The Pauli Exclusion Principle says, roughly, that no two atoms are allowed to occupy the same energy states at the same time. The result of this is apparently that every atom must change its energy state in response to every other atom so as to obey this rule. The well known physicist Brian Cox likes to mention this, such as in his book The Quantum Universe: Everything that Can Happen Does Happen, to say that this implies that the energy states of atoms billions of light years away from one another must change their energy states simultaneously in obedience of this rule. In his book, he assures the reader that this does not violate the theories of relativity because information can not be communicated by making use of this and so temporal paradox situations are avoided.
However, surely this is not good enough because relativity tells us that there is no universal time, each particle has its own time. So if the Pauli Exclusion Principle really does say what Brian Cox says, should that not imply that the energy states of atoms must also retroactively be changed at all time points so that the rule applies at some arbitrarily chosen time? In addition to this, which frame of reference is supposed to be the preferred one which every atom alters its energy state with respect to?