The Redundancy of Spacetime: Special Relativity as a Grammar and the Strangeness of ‘c’

Abstract

The argument that the indexical aspects of spatial and temporal concepts are ineliminable and incompatible with an interpretation of spatial and temporal relations in terms only of the locations and moments of a spatio-temporal manifold that is independent of the material system of the world would be greatly strengthened if it could be shown that the same conclusion can be arrived at from an analysis of the conceptual structure of physics itself. I shall try to show that by adding an argument drawn from the principle of covariance to the argument from indexicality, an overwhelming case for the redundancy of any form of independent spatio-temporal manifold can be made that is conceptually tied to the level of covariance at which the proof is obtained. For example, it can be shown that flat Newtonian space and time are redundant at the level of covariance expressed in Galilean relativity, that is for frames of reference in relative, rectilinear uniform motion to one another. I take the principle of covariance to assert that the laws of nature are of the same form relative to whatever frame of reference they are measured, in a set of such frames that are mutually related by some such relation as relative spatial or temporal displacement, or that differ in relative uniform linear velocity. And this, even though the measures of the common, frame-independent process the laws describe differ from the measures obtained by investigators in other frames of refence related in the relevant way. If we want to know the results obtained by investigators in another frame of reference we can translate them into the terms of our frame by the use of a coordinate transformation, serving as translation manual.