could just say:

|1H>|23ψ-|4>
|1H>|23ψ+|4>
|1V>|23ψ-|4>
|1V>|23ψ+|4>

e. But what we needed is this result after the swap:
|14ψ->|23ψ->
|14ψ+>|23ψ+>

f. If you don't want to comment on these, that's fine. You've invested a lot of time already. 5. I know, hence the Xs. But there is no actual explanation of how "conflicting" states - the ones with Xs - are suppressed. After all, they are measured in separate places too far apart for any updating to be connected in a manner consistent with locality.6. Agreed.7. Probably sufficiently so in terms of this thread.

Locality in MWI:
No one has put up an argument that MWI is local, other than a few quoted claims of a few MWI proponents - who themselves don't seem to agree fully. By any reasonable analysis (of course represented in this thread LOL), MWI is as nonlocal as standard interpretations of QM. And certainly no less so.

Determinism in MWI:
a. And when we say MWI is deterministic: we simply mean every branch occurs - and which one we are in (consciously) is random.
b. And when we say MWI is deterministic: we also mean that it is NOT possible to trace back in time what branching occurred (or when or where); and we cannot select any particular prior branch as being a branch which gave "birth" to the one we are in.
c. And finally, when we say MWI is deterministic: we also mean that there is no way even in principle to predict what future branch we will occupy at any future date. Which is exactly the same as in every indeterministic interpretation of QM.
d. Moreover: Anything is possible, in fact every outcome is possible. In fact: not only is everything possible, everything WILL occur.

I guess ol' LaPlace's Demon wouldn't much recognize this "deterministic" universe.

 

[PeterDonis]

Indistinguishability is an absolute requirement of a swap. It is, by definition, not reversible

I'm not sure what you mean. "Indistinguishability" by itself is not an operation, it's a precondition for an operation. The actual operation, namely the unitary operator I called $U_{S}$, is reversible--all unitary operators are. In this particular case, as I think I commented in a previous post, since the "swap" case involves one photon in each output arm of the BSM, just put in a mirror and a second beam splitter so you have a Mach-Zehnder interferometer for photons 2 & 3, and after the second beam splitter, the swap is reversed.

What makes the swap irreversible is the detection of one photon in each output arm of the BSM. But that means you have put detectors there instead of mirrors and a second beam splitter. You can't do both.

I am trying to differentiate the branching according to a specific time line

I did that already for every case I covered. As I said before, the only change you appear to be introducing is to capture the timing of the arrival of photons 2 & 3 at the BSM, in order to evaluate the indistinguishability criterion, separately from the operation of the BSM itself. But there is no measurement of the arrival times of photons 2 & 3 at the BSM, so there is no branching due to that. The only branching is due to the detection of photons (or not) in the output arms of the BSM. For my analysis, I separated out just one of the possible outcomes of that detection, namely "one photon detected in each output arm of the BSM", and called that the "swap" outcome; the other three possible outcomes, namely "photons only detected in output arm A", "photons only detected in output arm B", and "no photons detected in either output arm", were all included in the "no swap" outcome, because, as I said, they all correspond to the same operator on the photon 2 & 3 degrees of freedom, namely "nothing" (the identity). One could of course separate out the "no swap" outcomes further, but I didn't see the point for this analysis.

there is no actual explanation of how "conflicting" states - the ones with Xs - are suppressed

I don't understand this. I explicitly showed in the math exactly how this happens. You even reproduce the same math in your post, where you recognize that the "X" outcomes are ones that are eliminated in the wave function because they have zero amplitude. That is the explanation. What more do you want?

No one has put up an argument that MWI is local

I agree. And as I said, I do not think it is, due to the nonlocal nature of the wave function.

when we say MWI is deterministic: we simply mean every branch occurs

Yes.

and which one we are in (consciously) is random

No. In so far as "consciousness" comes into play at all, it would have to be there in every branch. There is nothing in the wave function that would pick out any particular branch; there is no "random" element anywhere to make any such choice.

