A Is MWI Considered Local in Quantum Mechanics?

[DrChinese]

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

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

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

d. I have already answered this question. And I have repeatedly referred you to my answer when you have repeated this question in previous posts. I don't know why you keep ignoring what I have already said. ... I disagree. I have made one, and I have repeatedly referred you to it. In the interest of facilitating discussion, I'll repeat the gist of it once more: the wave function enforces the correlations. The wave function already contains all the correlations you describe. That is how the MWI explains them.

a. If there is action at a distance, then measurements might commute or they might not. In QM, there is no time ordering to its predictions. Therefore if there is AAD in QM, then they WILL commute.

On the other hand, if there is no AAD, then classically all such measurement also commute. So saying they commute only tell you that there is no AAD of the type which follow a direction from the past to the future.

b. No, I have never had the impression you are a particularly a proponent of MWI nor a proponent of the idea that MWI is local. I think you do an excellent job of discussing the wide variety of interpretations here. Often, you act as sort of a "devil's advocate". Sometimes that approach is useful, but not always.

c. Well, certainly there are a lot of claims made about MWI. I have attempted to distill what I believe is common to most descriptions, and I have read a few. They all pretty much claim that the wave function evolves locally. So how do nonlocal effects appear? If I have misrepresented some material point, how about YOU reference something rather than challenge me word by word? Fair is fair. If you don't have time to provide such reference, then skip the point rather than quibbling with me. I have made the question quite clear.

d. "The wave function enforces the correlations"? That's an answer? That isn't even a summary of an answer. The question from above is:

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

I'd like someone to walk us through the splitting and evolution of the systems point by point where they can be discussed. I think we start off in agreement, there is splitting when Photon 1 is measured (H> branch and V> branch). At that time, Photons 2 and 3 are distant to the Photon 1 measurement, but heading towards each other - soon to be swapped (or not) by the experimenter. Photon 4 is distant to Photons 2 and 3 (Photon 1 has ceased to exist). The polarization of Photon 4 will be measured last (not that ordering actually matters, it's just easier to discuss).

When and where do the H> and V> branches next split? And what are the consequences to the remaining Photons on the outcome of the branch they are in due to the splitting related to the measurement of Photon 1?

 

[DrChinese]

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

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

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

Ah, I can't go there. This is exactly the hand-waving I spoke of. Yes, I had seen that and intentionally did not include it because it makes no sense in this context.

It still does NOT explain how the wavefunctions would work in a swapping setup as I have established. So what if there is nonseparability in remote objects? Photons 1 and 2 are the remote object! Photon 4 has nothing to do with anything at this point!!

 

[DrChinese]

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

b. If, for example, you think Vaidman is claiming that the MWI does not predict Bell inequality violations, then I would expect Vaidman himself to object, since the MWI is an interpretation of QM and QM itself, independent of any interpretation, predicts Bell inequality violations.

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

a. Deterministic laws can (theoretically) be calculated forward and backward, true. But that's a far cry from 2 way causal laws. In retrocausal type interpretations, there are causal elements in both the future and the past. There aren't, as far as I know, any MWI proponents claiming causality works backwards to what we human perceive as the direction of time. So this is just another quibble that is not furthering the discussion.

b. Vaidman of course thinks Bell does not apply.

c. Agreed. I assume that Bell didn't think of Everett as local either, but I can't find detail on that specific point. Not that his opinion would decide the debate anyway, I just thought it is interesting to see his thoughts. Of course, GHZ only appeared right around the untimely death of Bell and no experiments had been done on that yet. And quantum teleportation much the same. Those would have certainly influenced Bell in some way.

 

[PeterDonis]

"The wave function enforces the correlations"? That's an answer? That isn't even a summary of an answer.

I disagree that it's not even a summary of an answer. And I have posted more than just that once sentence about it. But at least now you're acknowledging it and we can move on from there.

I'd like someone to walk us through the splitting and evolution of the systems point by point where they can be discussed.

Sure, I said I would take a stab at it and I will.

