A Is MWI Considered Local in Quantum Mechanics?

[PeterDonis]

the rule for a successful swap in the BSM is something labeled "indistinguishability"

I should note that in my analysis in the posts I have referenced, I don't make any specific assumption about how this works. All I assume is that at the BSM, there is some probability of a swap and a corresponding probability of no swap. So the unitary operator that I call $U_{S/N}$, that describes all of the possibilities of what can happen at the BSM, is just a linear combination of the "swap" operator, which I call $U_S$ and whose action I work out in post #79, and the "no swap" operator, which is just the identity. That is sufficient to do the analysis, but of course it leaves out a lot of detail about how the swap/no swap "decision" is made at the BSM in the actual experiments.

 

[PeterDonis]

I stand by my statement.

If you mean your statement that you think the MWI makes different predictions from standard QM, this is refuted by the posts of mine that I referenced. I explicitly do the math to show this.

the ordering will matter in MWI, at least that is what I am exploring

It doesn't. I explicitly do the math to show that the unitary operators involved commute, so the final state is the same regardless of what order the operations are done in.

 

[martinbn]

...
And they did this without any direct interaction, guided by a far distant experimenter's decision to execute a swap (or not).
...

Just to add a detail I think is important. The experimenter can choose to execute the swap or not, but if he chooses to do it there is no garantee that it will happen. In the standard scenario only one in four will result in a swap. Also the experimenters that measure photons 1 and 4 need to know on which trails there was actually a swap. Without it, they will not see any entanglement.

 

[Morbert]

@DrChinese I think we should stick with the simpler case of an experiment with one idealised nondestructive BSM apparatus for the moment, and the case with multiple apparatuses can be revisited later if need be.

We have an initial state $$|\Psi\rangle = |\Psi^1\rangle_{12}|\Psi^1\rangle_{34}|M^\mathrm{ready}\rangle|\epsilon^0\rangle = \sum_i c_i|\Psi^i\rangle_{23}|\Psi^i\rangle_{14}|M^\mathrm{ready}\rangle|\epsilon^0\rangle$$Where $M^\mathrm{ready}$ is the BSM device in a ready state and $\epsilon$ are environmental degrees of freedom around the BSM apparatus. Anticipating an objection (square brackets are my changes):

This idea - that the initial [4] photon system contains a subset in which 1 & [4] are entangled - is absolutely false. QM absolutely does not say this, and virtually every swapping paper makes clear that this is not the case.

No such claim is being implied when we choose the above representation of the initial wavefunction. The representation merely makes it easier to understand the processes involved when the 4-photon system and the BSM apparatus interact.

We also have dynamics such that we have unitary evolution to some time immediately after the BSM
$$U|\Psi\rangle = \sum_i^4 c_i|\Psi^i\rangle_{23}|\Psi^i\rangle_{14}|M^i\rangle|\epsilon^i\rangle$$The question is, under a given Everettian interpretation of QM, do we have action at a distance here?

Taking Wallace's account of Everettian QM, we introduce "spacetime state realism" which says that for any subsystem of the universe, the density operator of that subsystem represents all properties instantiated by the subsystem. The [1,4]-photon system is located in a region $R_1\cup R_4$, spacelike separated from the BSM, and the density operator in the region of the [1,4]-photon subsystem is obtained by tracing over the relevant degrees of freedom, giving us $$\rho =\mathrm{Tr}_{2,3,M}\left[U|\Psi\rangle\langle\Psi|U^\dagger\right]$$No entanglements in the [1,4]-photon subsystem, contingent on the spacelike-separated BSM outcomes, are instantiated, because we have traced over all degrees of freedom outside this region.

We now consider the spacetime region $R_1\cup R_4\cup R_{M}$ giving us$$\rho = \sum_i^4|c_i|^2|\Psi^i\rangle_{14}|M^i\rangle\langle M^i|\langle\Psi^i|_{14}$$Here we can identify four decoherent branches, capable of containing observers like us, with respective bell states of the [1,4]-photon system. This does not amount to action at a distance because unlike before, this region is not spacelike separated from the BSM.

We can, however, identify nonlocality of another kind: nonseparability. Nonseparability says that e.g. the states in regions $A$ and $B$ do not determine the state in region $A\cup B$. It is this distinction that I am trying to emphasise: locality as separability, and locality as a causal relation between states in different spacetime regions.

 

[Morbert]

My challenge to David Wallace after reading that passage would be to show me in the math where it says that branching travels outward at the speed of light. If you look at the math that I posted in posts #79, #81, #82, and #83, there is no sign of any such thing. Each branching event affects the whole wave function, which, as I pointed out in post #84, is nonlocal, so each branching event has nonlocal effects, even though, as I also pointed out in post #84, the unitary operation that causes the branching is local in the sense that it only operates on degrees of freedom in the wave function that are at its spatial location (photons 2 and 3 in the example I analyzed). Thus, in the MWI the nonlocality of QM is entirely contained in the wave function--but it's still there. The Vaidman article from SEP that @DrChinese referenced agrees with this, and also does not mention any speed of light expansion of branching.'

Wallace could, I suppose, object that I was implicitly using non-relativistic QM in my analysis; but then I would challenge him to show me the relativistic version that contains the speed of light expansion of branching.

And, finally, since the cases I analyzed include both spacelike and timelike separation of branching events, yet the results are still the same (since all of the operators involved commute), it is highly implausible on its fact that limiting branching to expand at the speed of light can be workable.

In his book "The Emergent Multiverse", section 8, Wallace considers a microscopic system surrounded by concentric layers of environmental baths, and discusses the propagation of the branching process. I will go through your posts when I get the chance, but I suspect the relevant point is the distinction Wallace makes between nonseparability and action at a distance: The formation of decoherent branches immediately containing entanglements extending across spacelike-separated regions vs the formation of decoherent branches immediately influencing spacelike-separated regions.

https://arxiv.org/pdf/0907.5294.pdf

As nonlocal forms of behaviour go, non-separability is fairly mild. It does not imply any sort of action at a distance: the quantum state of spacetime region A is dynamically determined by the state of its past light cone (more precisely: by the state of any spacelike slice of its past light cone). The state of A ∪ B may indeed be changed by operations in the vicinity of either A or B, but the state of B is unaffected by operations performed at A

[edit] - This paper also contains a more explicit discussion of Poincare covariance.

 

[PeterDonis]

I suspect the relevant point is the distinction Wallace makes between nonseparability and action at a distance

That may be, but it still doesn't show where in the math any "branching spreading at the speed of light" occurs. Nonseparability doesn't have a "speed".

I'll take a look at the paper you referenced.

