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i was reading and a question popped into my head and i could not find the answer anywhere
if photon destruction is instantaneous doesn't it mean that space-time is quantised?
here is my problem:
if space-time is continues and i can define the separate events of ""last point where a photon exists" and "the first point where said photon doesn't exist" there are infinitely many point in between all of witch have to be in some "in between" state and so the destruction of a photon is not instantaneous.
on the other hand:
if a photon is absorbed instantaneously then when an electron is absorbing a photon it "gets" the photons momentum and starts to move instantaneously witch means that if space-time is continues i can define the event of "last point that the electron had no velocity" and the event of "the first point that the electron had some velocity due to the absorption of the photon" and the same problem arises as before.
it all builds up on that "last point" "first point" argument is it valid?
i don't expect a simple answer but if someone can help me start to tackle the question that will be great
just to clarify i am not asking if space-time is quantised but if instantaneous events require a non continues function and there are instantaneous events like the the destruction of a photon how can space-time be continues (the electron does not experience a continues change in velocity?)