I'm somewhat curious about how the Pauli Exclusion Principle functions when relativistic time becomes a significant factor. Just to clear things up, my (possibly poor) understanding goes like this.
The PEP basically states that no two fermions can be in the same state at the same time.
Relativity states that in certain conditions, time is no longer really objective but can be quite subjective- passing at different rates depending on who is the observer, etc.
I'm curious, therefore, how this notion of "time" relates to the "time" required by PEP. For example, would it be possible from the perspective of one observer that two fermions could be in the same state at the same time from their perspective, but not from another perspective? And if the fermions in question are distinct particles, then logically they should be experiencing time at a different rate. So what would occur if fermion A tries to occupy the same state as fermion B in a position in time that from A's perspective is not the same position in time that B occupied it, but from B's perspective, it's still that position in time?
In short, the PEP seems to require that there's some sort of objective timekeeper that rules who can be in what states and when, but relativity seems to indicate that no such thing exists. How are these two ideas of time reconciled?