 

[DrChinese]

I should note that in my analysis in the posts I have referenced, I don't make any specific assumption about how this works. All I assume is that at the BSM, there is some probability of a swap and a corresponding probability of no swap. So the unitary operator that I call $U_{S/N}$, that describes all of the possibilities of what can happen at the BSM, is just a linear combination of the "swap" operator, which I call $U_S$ and whose action I work out in post #79, and the "no swap" operator, which is just the identity. That is sufficient to do the analysis, but of course it leaves out a lot of detail about how the swap/no swap "decision" is made at the BSM in the actual experiments.

Also, from @martinbn in post #93 above:

Just to add a detail I think is important. The experimenter can choose to execute the swap or not, but if he chooses to do it there is no garantee that it will happen. In the standard scenario only one in four will result in a swap. Also the experimenters that measure photons 1 and 4 need to know on which trails there was actually a swap. Without it, they will not see any entanglement.

------

Perhaps I was not sufficiently clear about the decision(s) of the experimenter at the BSM. She remains in the same role as in all of the variants of this example in recent months. That role is actually performed as described below:

Entanglement Between Photons that have Never Coexisted

"One can also choose to introduce distinguishability between the two projected photons. In this case, ... the first and last photons do not become quantum entangled but classically correlated. We observed this when we introduced a sufficient temporal delay between the two projected photons (see Fig. 3c). It is also evidence that the first and last photons did not somehow share any entanglement before the projection of the middle photons."

The rules are as follows:
a) When Photons 2 & 3 arrive within a narrow time window (around 10 ns) and are otherwise indistinguishable, a swap will always occur.
b) Of course this is the ideal case. Actual visibility of swapping is less than 100%, but is very high. We can ignore this for our purposes.
c) Although there are 4 Bell states that can result (randomly), at most only 2 of the 4 can be suitably identified. This is due to limits on current APD technology. The other 2 must have those trials discarded. Those are easy to identify, there is only 1 click at the BSM detectors instead of the required 2 clicks.
d) There are some swapping experiments in which only 1 Bell state is identified, and that is a consequence of practical considerations for that particular setup. We can ignore this for our purposes.

From the Zeilinger swapping experiment we've been discussing: "It allows to identify two out of four Bell states, as was first demonstrated in the experimental realization of dense coding [38]. This is the optimum efficiency possible with linear optics. ... All measurement results are, therefore, four-fold coincidence detection events, where the coincidence window has to be shorter than the delay between two successive pulses (∼ 13 ns)."

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

The purpose of explaining this is to convince you that the experimenter's decision to execute the swap is under her direct control, and is deterministic in this sense: Whenever the 2 identifiable Bell state cases arise (4 fold coincidences within 13 ns, per rules above; the 4 fold requirement means all of Photons 1/2/3/4 are registered):
i) A swap always occurs if no delay is introduced;
ii) A swap never occurs if delay is introduced;
iii) There are no other cases ignored.

There is no data filtering occurring in the BSM. By "filtering", I mean using the data to identify elements of Photons 2 & 3 that would otherwise indicate a swap. That meaning clicks at any 2 of the BSM's 4 detectors.

What occurs is - must be - a physical process, the nature of which is of course the great mystery. We know that the 2 & 3 photons must be indistinguishable in all degrees of freedom, sure, but what does that really mean or imply? Presumably, we end up with a superposition of Photon 2 going one way and Photon 3 going the other, and vice versa. And presumably the photons interact in some manner that has such a great impact, that entanglement of Photons 1 & 4 is created.

When a delay is added, of course there is no opportunity for interaction and no superposition results. But there are still 4 fold coincidences, so the resulting data set otherwise looks like a Bell state should have occurred. It doesn't, and it is the decision of the experimenter to turn swapping ON or OFF at her whim that is the sole determination of whether a Bell state is created for Photons 1 and 4 which are far away at this time. All of this is standard QM, easily discernable from the references provided.

 

[DrChinese]

1. @DrChinese I think we should stick with the simpler case of an experiment with one idealised nondestructive BSM apparatus for the moment, and the case with multiple apparatuses can be revisited later if need be.

2. We have an initial state $$|\Psi\rangle = |\Psi^1\rangle_{12}|\Psi^1\rangle_{34}|M^\mathrm{ready}\rangle|\epsilon^0\rangle = \sum_i c_i|\Psi^i\rangle_{23}|\Psi^i\rangle_{14}|M^\mathrm{ready}\rangle|\epsilon^0\rangle$$Where $M^\mathrm{ready}$ is the BSM device in a ready state and $\epsilon$ are environmental degrees of freedom around the BSM apparatus. Anticipating an objection (square brackets are my changes):No such claim is being implied when we choose the above representation of the initial wavefunction.

3. We also have dynamics such that we have unitary evolution to some time immediately after the BSM
$$U|\Psi\rangle = \sum_i^4 c_i|\Psi^i\rangle_{23}|\Psi^i\rangle_{14}|M^i\rangle|\epsilon^i\rangle$$The question is, under a given Everettian interpretation of QM, do we have action at a distance here?

Taking Wallace's account of Everettian QM, we introduce "spacetime state realism" which says that for any subsystem of the universe, the density operator of that subsystem represents all properties instantiated by the subsystem. The [1,4]-photon system is located in a region $R_1\cup R_4$, spacelike separated from the BSM, and the density operator in the region of the [1,4]-photon subsystem is obtained by tracing over the relevant degrees of freedom, giving us $$\rho =\mathrm{Tr}_{2,3,M}\left[U|\Psi\rangle\langle\Psi|U^\dagger\right]$$No entanglements in the [1,4]-photon subsystem, contingent on the spacelike-separated BSM outcomes, are instantiated, because we have traced over all degrees of freedom outside this region.

4. We now consider the spacetime region $R_1\cup R_4\cup R_{M}$ giving us$$\rho = \sum_i^4|c_i|^2|\Psi^i\rangle_{14}|M^i\rangle\langle M^i|\langle\Psi^i|_{14}$$Here we can identify four decoherent branches, capable of containing observers like us, with respective bell states of the [1,4]-photon system. This does not amount to action at a distance because unlike before, this region is not spacelike separated from the BSM.

5. We can, however, identify nonlocality of another kind: nonseparability. Nonseparability says that e.g. the states in regions $A$ and $B$ do not determine the state in region $A\cup B$. It is this distinction that I am trying to emphasise: locality as separability, and locality as a causal relation between states in different spacetime regions.

1. Completely agree. I provided the other reference per your request.

2. I object to any implication that the RHS of the initial state can be re-written or otherwise lead to the implication that Photons 1 & 4 have any relationship at all such as $$|\Psi^i\rangle_{14}
$$ and ditto for 2 & 3. The LHS is the only description I consider suitable for the initial state.

3. We hopefully agree that before the swap, we have $|\Psi^i\rangle_{12}\Psi^i\rangle_{34}$ and after we have $|\Psi^i\rangle_{14}\Psi^i\rangle_{23}$ except photons 2 & 3 no longer exist so it simplifies to $|\Psi^i\rangle_{14}$

So that means the initial states for 1 & 4 could only be considered as being in a Product State relative to each other, and the final state has them in an Entangled State relative to each other. And I am mostly OK with what you say about Wallace's position.

