Is MWI Considered Local in Quantum Mechanics?

[DrChinese]

No, in MWI, no change. MWI makes the same predictions as QM. Just as any QM interpretation does.

No, it claims it makes the same predictions. Again, the below statements are uncontroversial (or should be):

Start with an ordinary EPR pair, measure the polarization of photon 1.

In MWI, there is a splitting and there is an H> branch for photon 1. The paired photon 2 is H> always, even if it is distant at the time of measurement of photon 1, right? Note sure in the MWI world if that is proof of nonlocality (AAD). But let's skip that for the moment. What is unquestioned is that photon 2 is H> in the H> branch of photon 1, and continues to evolve deterministically in that branch. Further, it's polarization is DEFINITELY H> in that branch, there is nothing remaining to be settled about that point. Similar reasoning applies to the V> side. See this description from Blaylock (2009), explaining locality in MWI:

"For instance, two photons with entangled polarizations might be produced from the decay of a parent particle. In this case the entangled state is produced at one location, where the parent decays, and its immediate effects are limited to that one spacetime point. Thereafter, the photons may go their separate ways, and as they separate they carry the correlation to separate locations. It is the original correlation produced at a single location that guarantees measurements will always match in any experiment in any branch where observers compare notes. In this respect the spread of the correlation to distant locations is akin to the delivery of newspapers, where a common story is generated at a central location and disseminated all over the neighborhood. In the many-worlds context, however, different branches (which originally split at a common location) carry different editions of the newspaper."

There is nothing indefinite in this or any explanation of MWI regarding entangled pairs: Matching settings on photons 1 and 2 always produce matching results. In the H> branch, Photons 1 and 2 are both H> and evolve deterministically as such. (Ditto for the V> branch of course.) It couldn't be otherwise, as the H> photon 2 is going its separate merry way.

So if you place an H> filter in the path, then there should be no change to the results in the H> branch. But you acknowledge that no swap is later possible if that is done (which is what QM predicts of course). But QM predicts that for a completely different reason. In QM, it is the context that matters - a future context, and the full future context at that. But that cannot be the case in MWI, because no future nonlocal context can EVER be the basis for a deterministic theory's earlier evolution.

Deutsch 2011 on MWI (agreeing with Einstein): "Einstein's (1949) criterion for locality is that for any two spatially separated physical systems S1 and S2, ‘the real factual situation of the system S2 is independent of what is done with the system S1’."

Vaidman 2014 on MWI: Quantum theory is correct, but determinism is correct too. ... Consequently, Heisenberg Uncertainty Relations, Robertson Uncertainty Relations, Kochen Specker theorem, the EPR argument, the GHZ setup, and the Bell inequalities are all irrelevant for analyzing fundamental properties of Nature.

Clearly the tension between locality, determinism is present and recognized by authors. But nowhere do they address the obvious requirements of MWI that conflict with experiment. Photon 2 is H> if Photon 1 is H>. That means a choice by a distant experimenter to swap entanglement can't lead to new correlations between photons 1 and 4 (Deutsch via Einstein). And it means that the deterministic (Vaidman) evolution of photon 2 cannot lead to the swap needed for the Zeilinger et al experiment (which Vaidman denies is even relevant, although he did have a hand (hand-waving) at GHZ in one paper).

Every MWI proponent touts the benefits of determinism in MWI) a la Vaidman. Even those proponents of MWI who acknowledge some element of nonlocality agree with the essentials of Deutsch on locality. And I have yet to see the full MWI treatment on swapping and GHZ as I am trying to get here.

If you think that after the measurement of photon 1 as H> that MWI and QM have matching explanations, that is your opinion. But that is a matter of faith, not logic nor experiment. I reject the MWI claims unless the specifics can be explained to someone familiar with these new modern experiments. Basically, in the past 20 years, MWI proponents have struggled to get a grip on those experiments and have had to deny their relevance in order to maintain any degree of credibility.

 

[PeterDonis]

it claims it makes the same predictions.

Because it uses the same math, as all QM interpretations do. You're basically saying you don't believe the claim because you think it's inconsistent. Of course that's your prerogative, but it's not a valid basis for a PF discussion. If you're right, then at some point either MWI proponents will have to admit it, or the rest of the physicists who aren't MWI proponents will have to stop listening to them. And if either of those things happens, it will be reflected in the published literature. Unless and until that happens, it's not something we're going to resolve here.

