I've been considering a theoretical setup for a quantum experiment where 2 particles are prepared with entangled spin. They are then moved far away from one another where particle B is next to Bob who has set up a double slit experimental setup where the slit it goes through is determined by its spin.
While I know that what happens next shouldn't affect the result of the experiment, I do not understand how that is the case beyond "reality just must be consistent". (Also assume that every time an interference pattern is measured the entire setup is recreated for each particle in the final distribution)
Say I am in a reference frame in which Alice measures particle A to be spin up and then Bob preforms the double slit experiment with particle B. Now if Alice learns that Bob did not measure an interference pattern, that seems to be the expected scenario since Alice would know which slit each of Bobs particles went through and would "collapse" the wave function.
However if I am in a reference frame in which Bob preforms the double slit experiment before Alice measures her particle, then shouldn't he see an interference pattern? From his point of view, isn't the particle in a superposition of states, or does interference just not work with entanglement in that way?
Thanks for any clarification you can provide.