4. I am lost here. It seems we now have an extended spacetime region which is nonlocal in every respect - if you are saying the BSM is not spacelike separated from the rest of the system because it is now included in the overall system. I know your are channeling what Wallace would say, that's proper. But by my thinking it is circular to say there is no AAD as long as you consider a big enough subsystem. There is a person making a decision, and the entire extended system changes (or not) based on her decision.

5. OK, if you want to say that separability/nonseparability defines a kind of definition of locality, that makes some sense. But for it to apply, you still have to say 1 & 4 started in a Product State and ended in an Entangled State.

However: When Photon 2 was created, there is absolutely nothing whatsoever that indicates that it is later to overlap in the BSM with Photon 3 in particular. The Photon we call 3 could actually be a member of any entangled pair anywhere in the universe, created at any time before it meets Photon 2 at the BSM. There could be thousands of mutually distant sources of entangled pairs (I'm exaggerating of course for effect) which are vying to act as the Photons 3 & 4 in the swap.

So basically: if Wallace's definition were reasonable, we would need to include ALL potential sources in our equation. That essentially means a spacetime region that is not particularly limited in any way. Not the most useful of ways to avoid calling something "action at a distance".

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By the way, thanks for chiming in @Morbert. I hope you will continue as we work through these stages. Ditto to @martinbn and everyone else. And of course, as always, I thank @PeterDonis for his time and incredible diligence as well. His ability to not only check my references but also locate other confirming or countering arguments - and quickly - is a special gift.

Peter, this time the bold effect is for shouting.

 

[PeterDonis]

And of course, as always, I thank @PeterDonis for his time and incredible diligence as well. His ability to not only check my references but also locate other confirming or countering arguments - and quickly - is a special gift.

Peter, this time the bold effect is for shouting.

Thanks for the kudos!

 

[PeterDonis]

2. I object to any implication that the RHS of the initial state can be re-written or otherwise lead to the implication that Photons 1 & 4 have any relationship at all such as $$|\Psi^i\rangle_{14}
$$ and ditto for 2 & 3. The LHS is the only description I consider suitable for the initial state.

I don't see how one can object to a simple algebraic refactoring; the expression that results is mathematically equivalent and gives the same predictions. @Morbert explicitly said he wasn't making any claim about a "relationship" between photons 1 and 4.

 

[PeterDonis]

it still doesn't show where in the math any "branching spreading at the speed of light" occurs. Nonseparability doesn't have a "speed".

I'll take a look at the paper you referenced.

After reading through the paper I have a couple of further comments:

First: I think I now understand where Wallace is getting the notion of "branching spreading at the speed of light": it's just an obvious consequence of the locality of the unitary measurement operators, which I described before, plus the fact that branching requires decoherence, and decoherence is an actual physical process that requires the spreading of entanglement among more and more untrackable degrees of freedom in the environment--and that process can only spread at the speed of light (or slower if the actual dynamics is slower). Wallace expresses this as follows in footnote 23 (on p. 23 of the paper):

The structure of the decoherence-defined branching in the Everett interpretation, which is in turn determined by the local nature of the dynamics.

Second: however, this notion seems to me to be at odds with the notion of spacetime state realism as Wallace describes it. Basically, the idea is to attribute states to spacetime regions, but with the caveat that the state of two disjoint regions $A$ and $B$ does not completely determine the state of their union $A \cup B$. The reason for this is, of course, entanglement (Wallace uses the term "nonseparability"): if we look at things the other way around, we obtain the states of $A$ and $B$ from the state of $A \cup B$ by tracing over $B$ or $A$ respectively, and the tracing operation discards all the information about entanglement between the two regions. So there is no way of going in the other direction and reconstructing the complete state of $A \cup B$ from the states of $A$ and $B$.

But if this is true, it means that we also cannot capture all of the consequences of a unitary operation that takes place in $A$ alone, or in $B$ alone, just by looking at the local dynamics--because the local information does not include entanglement information. So we can't say that "branching expands at the speed of light" without qualification based on "the local nature of the dynamics" of decoherence. We have to be more careful about exactly how we describe branching and its effects, which includes, as should be familiar to anyone who has gone through an appreciable amount of the literature in this field, drawing the key distinction between what happens to the wave function and what it takes for us to collect the data that lets us confirm the correlations that the wave function tells us should be there.

 

[DrChinese]

1) First: I think I now understand where Wallace is getting the notion of "branching spreading at the speed of light": it's just an obvious consequence of the locality of the unitary measurement operators, which I described before, plus the fact that branching requires decoherence, and decoherence is an actual physical process that requires the spreading of entanglement among more and more untrackable degrees of freedom in the environment--and that process can only spread at the speed of light (or slower if the actual dynamics is slower). Wallace expresses this as follows in footnote 23 (on p. 23 of the paper):

The structure of the decoherence-defined branching in the Everett interpretation, which is in turn determined by the local nature of the dynamics.

2) Second: however, this notion seems to me to be at odds with the notion of spacetime state realism as Wallace describes it. Basically, the idea is to attribute states to spacetime regions, but with the caveat that the state of two disjoint regions $A$ and $B$ does not completely determine the state of their union $A \cup B$. The reason for this is, of course, entanglement (Wallace uses the term "nonseparability"): if we look at things the other way around, we obtain the states of $A$ and $B$ from the state of $A \cup B$ by tracing over $B$ or $A$ respectively, and the tracing operation discards all the information about entanglement between the two regions. So there is no way of going in the other direction and reconstructing the complete state of $A \cup B$ from the states of $A$ and $B$.

But if this is true, it means that we also cannot capture all of the consequences of a unitary operation that takes place in $A$ alone, or in $B$ alone, just by looking at the local dynamics--because the local information does not include entanglement information. So we can't say that "branching expands at the speed of light" without qualification based on "the local nature of the dynamics" of decoherence.

We have to be more careful about exactly how we describe branching and its effects, which includes, as should be familiar to anyone who has gone through an appreciable amount of the literature in this field, drawing the key distinction between what happens to the wave function and what it takes for us to collect the data that lets us confirm the correlations that the wave function tells us should be there.

1) This is how I picture what MWI is saying as well.

2) "So we can't say that "branching expands at the speed of light" without qualification based on "the local nature of the dynamics" of decoherence." I don't follow you here. If there is/was maximum entanglement between 1 & 2, there is no decoherence to consider... right?

3) "...what it takes for us to collect the data that lets us confirm the correlations that the wave function tells us should be there". I don't see how this can ever be an issue. If we have a demonstrable nonlocal effect of some kind (assume we do), and that effect can never be used for signaling (which is the accepted view): collection of ALL the data will (in the general case at least) require signaling to bring the data together. By this standard, all evidence of nonlocality would be rejected. That's circular logic. All I can say is my uncle did not die when I learned of his death, and neither do experiments conclude any more than when the experiment brings together all of the data points (or publishes the paper).

