I am not sure that paper knows it, but it is essentially showing that many worlds is correct-- that the wavefunction never collapses:
> the implications on conditional probabilities
hold for other measurements throughout the entire
spacetime, present and past. [emphasis theirs]
And the math in the paper which supports that statement works by keeping all the superpositions around and allowing us to project to them at any time. This is the picture of many worlds! Copenhagen says the opposite: When you make a measurement, the unmeasured superpositions go away. The paper confirms, that's nonsense! If you shade any region of the spacetime diagram where the superposition is gone ("collapsed"), you'll be wrong!
The author says: "Note: in this work, we will not make any reference to why this (apparent) collapse occurs. Not only is this a much harder issue, it is simply not relevant to discussion we will present."
Also: "It is important to note that arriving at our conclusions did not require introducing new physics. We only relied on elementary quantum mechanics: not on novel ‘backwards time’ concepts, nor on any particular interpretation: we only used the Born rule ‘as is’. [...] With the remarks and intuition presented here, there really is no mystery whatsoever in any of the discussed experiments."
This experiment is not more mysterious than the rest of QM, but of course if you find the whole theory unsatisfactory you won't be satistified with this explanation either.
That language is why I think the authors aren't aware that they are advocating many worlds.
Also, this is a fantastic example of the "don't ask questions" attitude I think is so shameful. If they had bothered to take the small step of asking, they'd have come to a clear, evidence-based refutation of Copenhagen! There are regions of spacetime after the measurement, where the wavefunction is not collapsed, which the authors explicitly point to. That's in direct contradiction to the premise of Copenhagen.
The point is that the order of the measurements is irrelevant: QM predicts the same probability distribution of outcomes. So the problem can be solved using either order and the response is the same. I am not sure what premise of Copenhagen is being contradicted.
Edit: solving the problem in the "natural" order would give the same probabilities but is much more difficult to handle. You need to get a probabilistic outcome for the position of each single photon on the screen, which "collapses" the state and determines the wave function of the other photon. At this point, the first photon has been detected somewhere but it can only be labeled as "interference" or "not interference" later after the detection of the second photon. The probability of being labeled as "interference" or "not interference" does depend on the position (because the collapsed wave function depends on what the outcome of the previous measurement was). When everything is said and done, looking at the subset of events labeled "interference" there is an interference pattern and looking at the subset of events labeled "not interference" there is not an interference pattern. There is no mystery.
> I am not sure what premise of Copenhagen is being contradicted.
Before measurement, the state of the particle system is Σ α_i|i>. Copenhagen says, "after you measure the system, all but one of the α_i go to zero". The authors don't do that, and in fact say that you can't. Unless I am misunderstanding something, they keep all the α_i around at all times and project the measurement for each particle separately, regardless of whether it has been (or will be) measured somewhere else. There is nothing philosophically or physically wrong with this, as they point out, but it is different than what Copenhagen says you should do when you measure something.
And if you look at what it means (which they refuse to do), you'll see that after Alice makes her measurement, Bob's quantum state is still explainable in terms of a superposition. When is the measurement (joint or individual) "finished"? Answer, per the authors: Never. The superposition permeates spacetime. That's how we escape the need for a causal connection between Alice and Bob's measurements, and, naturally, that's how many worlds does it.
(And if we take it further and ask, when Bob makes his measurement, "What is the state of Alice's particles?" we'll see that she is in a superposition of being entangled with each of the superpositions of the particle, which remains in superposition before, throughout, and after our ~measurement of~ entanglement with it).
Please see what I added to my previous comment. You could in principle do it in the "right" order and you would get the same result. They routinely solve quantum optics problems using standard QM and the experimental results match the predictions.
What he shows in that paper is that the order of the measurments is irrelevant [1]. So he does solve the problem in the reverse order where it can be done easily writing a few quantum states [2].
Note that QM is not about causal connections, is about correlation. Once a pair is correlated, the correlation may appear when measurements are done. But it's not that observing one outcome here and now "causes" a particular outcome there and later (or before). One doesn't need to keep superpositions to think it "correlation" terms (instead of "causal" terms).
