Seeing Further: The Story of Science and the Royal Society

by Bill Bryson

In the 1930s, the physicist Paul Dirac and the astronomer Arthur Eddington were struck by a strange relationship in basic physics and cosmology. The hydrogen atom is held together by an electromagnetic force between the proton and electron. There is also a tiny gravitational force of attraction between them. The ratio of these forces is a staggering 1040. How, wondered Dirac and Eddington, did such a large number come out of fundamental physics? (It remains a mystery today.) But the peculiar twist is that the same very large number crops up in a completely different context. The age of the universe – that is, the time since the big bang – is also about 1040 when expressed as a ratio using basic atomic units of time. Surely these two very large numbers are not the same by coincidence? Dirac at least thought not. He reasoned that they had to be linked deep down by some law of physics. However, because the age of the universe is not a fixed number – it gets bigger every day! – if there is such a linkage it implies that the ratio of forces must also increase with time, with gravity growing relatively weaker as the universe ages. Dirac developed an elaborate mathematical theory to incorporate this effect, and astronomers set about testing whether the force of gravity is indeed time-dependent.