Let's first describe the overall setup to be sure we have it right. We have four photons. In the initially prepared state, photons 1 and 2 are entangled, and photons 3 and 4 are entangled. Both entanglements are maximal so by monogamy of entanglement there can't be any other entanglements involved.

In the middle of the experiment, so to speak, photons 2 and 3 are brought together and an experimental choice is made of whether or not to induce an entanglement swap. If a swap is induced, then after the swap (where "after" does not refer to time ordering, since as already noted it is possible to run this experiment where, for example, the photon 1 and 4 measurements are in the past light cone of the photon 2 and 3 swap/no swap decision--"after" only refers to logical ordering in terms of the analysis we are doing), photons 2 and 3 are entangled, and photons 1 and 4 are entangled. Again, both entanglements are maximal.

At the end of the experiment (which might, as noted, be in the past light cone of the "middle" described above, but it is logically the end for purposes of analysis), photons 1 and 4 are measured. To keep it simple, we will assume they are both measured along the same polarization axis, so if they are entangled, the measurements will always agree. If they are not entangled, there is an equal chance for the measurements to agree or disagree.

Now we can talk about how the MWI describes what happens to the wave function in the above. The starting wave function is, schematically (and ignoring normalization, which I will do throughout):

$$
\ket{\Psi}_0 = \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{ready}}
$$

where the lower case $\psi$ kets on the RHS are subscripted with the photons that are entangled in them, and the "ready" ket describes the state of the swap/no swap decision apparatus.

When photons 2 and 3 come together, either a swap happens or it doesn't. So after that decision is made (and in the MWI, the dynamics of that decision would be encoded in the Hamiltonian and would affect the wave function), the wave function becomes

$$
\ket{\Psi}_1 = \ket{\psi}_{14} \ket{\psi}_{23} \ket{\text{swap}} + \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{no swap}}
$$

In MWI-speak, we have had a split into two worlds: in the first, the swap happened and the entanglements are changed; in the second, the swap didn't happen and the entanglements are not changed.

When the photon 1 and 4 measurements are done, we have the final state, which will be:

$$
\begin{matrix}
\ket{\Psi}_2 = \left( \ket{\text{1 and 4 up}} + \ket{\text{1 and 4 down}} \right) \ket{\psi}_{23} \ket{\text{swap}} \\
+ \left( \ket{\text{1 and 4 up}} + \ket{\text{1 up and 4 down}} + \ket{\text{1 down and 4 up}} + \ket{\text{1 and 4 down}} \right) \ket{\psi}_2 \ket{\psi}_3 \ket{\text{no swap}}
\end{matrix}
$$

Here we have two more splits of worlds, in MWI-speak: on the "swap" side, we have a split into two worlds, in one of which photons 1 and 4 are both up and in the other they are both down; on the "no swap" side, we have a split into four worlds, corresponding to the four possible combinations of photon 1 and 4 results (since if there is no swap they are uncorrelated). (Note that I have assumed that no measurements are made on photons 2 and 3, so they just stay however they were after the swap/no swap decision is made and executed.)

Of course none of this says that the MWI is "local". The wave function itself, I would say (and Zeh says in the paper you referenced from him), is a nonlocal object, because it includes degrees of freedom that are spatially separated. But it's a perfectly good explanation of the correlations: as I said, they are enforced by the wave function, and more specifically by the possibilities that appear in the wave function. "Perfect correlation" between photons 1 and 4 if there is a swap just means the only possibilities that appear in the wave function if there is a swap are ones in which the measurement results on photons 1 and 4 agree.

 

[PeterDonis]

This is exactly the hand-waving I spoke of.

It seems pretty clear to me: Vaidman is acknowledging that the wave function is a nonlocal object, just as Zeh says in his paper. In other words, he is saying that he agrees that the MWI is nonlocal. He agrees that the MWI predicts things like Bell inequality violations and entanglement swapping. He just doesn't think the MWI attributes these things to any "action at a distance".

 

[mattt]

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

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

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

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

I don't see anything controversial in those three points (and the rest of the article).

If you understand what he is trying to say, I find it a quite straightforward translation of the mathematics of quantum mechanics into the English words of the Huge Everett interpretation.

