I Bell test where observers never were in a common light cone

[greypilgrim]

Hi.

I wonder if following thought experiment (which is most probably impossible to be put into practice) could have any implications concerning interpretations of QM.

Consider five parties A, B, C, D and E, lined up in that order and with no relevant relative motion. No pair of them have ever been in a common light cone (so we assume a universe that expanded quickly after the Big Bang). So they don't even know about each other, but they're all superb physicists with a huge optimism about the existence of the other parties.

At some point B and D decide to create many entangled photon pairs and send one photon of each pair to C, the other to A and E, respectively. Whenever C receives a photon from B and D, he performs a Bell measurement on them, entangling two photons on the way to A and E, respectively (entanglement swapping). A and E receive them and measure them in bases that are suitable for a Bell inequality test. At this point, B, C and D are in a common light cone, but A and E are still outside.

After enough measurements have been performed, A, C and E meet. C tells the others the outcomes of his Bell measurements. A and E throw everything out where their choices of measurement basis and C's results don't allow for a Bell inequality test (since they cannot perform the usual Bell rotation in entanglement swapping protocols after already having measured). Finally, they check if the remaining measurements violate a Bell inequality.

So what I'm basically trying to construct is an experiment where no past event could have an Einstein causal effect on the choice of measurement basis of both A and E. Would this perhaps rule out a local or causal form of superdeterminism?
If yes, maybe we should start sending out entangled photons into the universe, measure incoming photons or entangle them and hope for the best...

 

[Strilanc]

Would this perhaps rule out [...] superdeterminism?

I don't think so. The only thing you're adding to the typical argument is "No pair of them have ever been in a common light cone". But superdeterminism doesn't respect light cones in the sense you need. Superdeterminism gets to set any initial state it wants, including initial states with pre-existing correlations between distant parties.

 

[greypilgrim]

Yes, that's why I said a "local or (Einstein) causal" form of superdeterminism. So no event in the past could determine the experimenters choices with only local interactions. Sure there could still be superdeterminism, but it would require nonlocality, which is a usual conclusion of the violation of the Bell inequality (in a different sense though).

 

[Nugatory]

If I understand inflation properly (and I may not) it caused various regions to separate much sooner than they otherwise would have, but still leaves the big bang in the past light cone of every event in the universe. If so, there's no way of achieving the thought experiment in the original post and no way of decisively falsifying superdeterminism.

We can establish new upper bounds on the plausibility of superdeterminism... but most people find the existing upper bounds to be quite satisfactorily small.

 

[PeterDonis]

If I understand inflation properly (and I may not) it caused various regions to separate much sooner than they otherwise would have, but still leaves the big bang in the past light cone of every event in the universe.

By "big bang" I assume you mean the hot, dense, rapidly expanding state at the end of inflation, correct? If so, this "big bang" is not a point, it's a spacelike hypersurface, and only a portion of that hypersurface will be in the past light cone of any event to the future of it. So you can still set up the OP's scenario.

If by "big bang", you actually mean the initial singularity, prior to inflation, then (assuming that there even is one, which might well not be the case) that singularity itself is not part of spacetime (like any singularity), so even though there is a sense in which it could be said to be in the past light cone of every event in the universe (and this would be the case whether or not there is inflation), that doesn't prevent the OP's scenario from being set up.