Is space-time quantised? [duplicate]

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?)

• Possible duplicates: physics.stackexchange.com/q/9720/2451 and links therein. – Qmechanic Feb 7 '18 at 21:04
• These argument are essential the same ones made by Zeno in the fifth century BC. The fundamental issue is with language. The words and thought patterns suitable for day to day life are inadequate to address these issues, but you can develop a precise language for talking about them and the result is mathematical subject 'real analysis'. Space-time might or might not be quantized, but you have to move a bit forward in time to find a starting place. – dmckee --- ex-moderator kitten Feb 7 '18 at 21:52
• If the real number line is continuous, I can define the "largest number less than 4" and the "smallest number greater than 4" and then there have to be infinitely many points in between these --- all of which have to be in some in-between state, neither less than 4 nor greater than 4. Do you see any problem with this reasoning? – WillO Feb 7 '18 at 21:56
• Can you not apply pretty much the same reasoning to any quantum event, in that once an event occurs it must go to completion? This may just be the same question you are asking, e.g. a transition between two energy levels of an atom can't be stopped, once begun, AFAIK. – user184116 Feb 7 '18 at 22:16