 

[martinbn]

@DrChinese This is a bit of a side questions, but it was said a few time, so I'd like to understand what the claim is. You said that quantum teleportation proves non-locality, but which form of non-locality? If you mean violations of Bell's inequalities, then no one disagrees. If you mean something else, what exactly? And why do you think the references you gave support that kind of nonlocality?

 

[PeterDonis]

the Huge Everett interpretation

Huge?

 

[Morbert]

@DrChinese I'm still interested in a reference re/post #42. I think it's useful to emphasise the timelike relation between the BSM and the preparation of both 2-photon systems that, according to MWI, gives rise to the resultant decoherent branches.

 

[DrChinese]

a. Let's first describe the overall setup to be sure we have it right.

b. We have four photons. In the initially prepared state, photons 1 and 2 are entangled, and photons 3 and 4 are entangled. Both entanglements are maximal so by monogamy of entanglement there can't be any other entanglements involved.

c. In the middle of the experiment, so to speak, photons 2 and 3 are brought together and an experimental choice is made of whether or not to induce an entanglement swap. If a swap is induced, then after the swap (where "after" does not refer to time ordering, since as already noted it is possible to run this experiment where, for example, the photon 1 and 4 measurements are in the past light cone of the photon 2 and 3 swap/no swap decision--"after" only refers to logical ordering in terms of the analysis we are doing), photons 2 and 3 are entangled, and photons 1 and 4 are entangled. Again, both entanglements are maximal.

d. At the end of the experiment (which might, as noted, be in the past light cone of the "middle" described above, but it is logically the end for purposes of analysis), photons 1 and 4 are measured. To keep it simple, we will assume they are both measured along the same polarization axis, so if they are entangled, the measurements will always agree. If they are not entangled, there is an equal chance for the measurements to agree or disagree.

e. Now we can talk about how the MWI describes what happens to the wave function in the above. The starting wave function is, schematically (and ignoring normalization, which I will do throughout):

$$
\ket{\Psi}_0 = \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{ready}}
$$

where the lower case $\psi$ kets on the RHS are subscripted with the photons that are entangled in them, and the "ready" ket describes the state of the swap/no swap decision apparatus.

f. When photons 2 and 3 come together, either a swap happens or it doesn't. So after that decision is made (and in the MWI, the dynamics of that decision would be encoded in the Hamiltonian and would affect the wave function), the wave function becomes

$$
\ket{\Psi}_1 = \ket{\psi}_{14} \ket{\psi}_{23} \ket{\text{swap}} + \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{no swap}}
$$g. Of course none of this says that the MWI is "local". The wave function itself, I would say (and Zeh says in the paper you referenced from him), is a nonlocal object, because it includes degrees of freedom that are spatially separated. But it's a perfectly good explanation of the correlations: as I said, they are enforced by the wave function, and more specifically by the possibilities that appear in the wave function. "Perfect correlation" between photons 1 and 4 if there is a swap just means the only possibilities that appear in the wave function if there is a swap are ones in which the measurement results on photons 1 and 4 agree.

a. Thanks as always for your time.

b. Agreed. For convenience of discussion, I am also specifying that the initial entangled states for each pair is HH+VV. That doesn't change anything of import.

c. Only difference here is I want to specify that the measurement of Photon 1 occurs prior to the swap, and the 2/3 swap prior to the Measurement of Photon 4. I recognize fully that there is no predicted difference to the outcomes, but this sequence more clearly highlights the conceptual problems of MWI. This is perfectly feasible if the experiments are performed in the same inertial reference frame.

Further: I assumed you understood that my use of the word "distant/distance" (which matches the Nobel committee's terminology) means a distance too great in spacetime to be traversed at c. Thus no signal can go from the measurement of Photon 1 to the location of the swap of Photons 2/3. Similarly, no light signal can go from the swap (BSM) on Photons 2/3 to the location of the measurement of Photon 4. And Photon 4 is likewise too far from Photon 1's measurement for any light signal to get their either.

