Background
LNH was Dirac's personal response to a set of large number 'coincidences' that had intrigued other theorists at about the same time. The 'coincidences' began with Hermann Weyl (1919), who speculated that the observed radius of the universe might also be the hypothetical radius of a particle whose energy is equal to the gravitational self-energy of the electron:
where re is the classical electron radius, me is the mass of the electron, mH denotes the mass of the hypothetical particle, rH is its electrostatic radius and RU is the radius of the observable universe.
The coincidence was further developed by Arthur Eddington (1931) who related the above ratios to N, the estimated number of charged particles in the Universe:
In addition to the examples of Weyl and Eddington, Dirac was influenced also by the primeval-atom hypothesis of Georges Lemaitre, who lectured on the topic in Cambridge in 1933. The notion of a varying-G cosmology first appears in the work of Edward Arthur Milne a few years before Dirac formulated LNH. Milne was inspired not by large number coincidences but by a dislike of Einstein's general theory of relativity. For Milne, space was not a structured object but simply a system of reference in which Einstein's conclusions could be accommodated by relations such as this:
where MU is the mass of the universe and t is the age of the universe in seconds. According to this relation, G increases over time.
Read more about this topic: Dirac Large Numbers Hypothesis
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