Dirac's Interpretation of The Large Number Coincidences
The Weyl and Eddington ratios above can be rephrased in a variety of ways, as for instance in the context of time:
where t is the age of the universe, is the speed of light and re is the classical electron radius. Hence, in units where c=1 and re = 1, the age of the Universe is about 1040 units of time. This is the same order of magnitude as the ratio of the electrical to the gravitational forces between a proton and an electron:
Hence, interpreting the charge of the electron, the mass / of the proton/electron, and the permittivity factor in atomic units (equal to 1), the value of the gravitational constant is approximately 10−40. Dirac interpreted this to mean that varies with time as, and thereby pointed to a cosmology that seems 'designer-made' for a theory of quantum gravity. According to general relativity, however, G is constant, otherwise the law of conserved energy is violated. Dirac met this difficulty by introducing into the Einstein field equations a gauge function β that describes the structure of spacetime in terms of a ratio of gravitational and electromagnetic units. He also provided alternative scenarios for the continuous creation of matter, one of the other significant issues in LNH:
- 'additive' creation (new matter is created uniformly throughout space) and
- 'multiplicative' creation (new matter is created where there are already concentrations of mass).
Read more about this topic: Dirac Large Numbers Hypothesis
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