 

[DrChinese]

a. It would be nice if someone had a reference from an MWI proponent that gives an MWI viewpoint on the entanglement swapping experiments you have given references for.

b. Unfortunately, so far despite a fair bit of searching I have not been able to find one. So I am doing the best I can myself to give what I believe to be the MWI viewpoint.

a, Agreed, and thanks.

b. The reason of course is that these newer experiments are closing so many of the early loopholes, it is unintentionally infringing on MWI (especially to the extent it claims to be local realistic). No serious experimentalist today believes in local realism, this is more the viewpoint of a set of theorists.

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

I don't think you and I can go much further if your opinion is that MWI makes no assumptions over and above orthodox QM. Or that such assumptions don't make any difference to the predictions of MWI vis a vis QM. I think those differences (deterministic evolution of the wavefunction at all times, locality, separability of distinct branches) are certainly subject to a deeper examination. And I think my example shows clearly how different MWI really is.

 

[PeterDonis]

I don't think you and I can go much further if your opinion is that MWI makes no assumptions over and above orthodox QM.

That's not what I said. I said the MWI makes the same predictions as basic QM, the same thing I say about all QM interpretations. If you disagree, then you're right, we don't have a valid basis for discussion, because that's how we define "QM interpretations" in this forum. Unless and until the published literature ceases to regard the MWI as a QM interpretation and instead treats it as something else, we can't resolve any such dispute here.

 

[PeterDonis]

MWI (especially to the extent it claims to be local realistic)

I don't agree that MWI proponents claim that it is a local realistic model. MWI proponents, or at least most of them, say that "realism" requires measurements to have single outcomes. Of course you disagree with them when they make that claim, but, as I've said, that's not something we're going to resolve here.

 

[PeterDonis]

I don't agree that MWI proponents claim that it is a local realistic model.

As far as "local" is concerned (as opposed to "realistic", which I addressed in my previous post just now), Zeh, as I've already remarked, seems to have no problem with saying that the MWI is nonlocal. (He would probably say it is realistic because it treats the wave function as real; but he would not say it is "local realistic".)

 

[DrChinese]

Because it uses the same math...

Not really, it's turtles. I will present a specific example Vaidman regarding GHZ showing where he deviates. I will place that in a different thread because it is far different than the swapping experiment here.

 

[PeterDonis]

I will present a specific example Vaidman regarding GHZ showing where he deviates. I will place that in a different thread because it is far different than the swapping experiment here.

Fair enough. I would note, though, that by the definitions we usually use in this forum, that would make Vaidman's proposed model a different theory from standard QM (since if he's using different math, he should be getting different predictions), rather than an interpretation of QM (just as we call the GRW stochastic collapse model a different theory, not a collapse interpretation, because it uses different math and makes different predictions from standard QM).

 

[PeterDonis]

(2) You need to ask how the basic math of QM--independent of any interpretation--accounts for entanglement swapping under the conditions I just described. And the answer to that is that it just handwaves it: it says, without any supporting argument, that we have to apply the photon 1 and 4 measurement operators to the state ##\ket{\Psi}_1##, not the state ##\ket{\Psi}_0##, even if the photon 1 and 4 measurements occur in the past light cone of the swap/no swap decision. (Your claim that "QM is contextual" explains this is not basic QM independent of any interpretation; it's a particular interpretation.) And then you need to explain why QM interpretations can't just handwave that the same way.

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. I should have followed up that hint sooner.)

To work through this, we will need to add something I didn't write down in my previous posts about the math: what does the "swap" operation actually do? That is, what unitary transformation does it induce on the wave function?

We can work that out by looking at the states ##\Psi_0## and ##\Psi_1##. (Note that I'll switch in this post and the following ones to using the singlet state ##HV - VH## as the entangled state, since that is the one that seems to be most often used in the experiments that have been referenced. Also, I'll omit the kets around the state labels in this post, there's enough typing already as it is. ) Call the swap unitary transformation ##U_S##. (The "no swap" operation is of course just the identity.) Then we have that ##\Psi_1 = U_S \Psi_0##. If we expand out those states, we get, schematically (using ##H## and ##V## for the two polarization states in the basis we are using):

$$
\Psi_0 = H_1 V_2 H_3 V_4 - V_1 H_2 H_3 V_4 - H_1 V_2 V_3 H_4 + V_1 H_2 V_3 H_4
$$

$$
\Psi_1 = H_1 H_2 V_3 V_4 - H_1 V_2 H_3 V_4 - V_1 H_2 V_3 H_4 + V_1 V_2 H_3 H_4
$$

Looking at the photon 2 and 3 states, since those are the photons that undergo the swap operation, we can see that we must have:

$$
\begin{matrix}
U_S ( V_2 H_3 ) = H_2 V_3 - V_2 H_3 \\
U_S ( H_2 V_3 ) = - ( H_2 V_3 - V_2 H_3 ) \\
U_S ( H_2 H_3 ) = U_S ( V_2 V_3 ) = 0
\end{matrix}
$$