From Gisin et al 2023:
"Note that a quantum measurement is completed at the moment when the classical outcome is produced, even if the readout for a single observer may require to collect (through classical communication) different pieces of classical information."

If I misunderstood where you were going with this, my apologies.

 

[PeterDonis]

If there is/was maximum entanglement between 1 & 2, there is no decoherence to consider... right?

No. There is decoherence whenever a measurement is made. That includes the detection of whether or not a swap is made at the BSM, by the photon detections that happen at the detectors at the BSM. Whatever happens at those detections, once they have taken place, there is no longer any maximal entanglement between 1 & 2 (or between 3 & 4). Either the maximal entanglement was swapped at the BSM (if a swap is detected), so it is now between 1 & 4, and 2 & 3, and the detection then ends the maximal entanglement between 2 & 3 by absorbing those photons at the detectors; or there was no swap and absorbing photons 2 & 3 at the detectors ends the maximal entanglement between 1 & 2 (and 3 & 4), and leaves no entanglement at all between any of the photons. (If one possibility in the "no swap" case involves no detection of photons 2 or 3, then decoherence occurs once those photons have interacted with the environment enough, which will inevitably happen--they can only stay coherent for a finite time.)

Decoherence of course does involve entanglement, but it is not maximal between any particular pair of degrees of freedom; it is spread out among a very large number of degrees of freedom in the environment that are not individually trackable, so the entanglement between any two particular degrees of freedom is very small.

I don't see how this can ever be an issue.

It's not an issue as far as the question of whether there is nonlocality: of course there is. How you collect the data can't change that. But the evidence that you use to confirm that there is nonlocality does have to be collected all at one place to do the analysis and confirmation; that is what I was referring to. I was not trying to conflate the two myself; I was saying that writers like Wallace might be conflating the two by failing to draw the key distinction between the nonlocality itself and how we collect and analyze the evidence for it.

 

[DrChinese]

1) Actually, on working through the math some more, I was too pessimistic about the basic math of QM here. In fact, the basic math of QM can handle the case I described without any handwaving at all. (As you will see, this is actually an obvious consequence of the fact I have already mentioned, that all of the operations involved in these experiments commute. )

...2) So the straightforward math of QM predicts that the results of entanglement swapping experiments are the same no matter what the time ordering of the operations involved is!

3) I'll go back and revisit how the MWI deals with all this in a follow up post.

1) I know you are doing this to start with the QM version and then move to the MWI case. But your statement "all of the operations involved in these experiments commute" means nothing in QM, whether local or nonlocal *random* effects are present. As I have tried to point out, such a statement is another way of saying that certain nonlocal effects cannot exist. That's circular logic. Quantum nonlocality has been demonstrated to lack the classical view of causality in which causes must precede effects. In fact, quantum nonlocality - as generally accepted by the physics community - has been demonstrated to create both spatial and temporal nonlocality.

https://arxiv.org/abs/1209.4191
"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."

I know that you often quote the QFT concept of microcausality (which is a reasonable assumption), but that concept applies only to eliminating superluminal signaling (see various articles based on Sorkin's "impossible measurements" such as this. But that assumption cannot be used to rule out what is experimentally obvious and does not contradict quantum theory. For example:

Peacock: "...a proof of a result based on a theory which was ‘constructed to ensure’ that result is no proof at all"
Mittlestaedt: "The micro-causality condition of relativistic quantum field theory excludes entanglement induced superluminal signals but this condition is justified by the exclusion of superluminal signals. Hence, we are confronted here with a vicious circle, and the question whether there are superluminal EPR-signals cannot be answered in this way."2) This conclusion was never in question. It is a true statement that our experimenter can choose to execute the swap *after* both Photons 1 & 4 are measured, just as readily as before - without any result changing. You could even say that is an example of the future changing the past (of course still no signaling applies).

But that is not what I am trying to demonstrate. In MWI, after Photon 1 is measured, we have an H> world and a V> world for Photon 1. Later the distant (nonlocal) experimenter makes a decision to swap or not. That decision changes the later statistical correlation of distant (nonlocal) Photon 4 with the earlier measurement of Photon 1, which has never been in a common light cone with Photon 1 or the experimenter. 3) That effect should not be explainable in MWI. Again, no question this matches the predictions of QM - since distance in spacetime is not an issue.

 

[PeterDonis]

your statement "all of the operations involved in these experiments commute" means nothing in QM, whether local or nonlocal *random* effects are present.

The "random" effects come into play with collapse, and I am leaving out collapse because the MWI does not have it. In terms of standard QM, I am only doing the "apply the unitary operator corresponding to a particular measurement" part; I am not doing the "apply the collapse postulate to reflect the outcome of the measurement that is actually observed" part. I agree that if you do the latter part, the operations no longer commute, since applying the collapse postulate is non-unitary. But in the context of describing how the MWI explains what happens, the collapse part has to be left out. I should have made that clearer up front.

In MWI, after Photon 1 is measured, we have an H> world and a V> world for Photon 1. Later the distant (nonlocal) experimenter makes a decision to swap or not. That decision changes the later statistical correlation of distant (nonlocal) Photon 4 with the earlier measurement of Photon 1, which has never been in a common light cone with Photon 1 or the experimenter.

You need to read the rest of the posts I referred to. I address all of this in those posts. I said so in what you quoted; please take me at my word and don't assume that I must have failed when you haven't read what I wrote.

3) That effect should not be explainable in MWI.

Sorry, but it is. Read the rest of the posts I referred to.

 

[PeterDonis]

your statement "all of the operations involved in these experiments commute" means nothing in QM

I agree that if you do the latter part, the operations no longer commute, since applying the collapse postulate is non-unitary

I realized that I should clarify this, because it's a very important point. My statement in response to yours (@DrChinese) quoted above is correct--but it also means that even doing "standard" QM too strictly, and applying the collapse postulate immediately after every measurement, regardless of time ordering, means you can't account for the correlations!

In order to get the right answer even with "standard QM", you need to, as you yourself have said before, take into account the entire context, including future measurements that will be made on at least some of the quantum systems involved in the current measurement. In this case, that means that you have to not apply the collapse postulate until you have applied the unitary operators corresponding to all of the measurements in the context--and then, once you have the final state after all of those operators are applied, that state will contain all of the possible final sets of results, each with its correct amplitude, and you can correctly use the Born rule to predict the probabilities for each of the sets of results, and the collapse postulate to reduce the state to the one that reflects the set of results that was actually observed.