The only events in a common light cone is the initial entangled creation of Photons 1 & 2 (and likewise with the creation of Photons 3 & 4). So I accept that under MWI, the spreading of the "joint" wave function of Photons 1 & 2 (likewise 3 & 4) ultimately means that the swap brings together the wave functions of Photons 2 & 3. That despite the fact that no signal can go from there (location of the swap) to the location of Photon 4's measurement.

Please say if these specifications are not acceptable for our discussion, these variations have all been physically realized in various swapping experiments already.

d. Agreed that the Photon 4 measurement is to be done on same basis as Photon 1, so we desire the H> branch of Photon 1 to always contain the H> branch on Photon 4. And likewise we desire the V> branch of Photon 1 to always contain the V> branch on Photon 4. Note that the choice of H/V basis is arbitrary (I am sure no issue with that). And further that it is possible (but not important here, at least not at this time), that the choice of H/V basis could be selected midflight in a spacetime location isolated from the creation of the initially entangled pairs. Further, that basis choice need not be transmitted to the swapping mechanism (which is distant).

e. Agreed, we have a Product State of 2 entangled systems which have had no interaction of any kind. In fact, the only overlap they will ever have is if the swap is executed.

f. We are not agreed on this yet, because this is what we seek to prove. The MWI proponent (and I will not dispute) would say that immediately before the swap (which is after measurement of Photon 1), we have this:

f.i)
$$
\ket{\Psi}_1 = \ket{HH}_{12} \ket{\psi}_{34} + \ket{VV}_{12} \ket{\psi}_{34} {\text{ swap ready}}
$$

We want this to evolve somehow to what you say:

f.ii)
$$
\ket{\Psi}_1 = \ket{\psi}_{14} \ket{\psi}_{23} \ket{\text{swap}} + \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{no swap}}
$$

But this is not possible. QM predicts no swap can occur for either branch of the right hand side. It is an absolute requirement of swapping that Photons 2 & 3 are indistinguishable. They aren't any longer! Photon 2 is either in the H> branch or it is in the V> branch. In either branch (which by MWI tenet cannot interfere), Photons 2 & 3 can be distinguished on the basis of polarization. And this fact can be demonstrated by experiment: place an H> filter in the path of Photon 2. No swap will occur.

This point is not mentioned in the reference, as they assume everyone knows this. So I am providing the following reference:

Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
https://arxiv.org/pdf/1508.05949.pdf
"If the photons are indistinguishable in all degrees of freedom, the observation of ... [photons 2 & 3] in different output ports projects ... [Photons 1 & 4] into the maximally entangled state ..."
Note: photons are used for the swap in this particular experiment, and the final entangled pair is actually electrons. I modified the quote (in brackets []) to match our labeling.

Entanglement Between Photons that have Never Coexisted
https://arxiv.org/pdf/1209.4191.pdf
"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."

Further, it wouldn't matter if the order of events changed. In no version of branching will there be indistinguishable photons present for a swap unless (I guess) you specify the swap occurs before the measurement of Photons 1 & 4. But we already know from experiment that makes no difference at all, because explicit delayed-choice swaps (swap occurring after Photons 1 & 4 were measured) have been documented. See for example:

Experimental Nonlocality Proof of Quantum Teleportation and Entanglement Swapping
https://arxiv.org/abs/quant-ph/0201134
"Such a delayed-choice experiment was performed by including two 10 m optical fiber
delays for both outputs of the BSA. In this case photons [2] and [3] hit the detectors delayed
by about 50 ns. As shown in Fig. 3, the observed fidelity of the entanglement of photon [1] and
photon [4] matches the fidelity in the non-delayed case within experimental errors. Therefore,
this result indicate that the time ordering of the detection events has no influence on the
results..."

I am adding some specific MWI quotes in my next post as something of an extension to this one.

 

[DrChinese]

Quotes from the Vaidman article in SEP (my comments in brackets):

a) ...the ontology of the universe is a quantum state, which evolves according to the Schrödinger equation or its relativistic generalization... [which of course the Schrödinger equation evolves respecting c]. ... The Schrödinger equation itself does not explain why we experience definite results in quantum measurements.
b) The wave function of all particles in the Universe corresponding to any particular world will be a product of the states of the sets of particles corresponding to all objects in the world...
c) The difficulty with the concept of probability in a deterministic theory, such as the MWI, is that the only possible meaning for probability is an ignorance probability... [there is no actual uncertainty, since every outcome occurs there is realism at all times].

