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I found this PBS video regarding the delayed choice / quantum eraser experiment, which, like all the others I've seen, states that the interference pattern generated by the photons that pass through a quantum eraser apparatus depends upon whether the individual photons are "marked" with the "which-way" path information that identifies which slit they passed through, even though this marking takes place after the "top" photon (the one that does not go through the delayed choice portion of the apparatus) should have already hit the top detector.

My question is, if I fired a single photon through such an apparatus, which is then split into two entangled "twins", does the "top" photon give up its energy to the top detector the moment it hits the detector? Has this been confirmed experimentally?

EDIT: I've found another thread (link here) which seems to address this question partially, and based on my read, it seems that the top photon gives up its energy the moment it strikes the top detector. Further, it seems that the position of the top photon is determined by this initial "hit".

Why is it then that this experiment is touted as an example undermining causality? That doesn't follow at all, since the position of the top photon is determined by its own flight, and is completely independent of the flight of the bottom photon.

Isn't it far more reasonable to say that we simply get information about the flight of the top photon from the flight of the bottom photon? Rather than saying that the position of the top photon is determined by events related to the bottom photon (which cannot be the case, based on my read of the experiment), the bottom photon's path is determined by whether or not the top photon was subject to interference along its flight.

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Part of your confusion may come from the way you've formulated the question, e.g. the timing of energy exchange.

The strangeness of the DCQE largely vanishes if you instead ask "Do I have MORE or LESS information about the system at any given time?" Which should make clear that at no point is retrocausality necessary to explain observations. Causality is well preserved throughout DCQE, despite popular articles and documentaries playing up the non-intuitive nature of it at first glance.

Stripped down example that should illustrate this:

Remember that no interference pattern is ever observed at $D_0$ (assuming we're using the notation from the Wiki article citing Kim et al). The interference can be recovered by counting a subset of $D_0$ hits correlated with their sister hits at either $D_1$ or $D_2$.

If you observe a hit a (x,y) on $D_0$, this is perfectly compatible with a future hit at either $D_1$ (assuming $D_1$ interference pattern has a node at (x,y), or $D_3$, or $D_4$ (the which-way detectors which show no interference fringes). If we assume perfect interference, the only detector NOT compatible with (x,y) would be $D_2$... but of course given a lack of perfection, there remains a small probability of $D_2$ recording a correlated hit with (x,y) as well.

Given the above, it should be clear that the initial detection at $D_0$ serves to reduce the probability of detecting an entangled pair at a subset of the downrange detectors in a very forward-causal way. Going further, the choice to detect which-way path information on its entangled partner after the $D_0$ photon has been recorded is then just a further down-selection to either $D_1$ (no path info) or $D_3$/$D_4$ (path info), with $D_3$ or $D_4$ of course being random.

Just to drive it home: The idler photon deposits its energy as you'd expect at the $D_0$ detector, at the time of its registration while its sister photon is still "en route." The limited info you can gather from $D_0$ (x,y) photon position serves to update probabilities for which detectors may light up depending on what choice you make, whether to gather which-way or no which-way info, for its sister photon. There is no retrocausality, and therefore no deviations from standard physics.

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