Uniqueness of Simultaneity

Giulini, Domenico (2000) Uniqueness of Simultaneity.

Abstract

I invesigate the question of existence and uniqueness of simultaneity
structures in spacetimes whose automorphism group, Aut, is either
the inhomogeneous proper orthochronous Galilei or Lorentz group.
An absolute simultaneity structure is defined as Aut-invariant
equivalence relation whose equivalence classes are acausal sets.
It is unique for Galilean and non-existent for Lorentzian spacetimes.
Simultaneity relative to some additional structure X on spacetime is
defined analogously, where Aut is now replaced with the stabilizer
subgroup of X in Aut. It turns out that Einsteinian simultaneity is unique
if X is an inertial frame (foliation by timelike straight lines).
Finally I discuss the relation to work of others.