From Everett per SEP:
a) "All elements of a superposition must be regarded as simultaneously existing." [they are in different branches, of course]
b) [the following paraphrased by Barrett:] There is a sense in which A nevertheless gets a perfectly determinate measurement record...
c) "Let one regard an observer as a subsystem of the composite system: observer + object-system. It is then an inescapable consequence that after the interaction has taken place there will not, generally, exist a single observer state. There will, however, be a superposition of the composite system states, each element of which contains a definite observer state and a definite relative object-system state. Furthermore, as we shall see, each of these relative object system states will be, approximately, the eigenstates of the observation corresponding to the value obtained by the observer which is described by the same element of the superposition. Thus, each element of the resulting superposition describes an observer who perceived a definite and generally different result, and to whom it appears that the object-system state has been transformed into the corresponding eigenstate."
d) "... reality as a whole is rigorously deterministic. This reality, which is described jointly by the dynamical variables and the state vector, is not the reality we customarily think of, but is a reality composed of many worlds. By virtue of the temporal development of the dynamical variables the state vector decomposes naturally into orthogonal vectors, reflecting a continual splitting of the universe into a multitude of mutually unobservable but equally real worlds, in each of which every good measurement has yielded a definite result... [emphasis added].

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

Of course, Everett's work appeared pre-Bell so he had no clue of what was to come. Clearly, MWI imagines a worlds in which a measurement on Photon 1 leads to 2 different branches: one with the definite H> result for all time to follow, and another with the definite V> result for all time to follow. These branches can never lead to entanglement of Photon 1 with anything - unless of course we have action at a distance. Again, see post#60 for the explicit proof.

 

[DrChinese]

@DrChinese I'm still interested in a reference re/post #42. I think it's useful to emphasise the timelike relation between the BSM and the preparation of both 2-photon systems that, according to MWI, gives rise to the resultant decoherent branches.

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
Abstract: We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements (BSMs) one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an entangled state, as characterized by an entanglement witness. The experiment represents an important step towards a full quantum repeater where multiple entanglement swapping is a key ingredient.

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.

 

[PeterDonis]

Only difference here is I want to specify that the measurement of Photon 1 occurs prior to the swap, and the 2/3 swap prior to the Measurement of Photon 4.

That's fine. I already included cautions about time ordering vs. logical ordering in my post. As you say, the results are the same regardless of the time ordering, so any time ordering you want to specify is fine. It doesn't change anything I posted.

no signal can go from the measurement of Photon 1 to the location of the swap of Photons 2/3. Similarly, no light signal can go from the swap (BSM) on Photons 2/3 to the location of the measurement of Photon 4. And Photon 4 is likewise too far from Photon 1's measurement for any light signal to get their either.

Ok, so all of the measurements are spacelike separated. Again, the predictions are the same regardless, so if you want to specify this, that's fine. It doesn't change anything I posted.

The MWI proponent (and I will not dispute) would say that immediately before the swap (which is after measurement of Photon 1), we have this:

f.i)
$$
\ket{\Psi}_1 = \ket{HH}_{12} \ket{\psi}_{34} + \ket{VV}_{12} \ket{\psi}_{34} {\text{ swap ready}}
$$

That's the same state I wrote down, you're just expanding out what I wrote as $\ket{\psi}_{12}$.

We want this to evolve somehow to what you say:

f.ii)
$$
\ket{\Psi}_1 = \ket{\psi}_{14} \ket{\psi}_{23} \ket{\text{swap}} + \ket{\psi}_{12} \ket{\psi}_{34} \ket{\text{no swap}}
$$

Yes.

But this is not possible. QM predicts no swap can occur for either branch of the right hand side.

