Relativity in Euclidean Space and in Spacetime

Summary

The main idea of this chapter has been to exploit the similarities between Euclidean space and spacetime. As the members of the radical research team wanted to find a way to test their major hypothesis — that spacetime is real — they found an extremely simple but effective way to deduce predictions from the spacetime hypothesis. If spacetime is a real four-dimensional space then relations between lines in Euclidean space should have analogs in spacetime. And indeed, when the radical research team ‘translated’ the Euclidean relations into the corresponding spacetime relations, it turned out that the consequences of special relativity are, in fact, manifestations of the four-dimensionality of spacetime.

At this point some might object that this proves nothing — what the radical research team did was an interesting exercise, but just an exercise, which does not force us to change our views on the world. What we have seen in this chapter is that, if the world is four-dimensional, there will be manifestations of its four-dimensionality which coincide with the consequences of special relativity. In Chap. 5, I will argue that those consequences would be impossible if the world were threedimensional.