shall see presently that Einstein has a theory of the world in which the return can actually happen; but in de Sitter's theory it is rather an abstraction, because, as he says, "all the paradoxical phenomena can only happen after the end or before the beginning of eternity."
The reason is this. Owing to curvature in the time dimension, as we examine the condition of things further and further from our starting point, our time begins to run faster and faster, or to put it another way natural phenomena and natural clocks slow down. The condition becomes like that described in Mr H. G. Wells's story "The new accelerator."
When we reach half-way to the antipodal point, time stands still. Like the Mad Hatter's tea party, it is always 6 o'clock; and nothing whatever can happen however long we wait. There is no possibility of getting any further, because everything including light has come to rest here. All that lies beyond is forever cut off from us by this barrier of time; and light can never complete its voyage round the world.
That is what happens when the world is viewed from one station; but if attracted by such a delightful prospect, we proceeded to visit this scene of repose, we should be disappointed. We should find nature there as active as ever. We thought time was standing still, but it was really proceeding there at the usual rate, as if in a fifth dimension of which we had no cognisance. Casting an eye back on our old home we should see that time apparently had stopped still there. Time in the two places is proceeding in directions at right angles, so that the progress of time at one point has no relation to the perception of time at the other point. The reader will easily see that a being confined to the surface of a sphere and not cognisant of a third dimension, will, so to speak, lose one of his dimensions altogether when he watches things occurring at a point 90° away. He regains it if he visits the spot and so adapts himself to the two dimensions which prevail there.
It might seem that this kind of fantastic world-building can have little to do with practical problems. But that is not quite certain. May we not be able actually to observe the slowing down of natural phenomena at great distances from us? The most remote objects known are the spiral nebulae, whose