If this claim of yours is correct, it means QM cannot make correct predictions for entanglement swapping. Nothing I have written down is specific to the MWI; it is just basic QM, unitary evolution from $\ket{\Psi}_0$ to $\ket{\Psi}_1$ using the Schrodinger Equation with an appropriate Hamiltonian. If that does not produce $\ket{\Psi}_1$, then QM cannot make correct predictions, because $\ket{\Psi}_1$ is the correct state to describe the possible results of the swap mechanism. MWI interprets that ket to describe two branches that both "exist", instead of just describing possible results, but that's interpretation, not math. The math is the same on any interpretation.

So at this point I don't understand what your argument is. Are you arguing that we have to change how QM makes predictions in order to correctly predict the results of entanglement swapping?

It is an absolute requirement of swapping that Photons 2 & 3 are indistinguishable. They aren't any longer!

They aren't after a swap takes place, if a swap does take place. But the swap only requires that they are indistinguishable before the swap takes place. In other words, we have a Hamiltonian that describes the swap process; the input state that enables that process has to have photons 2 & 3 indistinguishable; but the output state after the Hamiltonian is applied does not have photons 2 & 3 indistinguishable (because once a swap has taken place, they aren't).

Photon 2 is either in the H> branch or it is in the V> branch.

If you are referring to $\ket{\Psi}_0$, the state before the swap Hamiltonian has been applied, there are no such branches. There is only one branch of the wave function at that point, according to the MWI. That's why I wrote it as a single term. Splitting what I wrote as $\ket{\psi}_{12}$ into two terms doesn't change the fact that there's only one branch; it just obfuscates it. Branching occurs in the MWI when decoherence occurs, and no decoherence has occurred at the point where $\ket{\Psi}_0$ is the overall wave function.

In either branch (which by MWI tenet cannot interfere), Photons 2 & 3 can be distinguished on the basis of polarization. And this fact can be demonstrated by experiment: place an H> filter in the path of Photon 2. No swap will occur.

You've changed the experiment. If there is an H filter in Photon 2's path, the Hamiltonian changes, and therefore so does the resulting state. We're not analyzing that different experiment. We're analyzing the experiment where it is possible for a swap to take place. In that experiment, there are no interactions except the swap operation. Other than photons 2 & 3 being "inside" the swap mechanism, where if they are indistinguishable a swap can occur, the photons travel freely and there are no unitary operations done on them besides free propagation. That is the experiment we are analyzing.

 

[DrChinese]

@DrChinese This is a bit of a side questions, but it was said a few time, so I'd like to understand what the claim is. You said that quantum teleportation proves non-locality, but which form of non-locality? If you mean violations of Bell's inequalities, then no one disagrees. If you mean something else, what exactly? And why do you think the references you gave support that kind of nonlocality?

The specific form of nonlocality - action at a distance (AAD) - that I claim is the generally accepted science is the remote change of quantum state by an experimenter's choice. That experimenter can choose to teleport/change the quantum state of a remote system (as measured by c). Note that entanglement swapping uses the same essential protocol as quantum teleportation. See any of the swapping experiments I have referenced such as these by teams associated with Zeilinger:

https://arxiv.org/pdf/quant-ph/0201134.pdf (2002-2008)
https://arxiv.org/pdf/0809.3991.pdf (2008)

As mentioned, the 2022 Nobel committee summarized these works and others as follows: [Anton Zeilinger's] research group has demonstrated a phenomenon called quantum teleportation, which makes it possible to move a quantum state from one particle to one at a distance."

If you want to claim it was not mainstream physics before 2022, then go ahead. Not sure how much clearer one needs to be here, this stuff has been around for 20 years. The GHZ experiments prove exactly the same thing as swapping experiments do, but the complexity of the math and the implementation is much more complex. With GHZ, you can remotely change a quantum state as well by the experimenter's choice of basis. If the experimenter makes a choice here that measurably changes a state there, how is that not action at a distance?

I strictly follow mainstream physics based on the thousands of papers I have scanned (unless I occasionally note otherwise). You probably have noted that I keep a lot of bookmarks on the best. So what I am saying is well accepted by the experimental community. All I can say is that there are a lot of people that have entrenched positions of denial that might do well to read a new more experiments and take a fresh view.

