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I am trying to make sense of the Delayed Choice Entanglement Swapping:

In the entanglement swapping procedure, two pairs of entangled photons are produced, and one photon from each pair is sent to Victor. The two other photons from each pair are sent to Alice and Bob, respectively. If Victor projects his two photons onto an entangled state, Alice's and Bob's photons are entangled although they have never interacted or shared any common past.

To me this seems to mean that no temporal paradoxes can exist. The way I see it, this experiment uses 2 types of systems: one in which time evolves normally(our reality) and one which has no time(photons are locked/frozen in time, the spacetime distance is 0 for them).

In my understanding the experiment tries to introduce a time paradox by altering in the future(the delayed aspect of the experiment) a condition of the past(the entanglement). However because the photons experience no time, they make no distinction between future, present or past and so when Victor introduces a new entanglement(between the pairs of photons he receives) the entanglement is also measurable in the past(as all 4 photons are entangled).

If I'm correct this would prove there can be no time paradoxes, future action(from our perspective) is visible in the past(from our perspective) because for the photons future and past are the same.

If time paradoxes cannot exist(at least not for photons) this would be a very powerful finding with some very interesting applications as it would violate some assumptions that have been made so far in physics.

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The absence of such paradoxes in quantum mechanics simply comes from the fact that solutions to the Schrodinger equation exist and are unique. For an example of such an existence and uniqueness theorem, see Yajima, "Existence of solutions for Schrödinger evolution equations," Comm. Math. Phys. Volume 110, Number 3 (1987), 415-426. https://projecteuclid.org/euclid.cmp/1104159313

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