Simultaneity Relations Relative to Multiple Observers in Special Relativity

Abstract

It is a standard practice in special relativity to define a simultaneity relation relative to an inertial observer or frame of reference. This practice is based on two assumptions: (1) A simultaneity relation relative to an inertial observer should be defined from the worldline of the observer (and the structural features of Minkowski spacetime); and (2) a simultaneity relation of special relativity should be defined relative to a single inertial observer, not relative to multiple observers as such. I challenge these two assumptions by presenting simultaneity relations defined relative to multiple inertial observers. I show that they are operationally definable and that they are also explicitly definable from the causal connectibility relation and the worldlines of the observers. They are thus legitimate simultaneity relations, and so the relative simultaneity relation of special relativity is not uniquely definable from the causal connectibility relation.