Eddington number



In astrophysics, the Eddington number, $N_{Edd}$, is the number of protons in the observable universe. Eddington originally calculated it as about $1.57$; current estimates make it approximately $$.

The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of $N_{Edd}$ and to explain why this number might be important for physical cosmology and the foundations of physics.

History
Eddington argued that the value of the fine-structure constant, α, could be obtained by pure deduction. He related α to the Eddington number, which was his estimate of the number of protons in the universe. This led him in 1929 to conjecture that α was exactly 1/136. He devised a "proof" that NEdd = 136 × 2256, or about $1.57$. Other physicists did not adopt this conjecture and did not accept his argument.

In the late 1930s, the best experimental value of the fine-structure constant, α, was approximately 1/137. Eddington then argued, from aesthetic and numerological considerations, that α should be exactly 1/137.

Current estimates of NEdd point to a value of about $$. These estimates assume that all matter can be taken to be hydrogen and require assumed values for the number and size of galaxies and stars in the universe.

During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge, Eddington averred that:

"I believe there are 15 747 724  136  275  002  577  605  653  961  181  555  468  044  717  914  527  116  709  366  231  425  076  185  631  031  296 protons in the universe and the same number of electrons."

This large number was soon named the "Eddington number".

Shortly thereafter, improved measurements of α yielded values closer to 1/137, whereupon Eddington changed his "proof" to show that α had to be exactly 1/137.

Recent theory
The modern CODATA recommended value of α$−1$ is

Consequently, no reliable source maintains any longer that α is the reciprocal of an integer. Nor does anyone take seriously a mathematical relationship between α and NEdd.

On possible roles for NEdd in contemporary cosmology, especially its connection with large number coincidences, see (easier) and  (harder).