The number that fascinates physicists above all others

Alpha also raises some profound theoretical questions. If it is compared to another fundamental force, gravitation, the ratio is a huge number – about 1040 – which expresses the weakness of gravity compared to the electric and magnetic forces. Physicists and cosmologists have long wondered where these numbers, 1/137.03599913 and 1040, come from. Are they arbitrary, or do they flow from some deeper theory of the Universe?

There is a long history of attempts to derive α from physical theory or to concoct a mathematical formula that has this value. For a brief time in the 1920s, when it looked as if α might be exactly 1/137, astronomer Arthur Eddington searched for a theory that would throw up both the numbers 137 and 1040 naturally, but his ideas ultimately led nowhere. Then in 1969 a young Swiss mathematician, Armand Wyler, pointed out that (9/16π3)(π/5!)¼ comes close to 1/137.036, which matched the value of α to the precision known at the time. However, his formula was not accompanied by any credible theory and was regarded as little more than a numerical curiosity. Several other attempts at α numerology have been made since, none of which have gained traction in the physics community.

So what are we to make of 1/137.03599913? Is there a deep reason why α has to be precisely this number for the world to function as it does? Suppose by some magic we woke up tomorrow and α was 1/138 instead, would it make much difference?