Sequentiality Restrictions in Special Relativity

Abstract

Observers in different inertial frames can see a set of spacelike separated events as occurring in different orders. Various restrictions are studied on the possible orderings of events that can be observed. In 1+1-dimensional spacetime {(1 2 3), (2 3 1), (3 1 2)} is a disallowed set of permutations. In 3+1-dimensional spacetime, any four different permutations on the ordering of n events can be seen by four different observers, and there is a set of four events such that any of the 4!=24 possible orderings can be observed in some inertial reference frame. A more complicated problem is that of five observers and five events, where of the 7,940,751 choices of five distinct elements from S_5 (containing the identity), all but at most one set of permutations can be realized, and it is shown that this remaining case is impossible. For six events and five observers, it is shown that there are at least 7970 cases that are unrealizable, of which at least 294 do not come from the forbidden configuration of five events.