A Post-Selection: Pre-existing Correlations or Action At A Distance?

[DrChinese]

On @DrChinese's interpretation, both of these mathematical facts have physical meaning. Fact (1) physically describes the state of the 4-photon system at the start of each individual run. He is not using an ensemble interpretation, so to him the math describes individual runs, not ensembles of runs. On his interpretation, fact (2) physically describes the state of the 4-photon system for those runs in which the BSM gives an "event ready" signal. He doesn't care that this is a "subensemble", because he's not using an ensemble interpretation: on his interpretation, the BSM is a physical operation that is performed on the 4-photon state that changes it from the fact (1) state that was originally prepared, to some other state. Which other state depends on the outcome of the BSM, and the way the experiment is set up, only one BSM outcome gives an "event ready" signal, and on the runs where that signal is given, the fact (2) state is the one that the BSM produces.

Very well said.

What is interesting is that the experimental papers only talk about cases where a BSM occurs. And when I say BSM, of course what I really mean is: The [2] and [3] photons are NOT distinguishable, and then looking that corresponding Bell States (Psi+, Psi- etc.) ARE distinguishable. They don't really think in terms of subensembles, as they are looking for [2] and [3] photons are being indistinguishable as their universe. Much like with PDC itself: only 1 photon in maybe 10 million down converts. The photons that don't are not discussed.

If the [2] and [3] photons are indistinguishable, they will cause a swap on [1] and [4]. Although of course there are 4 different Bell States (for 2 photons), and there is approximately equal probability for each.

 

[Morbert]

The intuitive reasoning of the model is still the same reasoning that we already know cannot account for violations of the Bell inequalities.

My use of the model is absolutely fine and 100% appropriate in this thread, because I am discussing ways in which the intuitive reasoning of the model can be recovered in a quantum context. I am not (as you seem to think) presenting the model as accounting for violation of Bell inequalities observed in experiment.

There are interpretations of QM that are consistent with experiment, and understand measurements like the BSM as selecting subensembles that exhibit some property, without needing to posit some superluminal creation of this property post-BSM, in the same way that, if we measure one of Bertleman's socks, we do not need to posit a superliminal creation of the other sock to accommodate our inferences.

This does not mean, however, that QM is reducible to a Bertleman sock model of variables.

 

[Nullstein]

1. Here is the notation for the BSM group/subset/ensemble/whatever, as originally supplied by @vanhees71 (let's stick with this since we should use this preferred format):

We have also established that the final quantum state is a Product State of 2 entangled pairs: $$\hat{\rho}'=\hat{\rho}_{23} \otimes \hat{\rho}_{14}.$$

You haven't established anything, you just claim it. I have established that your claim is incorrect by citing standard references, where the exact opposite is proved from the basic interpretation-independent axioms of QM.

2. The Zeilinger team says: "We confirm successful entanglement swapping by testing the entanglement of the previously uncorrelated photons 1 and 4." They were previously uncorrelated, and later they were correlated. Is there something ambiguous in the phrase "previously uncorrelated" that I don't understand?

No, but you are ignoring the fact that Zeilinger et al. make a much weaker statement than you do. The statement is that one can obtain an entangled subensemble by conditioning on the measurement result. Your additional claim is that something physical has happened to the 1&4 pair. There is no evidence for it and Zeilinger et al. don't imply this. In fact, Zeilinger has the exact opposite viewpoint.

3. No, the math of QM says: After a BSM, ALL successfully swapped [1 & 4] pairs are entangled and NONE of the corresponding [1 & 2] pairs are entangled. You can deduce that from the notation.

No, it doesn't. The math says that there is no entanglement in the 1&4 system even after measurement. The math says that there are entangled subensembles. Whether the entangledment arises due to spooky action or due to post-selection is a matter of interpretation and both viewpoints are viable.

 

[PeterDonis]

I have established that your claim is incorrect by citing standard references

No, you haven't. You have simply repeatedly established that you are using a different interpretation from @DrChinese.

 

[PeterDonis]

Thread closed.