In other words, when you insist on taking into account the entire future context in order to properly account for the results, you are doing the same thing that the MWI does! The only difference is that you are applying the collapse postulate at the end. Everything up to that point has to be entirely unitary, with no collapse, in order to properly take into account the entire context. And that is exactly what I did in post #79. If you look at the final state I come up with in post #79, and put back in the correct normalization factors, you will see that it reflects all of the possible sets of outcomes of the three measurements (BSM, Photon 1, Photon 4), each with its correct amplitude. And if you go back and apply the collapse postulate to one of the intermediate states, and then apply further measurement operators, you will see that you don't get the correct final state with the proper correlations in it (unless you are doing the easy case where the BSM happens first).

 

[DrChinese]

1) There is decoherence whenever a measurement is made. That includes the detection of whether or not a swap is made at the BSM, by the photon detections that happen at the detectors at the BSM. Whatever happens at those detections, once they have taken place, there is no longer any maximal entanglement between 1 & 2 (or between 3 & 4).

Either the maximal entanglement was swapped at the BSM (if a swap is detected), so it is now between 1 & 4, and 2 & 3, and the detection then ends the maximal entanglement between 2 & 3 by absorbing those photons at the detectors; or there was no swap and absorbing photons 2 & 3 at the detectors ends the maximal entanglement between 1 & 2 (and 3 & 4), and leaves no entanglement at all between any of the photons. (If one possibility in the "no swap" case involves no detection of photons 2 or 3, then decoherence occurs once those photons have interacted with the environment enough, which will inevitably happen--they can only stay coherent for a finite time.)

2) Decoherence of course does involve entanglement, but it is not maximal between any particular pair of degrees of freedom; it is spread out among a very large number of degrees of freedom in the environment that are not individually trackable, so the entanglement between any two particular degrees of freedom is very small.

1) I don't see how decoherence figures into this discussion at all. If there is decoherence upon measurement of Photon 1 (or at the BSM), which I have no particular objection to assuming for discussion purposes: then you are saying that the entangled state of Photon 2 is over. Were that true by your reasoning, then Photon 2 is now has a definite polarization and is not in a superposition of polarizations as it previously was.

Obviously such definite states (for 1 or for 2 if Photon 1 was measured first) can never later become entangled with Photon 4 under any circumstances. And if the BSM occurs first, we have decoherence of photons 2 & 3 (at essentially the same time). Since you have decoherence as a physical process involving entanglement dissipation into the environment, exactly how do you think 1 & 4 are to become correlated?2) No particular disagreement with this description either, again in which decoherence is a physical process. Under your line of thinking, order *should* matter. Of course we agree it doesn't. Further, we know that the total entanglement cannot exceed a certain threshold due to Monogamy considerations, right?And in reality: the swap actually occurs at the BSM at the precise moment (or small time window) in which Photons 2 & 3 become indistinguishable, right? After all, that's an irreversible operation. And yet... what really happens is that they become entangled. It doesn't matter where Photon 1 is, where Photon 4 is, or for that matter if either have been measured by a polarizer or if they do or don't exist at all. Decoherence matters not.

Of course, I insist that the point at which Photons 2 & 3 become indistinguishable is the swap, and it being irreversible means it is a physical process. When the BSM detectors click, we learn what kind of Bell state we got.

 

[DrChinese]

I realized that I should clarify this, because it's a very important point. My statement in response to yours (@DrChinese) quoted above is correct--but it also means that even doing "standard" QM too strictly, and applying the collapse postulate immediately after every measurement, regardless of time ordering, means you can't account for the correlations!

In order to get the right answer even with "standard QM", you need to, as you yourself have said before, take into account the entire context, including future measurements that will be made on at least some of the quantum systems involved in the current measurement. In this case, that means that you have to not apply the collapse postulate until you have applied the unitary operators corresponding to all of the measurements in the context--and then, once you have the final state after all of those operators are applied, that state will contain all of the possible final sets of results, each with its correct amplitude, and you can correctly use the Born rule to predict the probabilities for each of the sets of results, and the collapse postulate to reduce the state to the one that reflects the set of results that was actually observed.

In other words, when you insist on taking into account the entire future context in order to properly account for the results, you are doing the same thing that the MWI does! The only difference is that you are applying the collapse postulate at the end. Everything up to that point has to be entirely unitary, with no collapse, in order to properly take into account the entire context. And that is exactly what I did in post #79. If you look at the final state I come up with in post #79, and put back in the correct normalization factors, you will see that it reflects all of the possible sets of outcomes of the three measurements (BSM, Photon 1, Photon 4), each with its correct amplitude. And if you go back and apply the collapse postulate to one of the intermediate states, and then apply further measurement operators, you will see that you don't get the correct final state with the proper correlations in it (unless you are doing the easy case where the BSM happens first).

Of course I agree that ordering does not matter, and collapse should not be considered (or applied) as occurring a piece at a time. You must look at the full nonlocal, nontemporal context as highlighted. As you say, you can't get the answer right otherwise.

And yet: MWI claims itself local AND deterministic. The past causes the future in MWI, and not the reverse. (We should agree that because we consciously experience life as proceeding from past to future, it would be difficult to assert things actually work the other way.)

If deterministic, then it is fair game to assert that the ordering of events either local or nonlocal will change outcomes. That doesn't happen in actual experiments.

 

[DrChinese]

1) The "random" effects come into play with collapse, and I am leaving out collapse because the MWI does not have it.

2) You need to read the rest of the posts I referred to. I address all of this in those posts. I said so in what you quoted; please take me at my word and don't assume that I must have failed when you haven't read what I wrote.

1) QM Collapse = MWI branching? What's the difference here?

2) You have this somewhat backwards. I *am* working through your series 79/81/82/83/84 in order, but it's a lot to cover. I'm a bit slow, and not nearly as fast as you are.

And I am assembling a new thread post discussing GHZ and MWI, but I won't be finishing that until I have worked with you through 79/81/82/83/84. You did a lot of work on these, and they deserve proper study.

PS And yes, I do sometimes answer posts in a LIFO manner rather than the more disciplined FIFO approach. At least I avoid NIFO (Next In First out) which would require a leap into the future.

 

[PeterDonis]

@DrChinese, I don't even want to respond to most of what is in your posts #107, #108, and #109, because until you have read through all of the previous posts of mine that I referenced, I think discussion is premature. I have no problem with it taking some time for you to work through those posts, they took me a fair bit of time to write and writing them is of course going to be easier for me than working through them will be for you. Take all the time you need, I'll still be here.

That said, there are a few things that it might help to clarify now:

If there is decoherence upon measurement of Photon 1 (or at the BSM), which I have no particular objection to assuming for discussion purposes: then you are saying that the entangled state of Photon 2 is over.

