Cycles of Time: An Extraordinary New View of the Universe

by Roger Penrose

It is important for the physical basis of general relativity theory that extremely precise clocks actually exist in Nature, at a fundamental level, since the whole theory depends upon a naturally defined metric g.[2.32] In fact, this time measure is something quite central to physics, for there is a clear sense in which any individual (stable) massive particle plays a role as a virtually perfect clock. If m is the particle’s mass (assumed to be constant), then we find that it has a rest energy[2.33] E given by Einstein’s famous formula E=mc2, which is fundamental to relativity theory. The other, almost equally famous formula—fundamental to quantum theory—is Max Planck’s E=hv (h being Planck’s constant), telling us that this particle’s rest energy defines for it a particular frequency v of quantum oscillation (see Fig. 2.21). In other words, any stable massive particle behaves as a very precise quantum clock, which ‘ticks away’ with the specific frequency in exact proportion to its mass, via the constant (fundamental) quantity c2/h.