Eddington–Dirac number

The Dirac large numbers hypothesis (LNH) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in the present cosmological epoch. According to Dirac's hypothesis, the apparent similarity of these ratios might not be a mere coincidence but instead could imply a cosmology with these unusual features:

Neither of these two features has gained wide acceptance in mainstream physics.

LNH was Dirac's personal response to a set of large number 'coincidences' that had intrigued other theorists of his time. The 'coincidences' began with Hermann Weyl (1919), who speculated that the observed radius of the universe, R_U, might also be the hypothetical radius of a particle whose rest energy is equal to the gravitational self-energy of the electron:

where r_e is the classical electron radius, m_e is the mass of the electron, m_H denotes the mass of the hypothetical particle, and r_H is its electrostatic radius.

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 Lemaître, 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 M_U is the mass of the universe and t is the age of the universe in seconds. According to this relation, G increases over time.

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