We may conclude by saying that it appears unjustified to refer to Einstein’s time and simultaneity determinations as depending on the behaviour of light. They depend on the processes of nature of which the behaviour of light is but a particular illustration. We must therefore amend Dr. Whitehead’s criticism of relativity, as making the very meaning of simultaneity depend on light signals, by replacing the words “light signals” by the words “physical processes.” But when amended [Pg 186] in this way, the criticism loses all its force. For we may speak of simultaneity throughout space, of an instantaneous space, as much as we please, but until we know enough about these evasive concepts to be able to distinguish events that are simultaneous from those which are not, we cannot claim to have any definite idea of what we are talking about. On this score, both classical science and relativity are in perfect agreement. [Pg 187] CHAPTER XVI PRACTICAL CONGRUENCE IN RELATIVITY IN a preceding chapter we mentioned certain of the most important aspects of the problem of physical space. We saw that the concept of spatial equality or congruence was deemed to have arisen from the facts of experience. Certain objects appeared to maintain the same visual aspect wherever displaced, provided we modified our own positions as observers in an appropriate way. But such fundamental recognitions were too vague to be of any use to science; hence congruent bodies were defined as those which, when maintained at constant temperature and pressure, coincided when placed side by side. Congruence, as thus defined, involved physical measurements with material bodies; and, as Poincaré remarked, all we could ever discover in this way would reduce to the laws of configuration of solid bodies, space itself transcending our experiments, since the bodies might behave one way or another in the same space. Poincaré’s attitude drives us to complete agnosticism so far as the geometry of space is concerned. If physical measurements are denied us, there is no means of solving the problem of space, for we have no a priori means of deciding that the structure of space is this or that. Logical arguments are of no avail, for they do not lead us to any definite solution, only to a variety of possibilities. We are thus thrown back on Poincaré’s main contention, i.e., “space is amorphous.” In it we can define congruence in any way we please (theoretical congruence), although for reasons of practical convenience it is necessary to be guided by the properties of so-called rigid bodies. Thus we obtain a physical definition of practical congruence, which permits us to determine the geometry that for all practical purposes is to be called the geometry of real physical space.