The Collapse of Collapse: the Indistinguishability Conflict, a Loophole for Superluminal Signaling

When Alice makes indistinguishable measurements on dual streams of identical, but independent photons, she expects a particular statistical outcome, thirds - in the heads/tails basis, 1/3 |HH>, 1/3 |H,T>, 1/3 |TT>. Had she made distinguishable measurements, she would have expected fourths - 1/4 |HH>, 1/4 |HT>, 1/4 |TH>, 1/4 |TT>.

Now let Alice receive dual streams of entangled photons. She receives photons 1 & 3, the cross pair, while Bob receives 2 & 4, the companion pair. Photon 1 is entangled with photon 2, and photon 3 is entangled with photon 4 – let the EPR pairs be independent.

Entanglement is a unique feature of quantum mechanics, undiminished by distance, unattenuated by interviewing material, and freakishly specific – entanglement has no effect on nearby particles.

What if Alice attempts indistinguishable measurements, but Bob, spacelike separated, chooses distinguishable measurements? Cannot his companion pair be used to distinguish her cross pair? And if they can be so used, then her attempt at local indistinguishable measurements will be thwarted by nonlocal choices – the very definition of superluminal signaling.

If they cannot be so used, then Alice will observe thirds and Bob will observe fourths, but now there is no way to preserve the entanglement correlations – at best 92% of the EPR pairs can still show correlations, perhaps as low as 58%.

Collapse fairs no better. Given a single EPR pair, Alice is free to claim that it is her measurement, over here, that instantly collapses Bob’s particle, over there, from a mixed state to a pure state, prior to his measurement, while Bob is free to claim that it is his measurement, over here, that instantly collapses Alice’s particle, over there, from a mixed state to a pure state, prior to her measurement. Not only does this ambiguous collapse paradigm violate relativity, but the causal stories are incompatible with each other. We put up with this causal ambiguity because, for a single EPR pair, the predicted statistical results are identical.

But given dual EPR pairs, the ambiguous collapse paradigm no longer yields the same predictions – indistinguishability is incompatible with entanglement and collapse.

This talk explores the indistinguishability conflict, its potential theoretical resolutions and the possibilities for testing them.