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I see your dilemma and acknowledge your points. Unfortunately I am not the person to bridge the published papers to your type of analysis. Without in any way taking away from your approach, I will simply point out your methodology/approach does not appear in the hundreds of papers I have read on the subject. Instead, the presentation is nearly identical in papers written in the 1999 to present time frame.PeterDonis said:Ok, I took a look. Here's the problem. From the 2002 paper, p. 5:
"A seemingly paradoxical situation arises — as suggested by Peres [4] — when Alice’s Bell-state analysis is delayed long after Bob’s measurements. This seems paradoxical, because Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured. Nevertheless, quantum mechanics predicts the same correlations."
a. My question is: how does QM predict the same correlations when the photons never coexist?
The way I did it when I did the math using the Schrodinger equation in a previous thread, there are no Bell states with photons 1 & 4. Ever. Anywhere. So that analysis, while it certainly supports the claim that QM predicts the same correlations, does not support the claim that it does so by means of Bell states with photons 1 & 4--because there are no such states anywhere in the analysis. (And you have already agreed that, if photons 1 & 4 never coexist, there is no time at which such a Bell state exists.)
b. The 2002 paper does not give any mathematical analysis to back up the claim I quoted above. So I have no way of knowing why they think that claim is true. Is it just because the experiments show the same correlations? Or is it because someone has actually done a mathematical analysis, not the same as the one I did, that does involve a Bell state with photons 1 & 4 even though they never coexist? I don't mean just writing down such a Bell state; I mean showing how such a Bell state can arise from the dynamics even though photons 1 & 4 never coexist.
c. The other paper, from 2012, does a very short mathematical operation to obtain such a Bell state: it takes the state in equation (2) and rearranges it, applying a time delay to photons 2 & 4 and algebraically refactoring, to obtain equation (3), which is an entangled superposition of the 4 possible "double biphoton" states for photons 1 & 4, and photons 2 & 3. Each photon 1 & 4 state in that superposition is a Bell State. (In actual experiments, as you have said, only 1 or at most 2 of these can actually be distinguished after all measurements are made. But that's not important for what we're discussing here.)
d. Perhaps the underlying assumption here is that standard NRQM, where you use the Schrodinger equation and you have a state of the system that evolves in time, is simply inapplicable to these types of experiments. But if that is the case, I would certainly like to see somebody justify that assumption and explain what should be put in its place.
a. The answer is that QM is not only quantum nonlocal (our agreed upon terminology), it is also quantum non-spatiotemporal. Now before anyone objects to my usage of the term as speculative or overreaching, let me show you how and why this has actually been evident for many decades. Further, it really shouldn't be a surprise to anyone.
It should be clear from my post #91 that there is actually a pattern at play in the 6 experiments I referenced there. Each is a variant of separation in spacetime and order of measurement. Specifically, please look at papers 1. and 4, which I am reposting.
- Basic Entanglement Swap with Bell State Measurement (photons 2 & 3) performed prior to observation of entanglement between (photons 1 & 4). See Zeilinger et al, etc.
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- Delayed Choice Entanglement Swap with Bell State Measurement (photons 2 & 3) performed subsequent to observation of entanglement between (photons 1 & 4). See Ma et al, etc.
So if your argument is that photon 1 cannot be placed in a Bell state (i.e. become an entangled component of a biphoton) after it ceases to exist, you're also gonna need to disavow all these referenced Delayed Choice experiments - as well as of all kinds of other Delayed Choice experiments as well. Whew, that's a lot of published material to deny! Check out this 28 page 2014 summary of "Delayed-choice gedanken experiments and their realizations" by top experimentalists Ma, Kofler and Zeilinger. The basic theme: The ordering of measurements (including delayed choice) has no affect on the quantum expectation value.
All of this goes back to Wheeler, circa 1978 and after, with speculations on whether choices made mid-experiment affect outcomes. The first application of delayed choice to entanglement swapping that I am aware of is "Delayed choice for entanglement swapping" (Peres, 1999). His analysis of Bell states looks almost identical to those I have presented in various posts. He shows how the initial Product state of 2 entangled pairs becomes of the 4 Bell states. He famously said: "In summary, there is nothing paradoxical in the experiments outlined above. However, one has to clearly understand quantum mechanics and to firmly believe in its correctness to see that there is no paradox."
b. I think post #98 in its entirety shows plenty of mathematical analysis, all saying the same thing. It is normal and natural for authors to reference other works, without an expectation that every individual formula presented need be justified. I scanned backwards in the literature and found a variety of interrelated papers in the 1990's by Gisin, Peres and stuff like this.
I have never seen you demand a fraction of what I have presented so far in any thread, much less a thread in Quantum Foundations. You have asked for citations, and received them - gold ones, by any standard. All I can say at this point is: Asked and answered. Again, if you or anyone have a counter-reference unrelated to a specific interpretation of QM, then that would be welcome.
c. Agreed.
d. I think any survey of the literature is going to show about the same as what I have shown already. Obviously, the type of explanation you seek is absent. You can deduce anything you like from that. I think it is odd that in all my searching, not a single author has expressed any concerns along the lines of yours (that some key assumption is "missing" from the literature). I checked many of the references in a variety of papers looking for something like that, but they pretty much all start from the 4 Bell states. I only went back to the 90's though.
Now obviously, almost every interpretation tackles experiments like those presented in a different manner. So I am not trying to make any statement about that. But the experimental results should be accepted without question. And the description (mathematical or otherwise) of the authors of these papers should be accepted as that of garden variety QM. This is stuff that has been out there for literally decades.
So I am hoping that we can return to the discussion of Measurement in QM/QFT. What is it? Is it physical? When does it occur? What triggers it? Where does it occur? And I certainly hope that the cited experiments co-authored by a Nobel prize winner (and others equally well-regarded) can be used for discussion purposes without further debate.