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So I was trying to understand quantum entanglement and the example that was used to describe an entangled pair of particles was of an electron and positron after it is formed from a photon in pair production . So I was wondering why is it assumed that the particles produced from a photon in pair production have opposite spin?
If anyone is looking for the video that I saw https://www.youtube.com/watch?v=tafGL02EUOA Here is the link
The video is wrong on this point, at 4:47 he talks of a "photon spontaneoulsy creating an electron positron pair". The speaker is using a wrong example because there is no way a single photon can "decay" spontaneously , as mentioned in comments, due to energy and momentum conservation at the center of mass of the pair. The photon has no center of mass frame as its mass is zero.
The photon needs to interact with a field, with a virtual photon, in order to create a pair, and then all spin possibilities are open as it is a three body effect.
A correct example of entanglement is the $π^0$ decay into two photons, where the photons have to have opposite spins because the $π^0$ has spin $0$. Also the decay of the $Ψ$ resonance to a pair would be correct, it is spin 1 and decays to a pair.