Now, let's take "time ordering" at face value, and see what happens when we vary it. In the above, when we applied the swap operator ##U_S## to ##\Psi_0##, we were assuming, if we take time ordering at face value, that the swap operation (if it occurs) occurs before the photon 1 and 4 measurements. But suppose that isn't the case? Suppose, for example, that we measure photon 1 in the past light cone of the swap? (This is what is being done in the 2012 paper by Megidish et al. that @DrChinese referenced.)

Let's see what happens in that case. The photon 1 measurement operator ##M_1##, if we are using unitary evolution alone (no collapse), looks like this:

$$
M_1 \Psi_0 = \bar{H}_1 V_2 \left( H_3 V_4 - V_3 H_4 \right) - \bar{V}_1 H_2 \left( H_3 V_4 - V_3 H_4 \right)
$$

where the bar over the photon 1 states indicates that we now have a macroscopic recording of the state, so the two terms in the above are decohered. The rule with decoherence is that we have to apply any further unitary operations separately to any decohered terms; we can't combine them because decoherent branches can't interfere. So any term with one or more bars in it has to be evolved forward separately. (Also, barred terms don't change under unitary evolution, since we are assuming that unitary evolution preserves anything that is macroscopically recorded.)

So if we call the state we just wrote down ##\Psi_{1A} = M_1 \Psi_0##, and then we apply ##U_S## to it, what do we get? We get this:

$$
U_S \Psi_{1A} = \bar{H}_1 U_S \left( V_2 H_3 V_4 - V_2 V_3 H_4 \right) - \bar{V}_1 U_S \left( H_2 H_3 V_4 - H_2 V_3 H_4 \right)
$$

Using the rules for ##U_S## above, this gives:

$$
U_S \Psi_{1A} = \bar{H}_1 \left( H_2 V_3 - V_2 H_3 \right) V_4 - \bar{V}_1 \left( H_2 V_3 - V_2 H_3 \right) H_4
$$

(Note that in the second term on the RHS above, we had two minus signs that cancelled: one from the sign of the ##H_2 V_3## term and one from the minus sign when ##U_S## is applied to that term.)

Now for the punch line: the state ##U_S \Psi_{1A}## is the same as the state ##M_1 \Psi_1##! This is easily verified: just put a bar over the photon 1 factors in ##\Psi_1## and collect terms. In other words, the operations ##M_1## and ##U_S## commute (which, as I noted at the top of this post, was a hint in earlier posts of mine that I should have followed up sooner): the states ##M_1 U_S \Psi_0## and ##U_S M_1 \Psi_0## are the same!

Similar math shows that the photon 4 measurement operator ##M_4## also commutes with ##U_S##. 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!

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

 

[Morbert]

Sure. You can have as many BSMs between Photons 1 & 4 as you like with quantum repeaters. Each intermediate (except the ones associated with photons 2 & 3) can be placed before or after measurement (or creation) of either Photons 1 or 4. The BSMs associated with photons 2 & 3 can only be placed after their creation of course. But can be placed before or after the measurement of photons 1 & 4.

So the point is that you can select to perform an experiment in just about in order you like. QM doesn't care. ordering is never a factor. But because MWI evolves deterministically to the future, that leads to important differences.

Multistage Entanglement Swapping
https://arxiv.org/abs/0808.2972

See Fig. 1, and note that there is no theoretical limit to the number of stages (BSMs) in repeaters of this type. In this experiment, Photons 1 & 6 are entangled even though they never share a common light cone with each other, and their partners 2 & 5 also need never share a common light cone.

