The Time Illusion (Kindle Single)

by John Gribbin

Minkowski realised that Einstein’s equations were telling us that we can do very much the same in four dimensions, specifying some kind of four-dimensional length a by the equation a2 = x2 + y2 + z2 - (ct)2, where t denotes a time interval and c is the speed of light, so the two of them combined together make a distance. Time, or rather ct, appears as a fourth dimension (not like a fourth dimension; it is a fourth dimension), with two special features. The first is that minus sign, which makes time a kind of negative dimension. When space expands, the time shrinks, and vice-versa. The second is that c. It means that one second of time is equivalent to 300,000 kilometres of space, and this is why relativistic effects only become important if things are moving at a large fraction of the speed of light. The equation tells us that the four-dimensional length of an object, usually known as extension, stays the same however the object moves. If the length contracts, the time stretches, by an equivalent amount, and vice-versa.