Entangled particles in curved spacetime

[Heidi]

i do not know if the question about entangled particles has found mainstream answers;
Suppose that pairs of maximally entangled particles are shared by Bob and Alice in a time independant gravitational field. Bob measures the spin in the direction of far fixed stars. There is a direction in which Alice would get the same results. how to find it ? with a parallel transport? in the direction of the same fixed stars?

 

[Demystifier]

To answer this, entanglement is not important. You can consider just one particle prepared initially in the state $|+_z\rangle$, where $z$ denotes the $z$-direction with respect to some local tetrad defined at the place where the particle is prepared. The particle is then moved to some other position in spacetime and the goal is to find the state after moving the particle. For that purpose you must solve the wave equation (e.g. Dirac equation for spin 1/2) in curved spacetime. I would guess the final answer can be approximated with a result obtained by parallel transport along the semiclassical trajectory of the particle, but I'm not certain about that.

 

[anuttarasammyak]

Atom interferometer https://en.wikipedia.org/wiki/Atom_interferometer is used as sensor of gravity. Does it assure that gravity affects QM ? And do we know it quantitively ? Or is gravity effect on spin yet unknown ?

 

[Demystifier]

Or is gravity effect on spin yet unknown ?

It's not unknown. For example, we know the Dirac equation in curved spacetime.

 

[anuttarasammyak]

Thanks. Very Informative. https://en.wikipedia.org/wiki/Dirac_equation_in_curved_spacetime