Thanks for the link. I now understand what you are referring to: Instead of a single BSM, we can construct an array of connected BSMs extended in space. The paper presents the initial state in equation 1 as $$|\Psi\rangle = |\Psi^-\rangle_{12}|\Psi^-\rangle_{34}|\Psi^-\rangle_{56}$$Using a change in notation: ##\Psi^-##, ##\Psi^+##, ##\Phi^-##, ##\Phi^+## ##\rightarrow## ##\Psi^1##, ##\Psi^2##, ##\Psi^3##, ##\Psi^4## this state can be rewritten as $$|\Psi\rangle = |\Psi^1\rangle_{12}|\Psi^1\rangle_{34}|\Psi^1\rangle_{56} = \sum_{i,j}c_{ij}|\Psi^i\rangle_{23}|\Psi^j\rangle_{45}|\Psi^{f(i,j)}\rangle_{16}$$Note that this is not an assertion that the [1,6]-photon system is pre-entangled. Instead it means that this state, evolved by local dynamics, can eventually interact with the two BSM systems and decohere into quasiclassical branches, some of which will exhibit an entangled [1,6]-photon system. The consequence of no action at a distance expresses itself like so:

As we would expect from the absence of action at a distance, then, branching is not a global phenomenon. Rather, when some microscopic superposition is magnified up to macroscopic scales (by quantum measurement or by natural processes) it leads to a branching event which propagates outwards at the speed of whatever dynamical interaction is causing decoherence—in practice, it propagates out at the speed of light

Each BSM interaction must therefore lie within the respective light cones of the relevant sources. Using Fig 1 as a reference, the left BSM must lie in the light cones of EPR sources I and II, and the right BSM must lie in the light cones of EPR sources II and III.

 

[PeterDonis]

how the MWI, with "deterministic evolution", explains entanglement swapping

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.)

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).

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.

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. In other words, in these "worlds", the "event ready" indicator that says that a swap occurred will never be observed. There is no branch of the wave function that has photons 1 & 4 both being measured ##H##, or both being measured ##V##, and a "swap" event ready signal. So in the "swap" case we have again just two final branches--the same ones we had in the other cases above.

So the MWI can in fact account for the entanglement swapping results, although the way it does so is indeed counterintuitive: the MWI has to tell a different story about what happens, depending on the order in which the events occur. In Case 1, its story is the simple "entanglement swapping" story: when the "swap" operation occurs, it swaps entanglements from 1&2 and 3&4 to 1&4 and 2&3. But in Cases 2 and 3, its story is that one photon is measured, and the result of the measurement is encoded in its partner (for example, photon 1 is measured and photon 2 encodes its result); then, if the swap operation occurs, it swaps, not entanglement, but the encoding of the result (from 2 to 4--or from 3 to 1 in the case where photon 4 is measured before the swap); and then, if the swap occurs, the swapped result encoding enforces the correlation between photons 1 & 4. And in Case 4, where both photons are measured before the swap/no swap decision, that decision encodes whether the already known photon 1 & 4 measurement results are consistent with a swap at all! Or, to put it another way, we get a "swap/no swap" branching in only two of the four branches that are produced by the photon 1 & 4 measurements; in the other two there is no further branching because only the "no swap" result is possible.

One is of course free to not like the above and to not want to adopt the MWI because of it. But in view of all the above, I don't think it's correct to say the MWI cannot account for the entanglement swapping results. It can--if you're willing to pay the price implied by all the above. But, as I noted in my Insights article on QM interpretations, there is no QM interpretation that does not entail paying some kind of fairly steep price. The question, at least until we can up our game to the point where we can figure out how to evolve what are now QM interpretations into actual different testable theories, is which price you find the least objectionable.

 

[PeterDonis]

the middle two terms in the above, the ones where the photon 2 & 3 kets are the same, get annihilated.

I should probably clarify this to avoid any misunderstanding due to the word "annihilated". I am not saying that any "worlds" get annihilated. All I am saying is that, whereas in the ##\bar{H}_1 \bar{V}_4## and ##\bar{V}_1 \bar{H}_4## branches, we get a further "swap" and "no swap" branching, in the ##\bar{H}_1 \bar{H}_4## and ##\bar{V}_1 \bar{V}_4## branches, we do not. We only get a "no swap" result. Or, to put it another way, even before photons 2 & 3 come together in the swap/no swap device, it is already predetermined that there will be a "no swap" result. So there is no further branching because there is no indeterminacy about the result.

 

[PeterDonis]

place an H> filter in the path of Photon 2. No swap will occur.

