PeterDonis said:
What definition of "locality" are you using?
You are aware, aren't you, that a very common definition of "locality" in the literature in this area is "does not violate the Bell inequalities"?
Yes I understand this. I am using John Bell's definition of locality. It can be shown that photons 1 & 2 violate locality and photons 3 & 4 violate locality and that photons 1 & 4 violate locality, but the violation of locality of 1 & 4 is different in that the violation does not imply a direct non-local influence between photons 1 & 4 in all cases. It is this difference that is important for interpretations and is what the paper is pointing out. Without recognizing this distinction, cause and effect interpretations could be ruled out by mistake. I am still not certain that is what Dr. Chinese is doing, but I want to make sure that this forum is being careful on this. We don't want to mislead anyone, correct? That is why I am so persistent on trying to understand the entanglement swapping experiment and is why I went through the process of writing a program to prove to myself that cause and effect is not ruled out by this experiment.
PeterDonis said:
Physics is not word games. You can of course define "locality" however you want for your own usage, but if you want me to adopt your definition, particularly if it's a highly non-standard one, you're going to have to first meet the very heavy burden of convincing me that I should care.
I am using John Bell's definition of locality. I don't want to play word games either.
PeterDonis said:
If you took the photons at the BSM test and measured their polarizations after that test was done, yes, you would find they were correlated.
This statement does not make sense to me. You can measure the polarization of photons 1 & 4 after the BSM test, but not 2 & 3, because photons 2 & 3 are destroyed in the BSM test measurement.
PeterDonis said:
But you would have to do the same post-selection on the BSM test results to see the correlations, that you do on the Alice and Bob measurement results to see the correlations.
Agree
PeterDonis said:
So by your argument, if the Alice and Bob correlations are artifacts of post-selection, normal EPR correlations that violate the Bell inequalities must be artifacts of post-selection too. Is that your argument?
No this is not an argument I am making. The argument I am making is that in the entanglement swapping experiment, the only results of measuring photons 1 & 4 that we look at are when the BSM test shows that photons 2 & 3 are entangled and that this is post selecting the answer to the question of "When does it look like photons 1 and 4 are entangled?". And in contrast to the EPR experiment, with the entanglement swapping experiment, specifically for the case where the BSM test is done in the absolute future of measuring photons 1 & 4, you can not say that being entangled (having a correlation that violates the Bell inequality) implies a direct non-local influence between photons 1 & 4.
A cause and effect process must be shown to be in principle reversible. If I can show that the entanglement swapping experiment is in principle reversible then it is consistent with a cause and effect explanation.
Lets do the entanglement swapping experiment in reverse as a thought experiment for the case where the BSM test is done in the absolute future of measuring photons 1 & 4.
1. Reading results of experiment show a bell violation of photons 1 & 4 when measurement angles differ.
2. BSM test on photons 2 & 3 show that photons 2 and 3 are identical in state.
3. Measurement of photon 1 changes the state of photon 2.
4. Measurement of photon 4 changes the state of photon 3.
5. Photons 1 and 2 meet and are identical in state.
6. Photons 3 and 4 meet and are identical in state.
The point of the paper and the point I am trying to show is that at no time did photon 1 & 4 influence each other in this sequence of events. Cause and effect is preserved.
Contrast this with the case where the BSM test is done in the absolute past of measuring photons 1 & 4 (again doing the events in reverse order):
First try to do this without 1 and 4 being allowed to influence each other directly:
1. Reading results of experiment show a bell violation of photons 1 & 4 when measurement angles differ.
2. Measurement at photon 1 changes the state of photon 2.
3. Measurement at photon 4 changes the state of photon 3.
4. BSM test done between photons 2 & 3 shows that photons 2 and 3 are identical in state.
5. At this point you are stuck, if photons 2 & 3 are the same, that means photons 1 & 4 must have started out the same in this reverse experiment which can't be true unless their measurement angles are the same.
Now do this case but allow an influence between 1 and 4 and you are ok:
1. Reading results of experiment show a bell violation of photons 1 & 4 when measurement angles differ.
2. Measuring photon 1 changes the state of photon 4.
3. Photon 4 is measured.
4. BSM test done between photons 2 & 3 shows that 2 and 3 are identical in state (no conflict with anything prior) and establishes a causal influence between photons 1 and 2 and establishes a causal influence between photons 3 & 4 and drops the causal influence between 1 & 4. In establishing the causal influence it implies 1 & 2 are now in the same state and 3 & 4 are now in the same state.
5. Photons 1 and 2 meet and are identical in state.
6. Photons 3 and 4 meet and are identical in state.
This thought exercise demonstrates that the entanglement swapping experiment is consistent with a cause and effect interpretation.