 

[DrChinese]

a. That's fine. I already included cautions about time ordering vs. logical ordering in my post. As you say, the results are the same regardless of the time ordering, so any time ordering you want to specify is fine. It doesn't change anything I posted.

Ok, so all of the measurements are spacelike separated. Again, the predictions are the same regardless, so if you want to specify this, that's fine. It doesn't change anything I posted.

b. If this claim of yours is correct, it means QM cannot make correct predictions for entanglement swapping. Nothing I have written down is specific to the MWI; it is just basic QM ... Are you arguing that we have to change how QM makes predictions in order to correctly predict the results of entanglement swapping?c. They aren't after a swap takes place, if a swap does take place. But the swap only requires that they are indistinguishable before the swap takes place. In other words, we have a Hamiltonian that describes the swap process; the input state that enables that process has to have photons 2 & 3 indistinguishable; but the output state after the Hamiltonian is applied does not have photons 2 & 3 indistinguishable (because once a swap has taken place, they aren't).d. If you are referring to $\ket{\Psi}_0$, the state before the swap Hamiltonian has been applied, there are no such branches. There is only one branch of the wave function at that point, according to the MWI. That's why I wrote it as a single term. Splitting what I wrote as $\ket{\psi}_{12}$ into two terms doesn't change the fact that there's only one branch; it just obfuscates it. Branching occurs in the MWI when decoherence occurs, and no decoherence has occurred at the point where $\ket{\Psi}_0$ is the overall wave function.

e. You've changed the experiment. If there is an H filter in Photon 2's path, the Hamiltonian changes, and therefore so does the resulting state. We're not analyzing that different experiment. We're analyzing the experiment where it is possible for a swap to take place. In that experiment, there are no interactions except the swap operation. Other than photons 2 & 3 being "inside" the swap mechanism, where if they are indistinguishable a swap can occur, the photons travel freely and there are no unitary operations done on them besides free propagation.

a. In QM, no change. In MWI, big change. And why is that?

QM is contextual. A future context - and ONLY a future context - dictates the quantum prediction. More importantly, the entire future context must be considered in QM. But that same statement cannot be made in MWI, because MWI evolves deterministically. Time and ordering are absolutely relevant, despite any MWI proponent's argument to the contrary. As each stage in the MWI version occurs, there is a branching (which is loosely akin to "collapse" in QM). But in indeterministic QM, there is only 1 collapse for the entire context. In deterministic MWI, there are many branching events for a swap - at least 3. Those lead to branches that do NOT match the QM result for all branches.

b. You have skipped the branching of MWI, your description is simply the QM version. No, of course I am not questioning that. I am citing mainstream physics here.

c. Again, you need to acknowledge that after Photon 1 is measured, there is an H> world and a V> world under MWI. This is absolutely and unquestionably a tenet of every version of MWI. If you can show me otherwise, please show me. On the other hand, I (the only one providing quotes and references) showed you otherwise in my post #61. In MWI, each observer sees a definite outcome.

d. If Photon 1 is H>, then by rule Photon 2 is H>. That is true in MWI. Nothing to see here. Of course, the swap polarization test can be performed at any angle, and if that angle is different than the Photon 1 test, we are now in counterfactual territory - so no claim is really possible for QM.

e. For MWI, it's no change if we add an H> filter when Photon 2 is already H>. After all, 100% of those will pass without any change. Of course we would lose the intensity from the V> stream.

 

[martinbn]

The specific form of nonlocality - action at a distance (AAD) - that I claim is the generally accepted science is the remote change of quantum state by an experimenter's choice. That experimenter can choose to teleport/change the quantum state of a remote system (as measured by c). Note that entanglement swapping uses the same essential protocol as quantum teleportation. See any of the swapping experiments I have referenced such as these by teams associated with Zeilinger:

https://arxiv.org/pdf/quant-ph/0201134.pdf (2002-2008)
https://arxiv.org/pdf/0809.3991.pdf (2008)

As mentioned, the 2022 Nobel committee summarized these works and others as follows: [Anton Zeilinger's] research group has demonstrated a phenomenon called quantum teleportation, which makes it possible to move a quantum state from one particle to one at a distance."