Not in the MWI, no. In the MWI, Photon 2 is still entangled after the Photon 1 measurement: it's just that the entanglement is no longer with Photon 1, but with all of the degrees of freedom that got involved in the Photon 1 measurement (and the degrees of freedom in the environment that that entanglement spreads to). What is true is that Photon 2 is no longer maximally entangled with any one of those individual degrees of freedom. But the overall entanglement of Photon 1 is still there. Note that none of the states I wrote down in my previous posts are product states of Photon 2 with something else; all of them are entangled.

In a collapse interpretation, yes, measuring one of a pair of entangled particles ends the entanglement, because the collapse forces the state to be a product state. But there is no collapse in the MWI, and the math in my posts reflects that.

Under your line of thinking, order *should* matter.

This is simply wrong, and is one of the things I really wish you would postpone discussion of until you have worked your way through all of my previous posts.

Further, we know that the total entanglement cannot exceed a certain threshold due to Monogamy considerations, right?

I already addressed this in post #103.

in reality: the swap actually occurs at the BSM at the precise moment (or small time window) in which Photons 2 & 3 become indistinguishable, right? After all, that's an irreversible operation. And yet... what really happens is that they become entangled.

If we want to break down the "swap/no swap decision" process, which I didn't do in my earlier posts, here is what I gather from your earlier posts and the papers you referenced. I am treating the idealized version where if a swap is possible at all, it always happens, i.e., the sole relevant variable is the experimenter's decision.

(1) The experimenter makes a decision that determines whether or not a swap occurs. We model this in the math as there being some amplitude $s$ for a swap to occur, and a corresponding amplitude $n$ for no swap to occur, such that $|s|^2 + |n|^2 = 1$. The operator that I called $U_{S/N}$ in my earlier posts can then be expressed as $s U_S + n I$, where $U_S$ is the unitary swap operator and $I$ is the identity.

(2a) If the experimenter decides that a swap will occur, photons 2 & 3 arrive at the BSM within a short enough time window to be indistinguishable, they go through the BSM, and one photon is detected in each output arm of the BSM. This provides the "event ready" indication that a swap has taken place. The state after the swap is given by the unitary operator $U_S$ applied to the state before the swap.

(2b) If the experimenter decides that a swap will not occur, photons 2 & 3 do not arrive at the BSM within a short enough time window to be indistinguishable, they go through the BSM, and a detection occurs either in just one output arm of the BSM, or no detection occurs at all in either output arm of the BSM. For our purposes we combine all of those possibilities into the "no swap" result. The state is unchanged in this case because the operator involved is just the identity.

In the short time between photons 2 & 3 going through the BSM and the detections (if any) in the output arms of the BSM, yes, photons 2 & 3 will be entangled if there is a swap. Once the detections take place, that entanglement spreads to all the degrees of freedom involved in the detections, and their environment. If there is no swap, the previous entanglements of photons 2 & 3 get transferred to either the detector degrees of freedom (if the photons are detected) or directly to the environment (if they aren't detected and just decohere naturally because of their finite coherence time).

Decoherence matters not.

It does if we want the results to be irreversible. Without decoherence, we could imagine, for example, recombining photons, as in a Mach-Zehnder interferometer, and undoing the swap operation.

If deterministic, then it is fair game to assert that the ordering of events either local or nonlocal will change outcomes.

In general it might, but in the case under discussion, it doesn't. You can't just assert that the ordering will change outcomes based on "determinism". You have to actually do the math and see. That's what I've done.

QM Collapse = MWI branching? What's the difference here?

MWI branching is unitary. Collapse is not.

For example, if I have two entangled photons in the singlet state, $H_1 V_2 - V_1 H_2$, and I measure Photon 1, collapse says the state becomes either $\bar{H}_1 V_2$ or $\bar{V}_1 H_2$; those are both non-unitary transformations from the original state. The MWI says the state becomes $\bar{H}_1 V_2 - \bar{V}_1 H_2$, which is a unitary transformation from the original state (the bars just mean spreading entanglement among the degrees of freedom in the Photon 1 detector and its environment). Those are different states. They are indistinguishable experimentally because the bars, indicating decoherence, mean that you can't interfere the terms any longer, so there is no way, for example, to build a Mach-Zehnder interferometer that undoes the Photon 1 measurement and allows us to distinguish the MWI state from either of the two collapse states.

 

[PeterDonis]

doing "standard" QM too strictly, and applying the collapse postulate immediately after every measurement, regardless of time ordering, means you can't account for the correlations!

Actually, after taking a further look at the math, I'm no longer sure even this is true, at least not for the cases we're discussing. But I'll postpone further posting along those lines for now since we have enough on the table at present.

 

[Morbert]

3. We hopefully agree that before the swap, we have $|\Psi^i\rangle_{12}\Psi^i\rangle_{34}$ and after we have $|\Psi^i\rangle_{14}\Psi^i\rangle_{23}$ except photons 2 & 3 no longer exist so it simplifies to $|\Psi^i\rangle_{14}$

Under Wallace's account of Everettian QM: Before the swap, we have $$|\Psi\rangle\langle\Psi| = |\Psi^1_{12},\Psi^1_{34},M^\mathrm{ready},\epsilon^0\rangle\langle \Psi^1_{12},\Psi^1_{34},M^\mathrm{ready},\epsilon^0|$$ after the swap (and now supposing the BSM is destructive but otherwise ideal), we have $$U|\Psi\rangle\langle\Psi|U^\dagger = \sum_{i,j}c_ic^*_j|\Psi^i_{14},M^i,\epsilon^i\rangle\langle \Psi^j_{14},M^j,\epsilon^j|$$

4. I am lost here. It seems we now have an extended spacetime region which is nonlocal in every respect - if you are saying the BSM is not spacelike separated from the rest of the system because it is now included in the overall system. I know your are channeling what Wallace would say, that's proper. But by my thinking it is circular to say there is no AAD as long as you consider a big enough subsystem. There is a person making a decision, and the entire extended system changes (or not) based on her decision.

So basically: if Wallace's definition were reasonable, we would need to include ALL potential sources in our equation. That essentially means a spacetime region that is not particularly limited in any way. Not the most useful of ways to avoid calling something "action at a distance".

The bit in bold needs to be made more precise. It is true that properties of the entire system can be affected by the BSM, but properties of subsystems, with spacelike separated instantiations, cannot. The BSM apparatus subsystem, for example, is spacelike separated from the [1,4]-photon subsystem. The state of the [1,4]-photon subsystem before BSM is $$\mathrm{Tr}_{2,3,M,\epsilon}|\Psi\rangle\langle\Psi| = \sum_i|c_i|^2|\Psi^i\rangle_{14}\langle\Psi^i|_{14}$$We can see that there is no entanglement. As you say, if the state was something like $|\Psi^i\rangle_{14}\langle\Psi^i|_{14}$, there would be entanglement. After the BSM, the state is $$\mathrm{Tr}_{2,3,M,\epsilon}U|\Psi\rangle\langle\Psi|U^\dagger = \sum_i|c_i|^2|\Psi^i\rangle_{14}\langle\Psi^i|_{14}$$We can see that the [1,4]-photon state has not changed. This isn't surprising since this subsystem is spacelike-separated from the BSM. This is what Wallace means by no AAD: The properties instantiated by the [1,4]-photon subsystem, represented by the above state, cannot be immediately affected by the BSM. We could introduce some nonrelativistic dynamics and break this constraint, but entanglement doesn't break this constraint.

