I wanted to re-open the question of quantum measurements across event horizons.

Question

I wanted to re-open the question of quantum measurements across event horizons. If I set up two slits or more generally a diffraction grating which crosses a black hole event horizon, and I shoot a stream of appropriate particles at the slits/grating, will I observe an interference pattern on a detector placed on the far side of the slit/grating and also crossing the event horizon?

It seems to me that the previous discussion was focused on the perspective of the observer or observers within or without the horizon, not the particles themselves. A double slit experiment does not involve EPR-like entanglements of multiple particles, if I understand correctly it works through the adding up of detections of "individual photons" (whatever that means; otherwise we can posit electrons or buckyballs which certainly seem to have some kind of particulate behavior at least sometimes). Very naively, if a photon or other particle is fired at a screen with a double slit, in which one slit is just outside and the other just inside the event horizon, it seems to me that there is still a potential problem regarding whether interference will occur. The wave function itself is not a mass-energy construct, hence does not obviously respond to the structure of spacetime. Given that the nonlocal aspects of QM leading to interference fringes are a problem even in flat spacetime, I don't see how they become any less difficult in curved spacetime. Is there a trivial objection to proposing that interference fringes would build up with multiple particles, just as in any double slit experiment, indicating that QM waves, whatever those are as well, are immune to event horizons? Clearly only that part of the detector screen lying outside the horizon would be accessible to the observer. Note that spin is not an issue in this experimental design, so some of the papers I have read which deal with the interaction between particles with spin with black holes (especially rotating ones) would not seem to be relevant in this design.

Explanation / Answer

When a diffraction grating is crossing an event horizon, it can't stay put. It has to keep falling to keep from flying apart. If you hold the part that is outside the horizon so that it isn't falling inward, the part that is past the horizon gets torn off and falls inside. If you shoot an electron past the diffraction grating (and apply an electric field to keep the electron from falling into the black hole) you will see diffraction only from the slits outside the black hole. The part of the electronic wavefunction which passes the horizon will not interfere with the outside part for any reasonable macroscopic size black hole, but will fall inward.

This is a near horizon phenomenon, and near the horizon, space is flat. So the effect doesn't require a black hole--- the exact same thing happens when you accelerate fast in Minkowski space. If you hold a large diffraction grating past your acceleration Rindler horizon, the apparent horizon you see when you accelerate, it will get torn off just the same.

In order for interference to happen, the two paths must be indistinguishable in a quantum sense, so that you can't know which one happened. If you have a particle with some miniscule internal consciousness of any sort, and you want it to diffract, you need to cool it down to absolute zero, shutting off any internal computation for a while. Then you do the diffraction, then you heat it back up again so that it turns back on. The diffraction is always necessarily happening on something unaware. If you isolate a person in a chamber, and you try to get the chamber to diffract, you will need a perfect isolation system to prevent any leaking of information about the internal quantum state to the exterior of the chamber. Then, in theory, you can get two paths of the chamber to diffract, but the person inside can't have any idea which path was taken, and wouldn't even know anything about the exterior world at all.

The issues for the diffraction grating which falls through the black hole are fully adressed by the viewpoints of the observer that falls along with it, and the one that stays outside, and are covered by this earlier question: Double slit experiment near event horizon

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