This subject is a lot to get ones mind around and the curator of this video replies in detail to this question on the video thread. (in case you are having a similar thought after watching this video)
Commenter Barry had this question:
I still don’t understand the paradox. If the two photons in Alain Aspect’s apparatus are known to be in complementary states, but the specific value of that state is otherwise unknown, then measuring any one of them allows us to infer the complementary value of its twin on the other side. Where is the paradox?
The video curator Muon Ray has this response:
It is a paradox of special relativity, which is based on the idea of local causality, i.e. in a given event in space-time the distance between cause and effect must be separated by a time lapse which depends on the speed of light. In quantum entanglement a measurement, of spin say, of one particle allows you to know the spin of the other particle without disturbing it, such that the measurement of one particle is imposing an equal, but opposite, property, i.e. spin, on the other.
This is a paradox of special relativity because no events can affect another in a non-local way and must be mediated by signals. However the entangled particles, separated in space, are not separated in time. They both share a common time, however mathematically the time of one particle is real and the other is complex (i.e.using complex or imaginary numbers). So in unifying quantum mechanics with special relativity we get scenarios where, instead of the states being predetermined, one state measures time in a negative frame relative to the other and so cancel out.
This is why, in drawing Feynman diagrams in space-time, it appears that antimatter particles move backwards in time relative to the matter particles in pair production events for example. The particles do not travel backwards in time, this is just a consequence of unifying a local theory, special relativity, and a non-local theory, quantum mechanics. The paradox lies within this, as why should the local nature vanish? we know “how” to interpret it but we cannot really know the “why”.
We hope you like the video and even if it is really out there, still got some value out of it.