If you want to claim it was not mainstream physics before 2022, then go ahead. Not sure how much clearer one needs to be here, this stuff has been around for 20 years. The GHZ experiments prove exactly the same thing as swapping experiments do, but the complexity of the math and the implementation is much more complex. With GHZ, you can remotely change a quantum state as well by the experimenter's choice of basis. If the experimenter makes a choice here that measurably changes a state there, how is that not action at a distance?

I strictly follow mainstream physics based on the thousands of papers I have scanned (unless I occasionally note otherwise). You probably have noted that I keep a lot of bookmarks on the best. So what I am saying is well accepted by the experimental community. All I can say is that there are a lot of people that have entrenched positions of denial that might do well to read a new more experiments and take a fresh view.

Two comments. First, action at a distance is ypur wording. Do you have a reference with that exact wording? Second, you are confused about how teleportation works. There is no remote change of state!

 

[PeterDonis]

In QM, no change. In MWI, big change.

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

If you are going to continue to make false claims about what the MWI says, there is no point in further discussion. I am quite willing to give more details about how the MWI explains the QM predictions. But I am not willing to entertain false claims that the MWI does not make the same predictions that QM does.

QM is contextual.

There is a sense of "contextual" in which this is true, but I'm not sure you are using the word in that sense. Again, you seem to be arguing based on "contextual" that the MWI does not make the same predictions that QM does. That is not a valid basis for discussion. See above.

I am citing mainstream physics here.

Not as far as your claims about the MWI's predictions are concerned. See above.

in indeterministic QM, there is only 1 collapse for the entire context

Please cite a reference for this very surprising claim. My understanding of "collapse" for interpretations that use that concept (I'm not clear about exactly what interpretation you are referring to as "indeterministic QM", but apparently it uses the collapse concept) is that it occurs when decoherence occurs. Decoherence occurs in at least 3 places in the experiment under discussion: when the swap/no swap decision is made, and when photon 1 and photon 4 are measured. So "collapse" would occur in all those places as well, on any "collapse" interpretation.

You have skipped the branching of MWI

I have done no such thing. I have given the correct MWI criterion for branching: it happens when decoherence occurs. That is the same criterion for when "collapse" happens in interpretations that use that concept, including whatever it is you mean by "indeterministic QM".

after Photon 1 is measured, there is an H> world and a V> world under MWI

That is at the end of the experiment--the state I labeled $\ket{\Psi}_2$. In that state, yes, there are separate branches for the two photon 1 measurement results. That state is the result of applying the appropriate photon 1 (and photon 4, since $\ket{\Psi}_2$ also takes into account that measurement) unitary measurement operators to the state $\ket{\Psi}_1$.

If Photon 1 is H>, then by rule Photon 2 is H>.

In state $\ket{\Psi}_0$, yes, that would be the case. But no measurement is carried out on that state.

For MWI, it's no change if we add an H> filter when Photon 2 is already H>.

False. MWI makes the same predictions as QM. See above.

 

[PeterDonis]

In QM, no change. In MWI, big change.

For MWI, it's no change if we add an H> filter when Photon 2 is already H>.

As I said in my previous post, both of these claims are false; the MWI makes the same predictions as basic QM does.

However, you also say:

MWI evolves deterministically.

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: 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. [Edit: I was too pessimistic with this item; the basic math can in fact explain the results without any handwaving. See post #79 and follow-ups to it below.]

 

[PeterDonis]

MWI evolves deterministically.

Btw, another comment on this can be made as well: the "deterministic evolution", the Schrodinger Equation, is in Hilbert space, not ordinary spacetime. Relating evolution in Hilbert space to evolution in ordinary spacetime is by no means straightforward (in fact one might say that that relationship is at the core of the issues with QM interpretations). So one can't just assume that "deterministic evolution" requires everything to go "forward in time" in ordinary spacetime.

 

[PeterDonis]

I (the only one providing quotes and references)

You have not given any references that support your claims that the MWI makes different predictions from standard QM.

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. 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.

 

[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".

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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.