I have read this question:
Where @AcuriousMind says:
Free electrons do not "have" classical trajectories any more than bound ones do.
Now we do know that the event horizon is not an object, rather it is a boundary between two regions of spacetime. Now if quantum particles do not have classical trajectories, then what happens in the moment they "pass" the event horizon?
Naively thinking, in a "classical" view, the particles just "fly" straight through the boundary that we call event horizon, and there is a classically well defined moment or event when and how this happens. I can always separate two events, first, the classical trajectory shows the particle being outside, and the next event is inside, and these two can be distinguished. There is no superposition.
However, quantum particles do not have this kind of classical trajectories, and they do not have a size (spatial extent), they are point like. They are allowed to be in a superposition of being inside and outside the event horizon.
So now we have a quite different picture, a point particle, passing through a boundary (event horizon) without the notion of a classical trajectory (like flying straight through). This particle is supposed to be in a superposition of both inside and outside the horizon which could be impossible because nothing can leave from inside, that is, once the particle is in superposition of being inside and outside, it cannot be just outside anymore. It might be that the solution is that it smoothly changes from being in a superposition into being just inside. But the question remains, how is this possible?
Question:
- Do quantum particles have classical trajectories or are they in superposition when falling through the event horizon?
