[53] We may mention that the physical existence of a finite invariant velocity is by no means impossible. It is acceptable mathematically, and the only question that we shall have to consider is whether it corresponds to physical reality.
[54] By an external event we do not necessarily mean an event occurring outside our body. We mean one that does not reduce to a mere awareness of consciousness. A sudden pain in our toe would constitute an external event in exactly the same measure as would the explosion of a barrel of gunpowder a mile distant.
[55] The relativity of simultaneity is a most revolutionary concept, as will be seen from the following illustration:
Consider two observers, one on a train moving uniformly along a straight line, the other on the embankment. At the precise instant these two observers pass each other at a point
, a flash of light is produced at the point
. The light wave produced by this instantaneous flash will present the shape of an expanding sphere. Since the invariant velocity of light holds equally for either observer, we must assume that either observer will find himself at all times situated at the centre of the expanding sphere.
Our first reaction might be to say: “What nonsense! How can different people, travelling apart, all be at the centre of the same sphere?” Our objection, however, would be unjustified.
The fact is that the spherical surface is constantly expanding, so that the points which fix its position must be determined at the same instant of time; they must be determined simultaneously. And this is where the indeterminateness arises. The same instant of time for all the points of the surface has not the same significance for the various observers; hence each observer is in reality talking of a different instantaneous surface.