Dirac Large Numbers Hypothesis

The Dirac large numbers hypothesis uses the ratio of the size of the visible universe to the radius of quantum particle to predict the age of the universe. 

The coincidence of various ratios being close in order of magnitude may ultimately prove meaningless or the indication of a deeper connection between concepts in a future theory of everything. Nevertheless, attempts to use such ideas have been criticized as numerology.

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 equivalence of these ratios might not be a mere coincidence but instead could imply a cosmology with these unusual features:

• The strength of gravity, as represented by the gravitational constant, is inversely proportional to the age of the universe:
• The mass of the universe is proportional to the square of the universe's age: .

Neither of these two features has gained wide acceptance in mainstream physics and, though some proponents of non-standard cosmologies refer to Dirac's cosmology as a foundational basis for their own ideas and studies, some physicists dismiss the large numbers in LNH as mere coincidences.

A coincidence, however, may be defined optimally as 'an event that provides support for an alternative to a currently favoured causal theory, but not necessarily enough support to accept that alternative in light of its low prior probability.' 

Research into LNH, or the large number of coincidences that underpin it, appears to have gained new impetus from failures in standard cosmology to account for anomalies such as the recent discovery that the universe might be expanding at an accelerated rate.

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