As a further follow-up to posts #79, #81, and #82, I'll work through this case. What we will find is that the statement just quoted is not entirely correct: it is still possible to have a swap with an ##H## filter in the path of photon 2. But it is true that one of the two "swap" branches that appears in previous posts, which analyzed the case without the ##H## filter, will no longer be there.

Since I have already established that the operators ##U_S##, ##M_1##, and ##M_4## all commute, I'll only work through one time ordering: to make things at least somewhat interesting, I'll do the ordering where photon 1 is measured first, then photon 2 passes through the filter, then the swap/no swap decision occurs, then photon 4 is measured.

Our starting state is the same as before, ##\Psi_0##. We then apply ##M_1## so we have ##M_1 \Psi_0##. Then we pass photon 2 through a filter that only allows ##H## photons to pass; ##V## photons are absorbed. Call this operator ##F##. Then we have the state:

$$
F M_1 \Psi_0 = F \left[ \bar{H}_1 V_2 \left( H_3 V_4 - V_3 H_4 \right) - \bar{V}_1 H_2 \left( H_3 V_4 - V_3 H_4 \right) \right]
$$

Applying the ##F## operator, this becomes:

$$
F M_1 \Psi_0 = \bar{H}_1 \emptyset_2 \left( H_3 V_4 - V_3 H_4 \right) - \bar{V}_1 H_2 \left( H_3 V_4 - V_3 H_4 \right)
$$

where I have used the "empty set" symbol to denote the branch where photon 2 gets absorbed. All we need now is to know what the swap/no swap decision machinery will do when the photon 2 channel is empty, and we do know that: we will always get a "no swap" result. That means the first branch on the RHS above does no further branching at the swap/no swap decision: its result is already predetermined to be "no swap". The second branch on the RHS still splits because a swap is still possible; so if we identify the full "swap/no swap" operator as ##U_{S/N}##, then the state after that operator is applied is:

$$
U_{S/N} F M_1 \Psi_0 = \bar{H}_1 \emptyset_2 \left( H_3 V_4 - V_3 H_4 \right) \bar{N} - \bar{V}_1 H_2 \left( H_3 V_4 - V_3 H_4 \right) \bar{N} + \bar{V}_1 H_2 V_3 H_4 \bar{S}
$$

where I have used ##\bar{N}## and ##\bar{S}## to denote the "no swap" and "swap" outcomes. Then the final state is just the operator ##M_4## applied to the above:

$$
M_4 U_{S/N} F M_1 \Psi_0 = \bar{H}_1 \emptyset_2 H_3 \bar{V}_4 \bar{N} - \bar{H}_1 \emptyset_2 V_3 \bar{H}_4 \bar{N} - \bar{V}_1 H_2 H_3 \bar{V}_4 \bar{N} + \bar{V}_1 H_2 V_3 \bar{H}_4 \bar{N} + \bar{V}_1 H_2 V_3 \bar{H}_4 \bar{S}
$$

So the only difference here is that there is now only one "swap" branch instead of two: the ##H## filter on photon 2 has eliminated one of the possible entangled outcomes for photons 1 and 4. There are still the same four "no swap" branches, so the filter has not affected those. In MWI-speak, what has happened is that, of the two possible outcomes of the photon 1 measurement that get encoded in photon 2, the filter has prevented one of them, the ##V## photon 2 outcome (which corresponds to the ##H## photon 1 outcome, since we are using singlet states), from being swapped to photon 4; only the ##H## photon 2 outcome (which corresponds to the ##V## photon 1 outcome) now gets swapped. And so the only "swap" branch we end up with is the one in which photon 1 is ##V## and photon 4 is ##H##. In other words, in the "swap" branch only the photon 4 outcome that is allowed to pass through the filter appears.

Note, btw, that the operators ##U_{S/N}## and ##F## do not commute; so if we analyze other time orderings, we need to move them in the time ordering as a unit, in the same order in which they appear above. But we can freely commute the combination ##U_{S/N} F## with the other operators.

Also, my claim that the four no-swap branches are "the same" might seem strange, since two of them now have the "empty set" states for photon 2 instead of the ones that appeared before. But the experiment does not measure those states; that's why they don't have bars over them. Only the barred states are used to define a branch, since branching only occurs when there is decoherence, and the bars identify where decoherence has taken place. So the four "no swap" branches are defined by the four possible combinations of barred photon 1 and photon 4 states--and all of them will of course have the barred ##N## to indicate no swap. Similarly, the "swap" branches are defined by the two possible combinations of barred photon 1 and photon 4 states for the singlet entangled state, with the barred ##S## to indicate a swap. In the above, as noted, only one of those two branches appears.

