Dirac large numbers hypothesis - Definition and Overview

The Dirac large numbers hypothesis refers to an observation made by Paul Dirac in 1937 relating ratios of size scales in the universe to that of force scales. Dirac noted that the ratio of the size of the visible universe, <math>ct<math> with <math>c<math> the speed of light and <math>t<math> the age of the Universe, to the size of a quantum particle <math>r<math> is about <math>ct/r = 10^{40}<math>. Hence in units <math>c = 1<math> and <math>r = 1<math> this large number can be taken as the age of the Universe, <math>t = 10^{40}<math>.

There is another ratio with this order of magnitude: the ratio of the electrical to the gravitational forces between two protons, <math>e^2/Gm^2<math>. Hence, taking the charge <math>e<math> of the electron and the mass <math>m<math> of the proton as units, the gravitational constant equals <math>G = 10^{-40}<math>. Dirac interpreted this to mean that <math>G<math> varies with time as <math>G = 1/t<math> and built what remains to this day a largely untested cosmology out of this idea . If correct, the connection between gravity and quantum mechanics would be unmistakable and may point in the direction of a theory of quantum gravity.

Some scientists believe that the hypothesis is the result of a numerological coincidence, and in 1961, Robert Dicke argued that carbon-based life can only arise when the hypothesis is true lest fusion of hydrogen in stars not occur. A few proponents of non-standard cosmologies refer to Dirac's cosmology as a foundational basis for their ideas.

Weblinks

• gr-qc/0111034 Guillermo A. Mena Marugan, Saulo Carneiro: Holography and the large number hypothesis (http://arxiv.org/abs/gr-qc/0111034)