You might not agree with this constraint being called "no AAD", but hopefully you can at least appreciate the distinction in the Everettian context. If AAD was permitted, then the properties instantiated by a subsystem could be affected by events outside the past light cone of the subsystem.

5. OK, if you want to say that separability/nonseparability defines a kind of definition of locality, that makes some sense. But for it to apply, you still have to say 1 & 4 started in a Product State and ended in an Entangled State.

The problem is an assertion about 1 & 4, unqualified, implies an assertion about properties of that subsystem alone. Before and after the BSM we have a mixed state, unaffected by the BSM. If we want to identify 1 & 4 entanglement. We have to e.g. consider a larger subsystem including the quasiclassical branches of the BSM, and identify the relative states: The state of 1 & 4 relative to each of the decoherent branches.

 

[vanhees71]

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.

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.

Non-relativistic physics has no notion of "locality" in this sense.

Now to the above statements.

I also don't know, what "global variables" should be too. I also have no clue, whether the many-worlds interpretation is local or not. For me MWI doesn't make sense at all.

Standard QM of course has "nonlocal elements", because Newtonian physics is nonlocal. There's no limiting speed in the Newtonian spacetime model, and instantaneous interactions are the standard way to describe interactions, and the assumption of the existence of instantaneous signal propagation is implicit in the assumption of an absolute time.

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, but that is a "non-locality" which is NOT at odds with the above defined notion of locality in the HEP-community sense. That's why I'd prefer it very much, if one could find another term, and I consider Einstein's definition of "inseparability" as in his Dialectica article of 1948 as very clear.

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.

I think, again the confusion is immediately gone when using the minimal statistical interpretation. In the entanglement swapping experiment you consider indeed the description of different ensembles (in the experiments realized as sufficiently large "statistical samples")

You start with two independently prepared entangled two-photon states, i.e., a state of the form
$$|\Psi \rangle=|\psi_{12} \rangle \otimes |\psi_{34} \rangle,$$
where for simplicity we may take the singlet states (it doesn't really matter, you can use either of the four Bell states you like, it's only important that you have maximally entangled two-photon states)
$$|\psi_{ab} \rangle=\frac{1}{\sqrt{2}} [\hat{a}^{\dagger}(\vec{p}_a,\text{H}) \hat{a}^{\dagger}(\vec{p}_b,\text{V}) - \hat{a}^{\dagger}(\vec{p}_a,\text{V}) \hat{a}^{\dagger}(\vec{p}_b,\text{H})].$$
Here, of course the photon pairs 2 and 3 as well as 1 and 4 are unentangled, i.e., the reduced polarization state is
$$\hat{\rho}_{23} =\frac{1}{4} \hat{1}_2 \otimes \hat{1}_3,$$
i.e., you simply have two independent unpolarized photons.

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 probablity 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" with each other by selecting a subensemble due to measurement results on photons 2 and 3. The cause of the entanglement of the photons 1 and 4 due to selection based on measurements on photons 2 and 3 is that the four photons have been prepared in the above given specific state, and this "preparation procedure events" (i.e., the creation of each of the entangled pairs by parametric down conversion) are in the past light-cone of the measurement event on photons 2&3 finding them in the said entangled state, and this implies the entanglement also of photons 1&4 for this subensemble.

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.)

Nothing is changed on photons 1&4, you only selected a subensemble due to an outcome of a local measurement on photons 2&3. The correlations between 1&2 as well as between 3&4, necessary for the entanglement of 1&4 in the subensemble, have been present already before the measurement on photons 2&3, i.e., due to the corresponding preparation of the four photons in the past light cone of this measurement.

There's nowhere any need for faster-than-light signal propgation or other "non-locality" violating Einstein causality as soon as you use the minimal statistical interpretation. I don't know, how MWI interprets the locality (in the HEP sense) though, i.e., what is considered observable in MWI. That's why I prefer the minimal interpretation, because it is an interpretation clarifying the meaning of the QT formalism in a way as applied by experimentalists when doing experiments in the real world. They never experience the splitting of the universe only because detector A makes a click and not detector B in their universe ;-)).

 

[Morbert]

@vanhees71 The relevant question is how this experiment is framed by MWI. E.g. "An experiment has a set of possible outcomes, one of which occurs" is replaced by "An experiment produces a set of decoherent branches".

So instead of the (ideal) BSM producing an outcome that we can use to select a subensemble. The BSM produces a branching event, and as observers enter the future light cone of this event, they self-locate themselves on one of the branches, and describe the world in terms of states relative to that branch.

 

[Morbert]

@DrChinese Maybe this approach will be helpful: Light cone diagrams used in Wallace's book, but applied to the entanglement swapping experiment. Shown below is a sketch of a spacetime diagram with two observers: Alice and Bob. Alice and Bob are both using frames of reference that agree on the simultaneity of events (though this is not needed)

At time t0, both alice and Bob say there is no entanglement in the distant [1,4]-photon subsystem (not shown).

At time t1, alice performs an ideal BSM, the light cone of which is shown as the black triangle. This event begins a branching process, and Alice will identify with one of the branches.

At time t2, Alice, identifying with one of the branches, will describe the [1,4]-photon subsystem with a state relative to her branch. She will say there is entanglement between photons 1 and 4. Bob, however, is outside the light cone of the BSM. He will continue to describe the [1,4]-photon subsystem the usual no-entanglement mixed state. He will also describe the Alice + BSM subsystem with a highly nonclassical macroscopic superposition: 4 branches with 4 Alices.

At time t3, Bob will have branched due to the BSM. Like Alice, he will now uniquely identify with one of the branches, and describe the [1,4]-system with a relative state. He will agree with the Alice on his branch that photons 1 and 4 are entangled.

 

[PeterDonis]

Alice will identify with one of the branches.

More precisely, there will be a branch of Alice corresponding to each of the branches that result from the BSM. Similarly, when Bob branches, there will be a branch of Bob corresponding to each of the branches that result from whatever event caused Bob to branch.

At time t3, Bob will have branched due to the BSM.

We need to be very careful here: as you state this, it can't be correct.

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

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.

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.

 

[DrChinese]

1) @DrChinese, I don't even want to respond to most of what is in your posts #107, #108, and #109, because until you have read through all of the previous posts of mine that I referenced, I think discussion is premature. I have no problem with it taking some time for you to work through those posts, they took me a fair bit of time to write and writing them is of course going to be easier for me than working through them will be for you. Take all the time you need, I'll still be here.