 

[PeterDonis]

As one more follow-up to my last few posts, I'll comment on "locality". What, if anything, is "local" in the MWI stories of these experiments?

One thing that clearly does not seem local is the wave function itself. The wave function, as has already been commented, includes degrees of freedom, which may be entangled, that are spatially separated. Any operation on a degree of freedom that is entangled with another degree of freedom that is spatially separated will produce nonlocal correlations--"nonlocal" in the sense of violating the relevant inequalities (Bell, CHSH, etc.).

But the operations themselves--the unitaries like ##U_{S/N}##, ##M_1##, and ##M_4##--do seem to be local, in the straightforward sense that they involve spatially localized devices that only operate on degrees of freedom at their spatial location. The "measure a photon" operators only measure the photon that is at their location. The "swap/no swap" operator only operates on the photons that are at its location. Any nonlocal effects are due to the nonlocality of the entangled wave function, not due to any nonlocality of the operations themselves.

It seems to me that this is consistent, in general, with what MWI proponents say, although I would have to admit that they aren't always as clear about it as they should be. (For example, consider Zeh's comments in his paper about the differences between David Deutsch's version of the MWI and his own.)

 

[DrChinese]

a. Note that this is not an assertion that the [1,6]-photon system is pre-entangled.

b. Instead it means that this state, evolved by local dynamics, can eventually interact with the two BSM systems and decohere into quasiclassical branches, some of which will exhibit an entangled [1,6]-photon system. ...

Each BSM interaction must therefore lie within the respective light cones of the relevant sources.

c. Using Fig 1 as a reference, the left BSM must lie in the [future] light cones of EPR sources I and II, and the right BSM must lie in the [future] light cones of EPR sources II and III.

a. Agreed, only the initial pairs are entangled.b. This is false, mostly. It is only true that each BSM requires 2 indistinguishable entangled photons as sources, and of course each of those sources must lie in the past light cone of the executed BSM. However, the following issues exist outside of that:

i. The BSMs themselves need not occur either before or after the neighboring BSM. And none of them need to occur either before or after the final entangled pair is detected.
ii. The BSMs themselves need not occur within the past light cone of the neighboring BSM. And none of them need to occur within the past light cone of the detection of the members of the final entangled pair.
iii. Even considering each initially entangled pair as a nonlocal system (i.e. with spatial extent), it is not required that the partners of the final entangled pair ever come into contact with each other, nor ever even exist in a common light cone.

As I have repeatedly said: the final entangled pair has evolved from a state in which they shared no entanglement, no correlations, and were in fact in a known completely different state than their ending state. And they did this without any direct interaction, guided by a far distant experimenter's decision to execute a swap (or not). And there is no limit to the distance they are apart at the time of detection.

So any concept of locality or local dynamics here is completely absent. As I also keep mentioning, here is a specific example to be worked through to demonstrate any such locality - whether with one BSM or more than one. Clearly it is easy to claim "locality" if distance is considered, but not associated elapsed time. (And of course, that's not even stepping into the discussion of causality.)c. Yes, this is the basic concept of quantum repeaters and their utility.

In other words, there is no upper limit to the distance D the final pair can be apart, and there is no lower limit on the time duration T between their final detection times. That makes D/T as large as you might like, and therefore as much higher than c as you might like. Of course, there is no useful information in the process that itself exceeds c at any time as the outcomes are still random (without additional signaling, which is limited to c).

 

[PeterDonis]

As I also keep mentioning, here is a specific example to be worked through to demonstrate any such locality - whether with one BSM or more than one.

See my posts #79, #81, #82, and #83 for a more detailed working through of the math and the MWI description of the one BSM case with all possible time orderings of the BSM relative to the photon 1 and photon 4 measurements, along with my comments in post #84 about what in the MWI description is and is not local, in my opinion.

 

[DrChinese]

Note that this is not an assertion that the [1,6]-photon system is pre-entangled. Instead it means that this state, evolved by local dynamics, can eventually interact with the two BSM systems and decohere into quasiclassical branches, some of which will exhibit an entangled [1,6]-photon system.

