Although this generalisation would turn out to be perfectly legitimate, its validity is by no means self-evident a priori. We can accept it only after we have convinced ourselves that the laws of physics, such as experiment has revealed them to be, can indeed be regarded as expressing relationships between entities (vectors and tensors) in space-time. Now, from a purely formal standpoint, it is conceivable that such might not be the case. Suppose, for instance, that the four-dimensional spatio-temporal background were characterised by some finite invariant velocity
greater than Maxwell’s constant
, which is given, as we know, by the velocity of light in vacuo. In an extended sense we could still regard our universe as a four-dimensional space-time, since, the invariant velocity being finite, and not infinite, the fusion of space and time would hold, just as it did in Minkowski’s space-time.
But, on the other hand, owing to the discrepancy between
and
, the laws of electromagnetics would cease to be covariant to a change of Galilean frame, hence to a change of space-time mesh-system. And so we could not view these laws as expressing relationships between the absolute entities of the fundamental space-time continuum.