The simultaneity of two events should be fixed
in such a way
that the natural laws become as simple as possible.
Henri Poincaré, 1898
In physics, a collection of ‘observers’ that agree on their clock readings is called a ‘reference frame’. Such a frame is usefully pictured as a lattice that is populated by a continuum of observers, each occupying a fixed point on the lattice and holding their own clock, who each record the positions and times of events only in their ‘very close’ vicinity. Local clock indications are factual, since they consist in spatial coincidences of material objects, like the coincidence of a pointer with a mark on a dial. This kind of events allow immediate observation.
In contrast, simultaneity cannot be perceived: local observers do not have immediate empirical access to distant simultaneity, as it involves a comparison between distant locations. Since local observers can only make local observations in a direct way, these observers need some rule (often called convention in this context) that tells how to establish simultaneity on the basis of facts that are observable. This gives empirical content to statements about simultaneity.
Such rules can be made in different ways, which gives rise to different but equivalent descriptions. Some choices may result in a simpler rule or lead to simpler laws. Physical experiments show that, in inertial systems, there is neither a preferred position or direction. Spacetime coordinates referring to physical events in inertial frames should therefore reflect these fundamental symmetries of the physical laws, i.e., the homogeneity and isotropy of space.
- The formulation of special relativity proposed by Hermann Minkowski (1908) explicitly relates properties of spacetime to the invariance properties of the physical laws; see Poincaré Group.
- This approach is opposite to the axiomatic approach in which the symmetries of spacetime are postulated and then imposed on the physical laws, see Axiomatic Relativity.