In other words, if I were to observe the result of one of the photon detections in this experiment, there would be two branches of my consciousness, just like there would be two branches of everything else, an "H" branch and a "V" branch. My consciousness, as far as the MWI is concerned, must be emergent from the wave function (though of course nobody has any real idea how), so there must be degrees of freedom in the wave function that underlie my consciousness, and those degrees of freedom are entangled with the detector ones so that the result I am conscious of is the result that is registered by the detector, in each branch.

it is NOT possible to trace back in time what branching occurred

In principle it is, because branching is unitary (all time evolution in the MWI is unitary). Whether it can be done in practice depends on what information is available to you. If you run an experiment that measures the time at which a particular detector gave its reading, and the reading is stored in a stable manner, then that information is sufficient to trace back in time what branching occurred.

we cannot select any particular prior branch as being a branch which gave "birth" to the one we are in

Yes, we can, if we have the necessary information. See above. The same information that tells you when a branching occurred also tells you what prior branch was the "parent" of all the branches produced at that branching.

we also mean that there is no way even in principle to predict what future branch we will occupy at any future date

No. "What future branch we will occupy" is not a well posed concept. "We" occupy all branches. See above.

every outcome is possible

Every outcome with a nonzero amplitude in the wave function is possible. Many MWI discussions are very cavalier about that qualifier, but it's crucial. You can't just wave your hands and assert that anything is "possible" in the MWI with no supporting argument. You have to actually do the work of showing how the wave function includes the possibility.

 

[PeterDonis]

I guess ol' LaPlace's Demon wouldn't much recognize this "deterministic" universe.

I think you have some misunderstandings about how the MWI actually works. See my previous post.

 

[mattt]

@DrChinese, the Many Worlds Interpretation has other problems (for example, the existence of conscious humans, in other branches, where they observe that the relative frequencies of the results of certain quantum experiments do not satisfy what we in this "our branch" call the Born rule), but it is of course completely deterministic.

What it changes is the ontology, "what there is" ("what the Universe itself is"), but given that its dynamics is entirely defined as a PDE, it is of course deterministic.

Most people don't like that it posits an ontology in which the versions of conscious beings in each branch can never "prove" the existence of the other branches.

But well, every interpretation of quantum mechanics has its own shortcomings...

It is nonetheless fun to dive in each of them, to see how the same mathematical structure can be dressed in so many different narratives.

 

[physika]

c. And finally, when we say MWI is deterministic we also mean that there is no way even in principle to predict what future branch we will occupy at any future date

Determinism is not the same that predictability, chaos theory is deterministic but unpredictable.

....

 

[PeterDonis]

Determinism is not the same that predictability, chaos theory is deterministic but unpredictable.....

Chaos theory relies on nonlinear dynamics. The unitary dynamics of QM is linear.

 

[Motore]

@DrChinese, the Many Worlds Interpretation has other problems (for example, the existence of conscious humans, in other branches, where they observe that the relative frequencies of the results of certain quantum experiments do not satisfy what we in this "our branch" call the Born rule), but it is of course completely deterministic.

Well, there are proponents who conclude that the Born rule arises more naturally in MWI than other interpretations using the Principle of indifference -> see attachment (not a peer review article).

 

[mattt]

Well, there are proponents who conclude that the Born rule arises more naturally in MWI than other interpretations using the Principle of indifference -> see attachment (not a peer review article).

I know how they try to recover The Born Rule in Many Worlds Interpretation, but that's not what I was trying to point out.

According to Many Words Interpretation, there will be conscious humans (there will be branches) that, in a quantum coin experiment (which according to what we, in this "our branch" call "The Born Rule", have a 0.5 probability of H and 0.5 probability of T) will observe 1,000.000 consecutives Heads (for example).

There will exist all kinds of "anomalous" branches (for example branches in which EVERY quantum coin experiment will give a million consecutive heads).

Of course the conscious humans in those anomalous branches will never develop a theory like "our" mathematical quantum mechanics with "our" Born Rule ("our" I mean the branch in which you and me are, where "our" Born Rule is actually satisfied in "our" quantum experiments), because "our" Born Rule and in fact "our" mathematical Quantum Mechanics does not describe correctly the results of their quantum experiments.

I was just trying to emphasize in my previous post that to many people, an interpretation that postulates the existence of so many "impossible to prove" strange things (that we will never observe in this our branch) is maybe too much.

 

[martinbn]

I know how they try to recover The Born Rule in Many Worlds Interpretation, but that's not what I was trying to point out.

According to Many Words Interpretation, there will be conscious humans (there will be branches) that, in a quantum coin experiment (which according to what we, in this "our branch" call "The Born Rule", have a 0.5 probability of H and 0.5 probability of T) will observe 1,000.000 consecutives Heads (for example).

There will exist all kinds of "anomalous" branches (for example branches in which EVERY quantum coin experiment will give a million consecutive heads).

