What If Instantaneous Relative Velocity Is Real In Special Relativity: Relative Simultaneity As Indexed Relation

Abstract

It is a standard view in Special Relativity that simultaneity relations are ternary relations that hold for three items: x is simultaneous with y relative to z. Noting the connection between clock synchrony and the one-way speed of light, I argue that if it is indeed a physical fact that the one-way speed of light has a certain value, then simultaneity relations in Special Relativity are about local facts that obtain in finite spatiotemporal regions, and so it is natural and plausible to take simultaneity relations to be quaternary relations among four items, i.e., x is simultaneous with y relative to z at p, where p is a spatiotemporal point in Minkowski spacetime. This has the added benefit of defusing Hanoch Ben-Yami (2006)’s argument that Standard Synchrony yields inconsistent results when applied to non-inertial observers.