[1] Using the projection postulate in the derivation: "Say we have indeed measured on B and got OB = bJ . The state then collapses onto ..." He concludes: "None of this looks very surprising, but we want to stress that the total probability to find OA = aI and OB = bJ does not depend on the place or time at which the measurements occur."
[2] He also uses the projection postulate here in the usual way: "So the experimental outcome (encoded in the combined measurement outcomes) is bound to be the same even if we would measure the idler photon earlier, i.e. before the signal photon by shortening the optical path length of the downwards configuration. Then, if the idler is detected at D4 for example, the above state ‘collapses’ onto ..."
Yep, I'm with you that we don't need to bring causality into it.
And yes, you don't need to ask "when does the wavefunction collapse" to manipulate joint probabilities of measurements that happen at disparate locations and times. In fact, that's my objection: If you do ask, you find that there is no consistent answer! (And I suggest it's because wavefunction collapse is not a thing the universe does).
Re: "interference tagging"-- do you have a link to some material? (I'd love to understand something specific before commenting).
EDIT: Also, I didn't see Appendix B at first-- The authors do understand and even advocate the Everettian view! Though I still don't quite understand/agree with their earlier timidity about finding and interpreting conflicts with Copenhagen.
> If you do ask, you find that there is no consistent answer!
I'm not sure what's the problem. Why do have to "ask" if the answer doesn't really matter? What answer more consistent than "it doesn't really matter" would you like? Anyway (standard) QM is a non-relativistic theory, QFT may be more satisfactory from that point of view.
Re: "interference tagging" - what I mean is that first you detect the photons and later check if they "did happen" to go through two slits (interference appears) or one slit (no interference). But the interference pattern is not visible for a single photon and at that point the individual events are still a superposition of both possibilities (so for the events at a certain position part of them will be in the end identified as coming trough one slit and some of them from both). Only after the second measurement is done you know how to group the previoulsy recorded events to see the interference. It's not that the later measurement causes interference to appear. Or at least it doesn't affect at all where the photons were detected, it just lets you know how to group the existing events to make it apparent (selecting only those where, once the full mesurement on the pair has been done, the path taken remains uncertain).
If all the events are taken together there is no interference pattern. But when they are grouped according to where the second photon is detected in two cases there is still no interference but in the other cases complementary interference patterns appear.
> Why do have to "ask" if the answer doesn't really matter?
You tell me; Copenhagen is the one that says collapse exists. It sounds like maybe we are on the same page that collapse isn't necessary to explain quantum mechanical observations? In that case, we are both Everettians :).
To explain quantum mechanical observations you need "collapse" (i.e. the projection postulate: immediately after a measurement the state of the quantum system is the projection on the corresponding eigenspace of the operator). I don't know what do you gain by saying that it's not "real" and that it's just "as if".
Because if we say that some of those alpha_i physically go to zero at any point (e.g., "after"), our predictions are wrong, in agreement with the paper. We have to account for the fact that those alpha_i|i> are still nonzero and "existing", and that our projection onto them is only zero for the time being. A different choice in EPR or a quantum eraser experiment may bring our projection onto those states back out of orthogonality-- or maybe not, if we never make those choices. But if we believe we have the physical freedom to manipulate our experiments, we can't get away with saying those extra "universes" (basis states) physically disappear.
In some cases it is a safe approximation to ignore those extra states for the remainder of our experiment/calculations, but with a small change to the experiment we can make that a bad approximation.
I am afraid that you have not understood the paper.
a) You do the measurement first on the "screen" side (and project the quantum state of the pair of photons according to the measurement, the "extra universes" disappear). You do then the measurements on the "idler" side (and project again the quantum state according to standard QM).
b) You modify slighly the setup to reverse the order of the measurements. You do the measurement first on the "idler" side (and project the quantum state of the pair of photons according to the measurement, the "extra universes" disappear). You do then the measurements on the "screen" side (and project again the quantum state according to standard QM).
QM predicts that the outcomes in the original experiment (a) and the "reversed" experiment (b) are the same. And those predictions are verified empirically.
