My watch list
my.chemeurope.com

# Dirac large numbers hypothesis

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, ct with c the speed of light and t the age of the Universe, to the size of a quantum particle r is about ct / r = 1040. Hence, in units c = 1 and r = 1, this large number can be taken as the age of the Universe, t = 1040.

There is another ratio with this order of magnitude: the ratio of the electrical to the gravitational forces between a proton and an electron, $\frac{4 \pi \epsilon_0 G m_{pr} m_e}{e^2}$ (≈ 4.4 × 10−40). Hence, taking the charge e of the electron, the mass mpr/me of the proton/electron, and the permittivity factor 4πε0 as units, the gravitational constant equals G = 10 − 40. Dirac interpreted this to mean that G varies with time as $G \propto 1/t\,$, 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.