This idea - that the initial 6 photon system contains a subset in which 1 & 6 are entangled - is absolutely false. QM absolutely does not say this, and virtually every swapping paper makes clear that this is not the case. The BSM is not a "filter". It is a projection device which makes a change to the state of remote photons (to cause them to become entangled, which is a different state). Each and every indistinguishable pair (in the ideal case of course) that enter the BSM are swapped (although current technology does not allow more than two of the four resulting Bell states to be identified).

I have already demonstrated this previously in both theory and experiment:

a) Theory: Monogamy of Entanglement (MoE) prevents maximal entanglement between AB and BC. This is standard QM. MWI would be immediately math-different if it said otherwise.
b) Experiment: The filtering option was in fact tested in the following experiment: 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."

 

[PeterDonis]

The consequence of no action at a distance expresses itself like so

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.

 

[DrChinese]

But if you are going to object to the MWI on these grounds, you need to make the correct objection. That requires doing at least two things:

(1) You need to specify the scenario so that time ordering makes a difference. But you have specified that, for this discussion, you want all three of the decoherence events--the photon 1 and 4 measurements, and the swap/no swap decision--to be spacelike separated. That means their time ordering can't make a difference. If you want to ask how the MWI, with "deterministic evolution", explains entanglement swapping, you need to, for example, put the photon 1 and 4 measurements in the past light cone of the swap/no swap decision, so that, at least on its face, "deterministic evolution" would require that the photon 1 and 4 measurements can't possibly be made on a state that has decohered due to the swap/no swap decision.

(2) You need to ask how the basic math of QM--independent of any interpretation--accounts for entanglement swapping under the conditions I just described. And the answer to that is that it just handwaves it: ...

(3) Your claim that "QM is contextual" explains this is not basic QM independent of any interpretation; it's a particular interpretation.

1) I have been clear about this. The measurements of 1 and 4 are spacelike separated from each other, and as well each spacelike separated from the experimenter and their BSM device. The order of execution in the same reference frame is: a) measure Photon 1; b) execute (or not) the swap); c) measure Photon 4. Because they are specified as spacelike separated (apparently you don't appreciate the word "distant"), no signal can propagate between any of these faster than c.

Yes, I also see why you recommend that both the 1 and 4 measurements should be placed before the BSM on 2 & 3. And your point on that is good, probably a better choice than what I specified actually. But the reason I selected this is that it forces the MWI issue of saying what happens when 1 is measured; and then forces the MWI issue of saying what happens when 2&3 are projected.

Of course, I know perfectly well that in QM the ordering does not change the quantum predictions. And I know what the quantum predictions are. But the ordering will matter in MWI, at least that is what I am exploring. Obviously, it shouldn't matter in MWI either but that just doesn't make sense based on any kind of deterministic dynamics. 2) I would say it is fair to say QM has handwaving in it. After all, the rule for a successful swap in the BSM is something labeled "indistinguishability". I don't question it, I just accept the rule because it works. (It's sort of like "irreversible measurements" or "collapse". All of these require a bit of handwaving or suspension of logic. I accept them because they mostly work.) But extra handwaving over and above whatever we must minimally accept should be identified as such.3) The contextuality of all QM interpretations is in the expectation value for entanglement. For example, polarization matches of entangled linear polarized photons is at the rate of cos^2(A-B) where A and B are the nonlocal future measurement settings. That's the definition of "context".

On its own, that of course doesn't say anything about an underlying mechanism. That part would be specific to the interpretation. But you'd have to admit that it's a pretty big hint if the quantum prediction doesn't include any variables from the circumstances of their creation (other than the Bell state). And also, features a nonlocal context when both A and B can be decided long after they are no longer capable of causal context.

So I stand by my statement. Again, that wouldn't mean on its own that theory couldn't be local or realistic. But it should be a clue. One thing that is missing in calling QM contextual is that there is no obvious hint of what (if anything) is responsible for random outcomes. Apparently, the effect of any putative hidden (or other) variables cancels out, leaving only the context for a prediction.

 

[PeterDonis]

@DrChinese, as I posted a little bit ago, please read my posts #79, #81, #82, #83, and #84. I have worked things out in considerably more detail since I made the post you quoted in your post #89, with regard to both the math and how the MWI would describe the various possible scenarios that you get by switching around the time ordering of the key events. I do analyze the spacelike separated case that you specified, but I also analyze the timelike separated cases. I also comment in post #84 about what aspects of the MWI description I think are and are not local.

 

[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".

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

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.