2) Not in the MWI, no. In the MWI, Photon 2 is still entangled after the Photon 1 measurement: it's just that the entanglement is no longer with Photon 1, but with all of the degrees of freedom that got involved in the Photon 1 measurement (and the degrees of freedom in the environment that that entanglement spreads to). What is true is that Photon 2 is no longer maximally entangled with any one of those individual degrees of freedom. But the overall entanglement of Photon 1 is still there. Note that none of the states I wrote down in my previous posts are product states of Photon 2 with something else; all of them are entangled.

In a collapse interpretation, yes, measuring one of a pair of entangled particles ends the entanglement, because the collapse forces the state to be a product state. But there is no collapse in the MWI, and the math in my posts reflects that.3) If we want to break down the "swap/no swap decision" process, which I didn't do in my earlier posts, here is what I gather from your earlier posts and the papers you referenced. I am treating the idealized version where if a swap is possible at all, it always happens, i.e., the sole relevant variable is the experimenter's decision.

(1) The experimenter makes a decision that determines whether or not a swap occurs. We model this in the math as there being some amplitude $s$ for a swap to occur, and a corresponding amplitude $n$ for no swap to occur, such that $|s|^2 + |n|^2 = 1$. The operator that I called $U_{S/N}$ in my earlier posts can then be expressed as $s U_S + n I$, where $U_S$ is the unitary swap operator and $I$ is the identity.

(2a) If the experimenter decides that a swap will occur, photons 2 & 3 arrive at the BSM within a short enough time window to be indistinguishable, they go through the BSM, and one photon is detected in each output arm of the BSM. This provides the "event ready" indication that a swap has taken place. The state after the swap is given by the unitary operator $U_S$ applied to the state before the swap.

(2b) If the experimenter decides that a swap will not occur, photons 2 & 3 do not arrive at the BSM within a short enough time window to be indistinguishable, they go through the BSM, and a detection occurs either in just one output arm of the BSM, or no detection occurs at all in either output arm of the BSM. For our purposes we combine all of those possibilities into the "no swap" result. The state is unchanged in this case because the operator involved is just the identity.

In the short time between photons 2 & 3 going through the BSM and the detections (if any) in the output arms of the BSM, yes, photons 2 & 3 will be entangled if there is a swap. Once the detections take place, that entanglement spreads to all the degrees of freedom involved in the detections, and their environment. If there is no swap, the previous entanglements of photons 2 & 3 get transferred to either the detector degrees of freedom (if the photons are detected) or directly to the environment (if they aren't detected and just decohere naturally because of their finite coherence time).4) It does if we want the results to be irreversible. Without decoherence, we could imagine, for example, recombining photons, as in a Mach-Zehnder interferometer, and undoing the swap operation.5) In general it might, but in the case under discussion, it doesn't. You can't just assert that the ordering will change outcomes based on "determinism". You have to actually do the math and see. That's what I've done.6) They are indistinguishable experimentally because the bars, indicating decoherence, mean that you can't interfere the terms any longer, so there is no way, for example, to build a Mach-Zehnder interferometer that undoes the Photon 1 measurement and allows us to distinguish the MWI state from either of the two collapse states.

1) All good, thanks.

2) I can accept all of this, no objections as presented.

3) Thanks for clarifying that we are using the ideal model where the experimenter is making the swap/no swap decision. Note that the clicks on the BSM detector occur in exactly the same manner whether there is a swap or not (we are still looking for 2 clicks). The only difference is that since they are distinguishable when there is no swap, one click occurs a bit outside the time window. That of course identifies the path in which a delay was added. For our discussion, we can combine all variations of "no swap" (either through experimenter choice or less than ideal conditions) as you say.

4) I agree that there is the ability to reverse the measurements of Photons 1 & 4 (by re-combining the outputs of a PBS). So I can accept your perspective about decoherence on this side from the QM perspective. Not sure how that fits in to the MWI perspective, but I am guessing I will understand that better shortly.

Not sure it matters for our discussion, but I am unaware of any manner in which 2 indistinguishable particles (the ones in the BSM) can later have distinguishability restored later. Seems like a contradiction in terms. Of course, after the detectors click, no reversibility is possible anyway.

5) Good.

6) Good with this view.

 

[PeterDonis]

I agree that there is the ability to reverse the measurements of Photons 1 & 4 (by re-combining the outputs of a PBS).

I don't think we can reverse the measurements, because "measurement" says that decoherence has occurred, so now it's not enough just to recombine PBS outputs, you would have to somehow find and reverse all of the entanglements that have spread through the environment, and that's not possible in practice (although since decoherence is unitary it is possible in principle, at least according to current theory).

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. That (I think--I haven't done the math) would restore Photons 2 & 3 to the states they had before the first beam splitter, and therefore would undo the swap. But all that requires that there is no decoherence anywhere between the beam splitters, which means you can't detect Photons 2 & 3 there (you could detect them after the second beam splitter, and you would then expect to see the appropriate correlations with Photons 1 & 4 that are predicted by the originally prepared state, where 1 & 2 and 3 & 4 are the entangled pairs).

 

[DrChinese]

@DrChinese Maybe this approach will be helpful: Light cone diagrams used in Wallace's book, but applied to the entanglement swapping experiment. Shown below is a sketch of a spacetime diagram with two observers: Alice and Bob. Alice and Bob are both using frames of reference that agree on the simultaneity of events (though this is not needed)

View attachment 336903

At time t0, both alice and Bob say there is no entanglement in the distant [1,4]-photon subsystem (not shown).

At time t1, alice performs an ideal BSM, the light cone of which is shown as the black triangle. This event begins a branching process, and Alice will identify with one of the branches.

At time t2, Alice, identifying with one of the branches, will describe the [1,4]-photon subsystem with a state relative to her branch. She will say there is entanglement between photons 1 and 4. Bob, however, is outside the light cone of the BSM. He will continue to describe the [1,4]-photon subsystem the usual no-entanglement mixed state. He will also describe the Alice + BSM subsystem with a highly nonclassical macroscopic superposition: 4 branches with 4 Alices.

At time t3, Bob will have branched due to the BSM. Like Alice, he will now uniquely identify with one of the branches, and describe the [1,4]-system with a relative state. He will agree with the Alice on his branch that photons 1 and 4 are entangled.

I agree with everything you say above, but it leaves out the part where Photons 1 & 4 are affected by Alice's actions. That occurs completely outside Alice's light cone. On the other hand, Bob's agreeing with Alice at t3 is simply a result of getting a message from Alice telling him what she observed.

So once you add in Chris and Dale, who at t3 remain outside Alice's light cone and are observing photons 1 & 4 (they can be at the same spot or at different locations), it seems everything falls apart there.

But your diagram is how I understand MWI to work.

 

[PeterDonis]

your diagram is how I understand MWI to work.

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