Of course the conscious humans in those anomalous branches will never develop a theory like "our" mathematical quantum mechanics with "our" Born Rule ("our" I mean the branch in which you and me are, where "our" Born Rule is actually satisfied in "our" quantum experiments), because "our" Born Rule and in fact "our" mathematical Quantum Mechanics does not describe correctly the results of their quantum experiments.

I was just trying to emphasize in my previous post that to many people, an interpretation that postulates the existence of so many "impossible to prove" strange things (that we will never observe in this our branch) is maybe too much.

 

[Motore]

will observe 1,000.000 consecutives Heads (for example)

And would conclude (if all other quantum measurements confirm QM and the coin is fair) that MWI is the correct interpretation :)
https://en.wikipedia.org/wiki/Quantum_suicide_and_immortality
Ok, we are veering of topic, so I will stop it here.

 

[mattt]

And would conclude (if all other quantum measurements confirm QM and the coin is fair) that MWI is the correct interpretation :)
https://en.wikipedia.org/wiki/Quantum_suicide_and_immortality
Ok, we are veering of topic, so I will stop it here.

But that's the problem. There is an infinite number of different ways in which a set of experimental results (no matter how large the number of repetitions, or how varied the quantum experiments themselves) will not be correctly described by our Born rule, and yet for each of those strange set of experimental results, there will be a branch with exactly those experimental results.

I know this is off topic here (and we could start a new thread called: "is it reasonable to expect that in each and every branch with human beings, they all will infer that "our" mathematical quantum mechanics with " "our" Born rule is the correct description of the Universe?"), but I guess that they will not.

For example, there will be branches in which the relative frequencies of the possible results of any quantum experiment will not approximate any concrete limit (as they make more and more repetitions). In those branches there are no regularities, not even probabilistic.

 

[PeterDonis]

we could start a new thread called: "is it reasonable to expect that in each and every branch with human beings, they all will infer that "our" mathematical quantum mechanics with " "our" Born rule is the correct description of the Universe?"

Yes, please start a new thread if you want to discuss that aspect of the MWI. It is a separate issue from the question under discussion in this thread, of whether or in what ways the MWI is local.

 

[DrChinese]

I'm not sure what you mean. "Indistinguishability" by itself is not an operation, it's a precondition for an operation. The actual operation, namely the unitary operator I called $U_{S}$, is reversible--all unitary operators are. In this particular case, as I think I commented in a previous post, since the "swap" case involves one photon in each output arm of the BSM, just put in a mirror and a second beam splitter so you have a Mach-Zehnder interferometer for photons 2 & 3, and after the second beam splitter, the swap is reversed.

What makes the swap irreversible is the detection of one photon in each output arm of the BSM. But that means you have put detectors there instead of mirrors and a second beam splitter. You can't do both.

1. I would love to see a reference for this experimental realization, because I don't think indistinguishability is reversible (by definition, else there is a distinguishable degree of freedom remaining). I have never seen any hint of this in the literature, but of course that alone means nothing.

Your idea, as I understand it: You place 2 mirrors in place of 2 PBSs, then recombine them at a new (second) BS. Are you saying they will then always emerge from that second BS in different directions, and they can therefore always be identified as to their source? I think your idea is that normally, constructive/destructive interference causes a photon to emerge from a single port of the second BS.

But I don't think entangled photons - at least in this case - will act the same as they would if they were not entangled. And of course, the entanglement is 1&2 and 3&4 until the swap occurs. Since the 1 photon could be used to determine which path information for photon 2, no constructive interference results. This isn't the greatest paper, but I think it shows the essential difficulty.

Two-Photon Interference Experiment in a Mach-Zehnder
https://opg.optica.org/directpdfacc...sk-7-2-113.pdf?da=1&id=194686&seq=0&mobile=no2. A technical point in your understanding of the swap variations of the BSM: 50% of the cases involve the 2&3 photons going into separate arms of the BSM, and 50% of the cases involve the 2&3 photons going into the same arms of the BSM. This is of course after the BS and before arriving at the PBS(s). Because only 2 of 4 Bell states can be identified, when the 2&3 photons go to the same arm, they must be polarized oppositely. From the reference:

"On the other hand, a coincidence detection event between either DQ1H and DQ1V or DQ2H and DQ2V indicates a projection on ψ+. [DQ1 is one arm, DQ2 is the other arm.]"

Of course, if there is an identifiable swap: 2 clicks occur at the BSM.