# Eddington number

In astrophysics, the Eddington number, NEdd, is the number of protons in the observable universe. Eddington originally calculated it as about 1.57×1079; current estimates make it approximately 1080.

The term is named for British astrophysicist Arthur Eddington, who in 1940 was the first to propose a value of NEdd 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.[1] This led him in 1929 to conjecture that α was exactly 1/136.[2] He devised a "proof" that NEdd = 136 × 2256, or about 1.57×1079. Other physicists did not adopt this conjecture and did not accept his argument.[citation needed]

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 1080.[3] 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.[4]

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

I believe there are 15747724136275002577605653961181555468044717914527116709366231425076185631031296 protons in the universe and the same number of electrons.[5]

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.[6]

## Recent theory

The modern CODATA recommended value of α−1 is 137.035999177(21).[7]

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 Barrow (2002) (easier) and Barrow & Tipler (1986, pp. 224–231) (harder).

## References

1. ^ A. S. Eddington (1956). "The Constants of Nature". In J. R. Newman (ed.). The World of Mathematics. Vol. 2. Simon & Schuster. pp. 1074–1093.
2. ^ Whittaker, Edmund (1945). "Eddington's Theory of the Constants of Nature". The Mathematical Gazette. 29 (286): 137–144. doi:10.2307/3609461. JSTOR 3609461. S2CID 125122360.
3. ^
4. ^ H. Kragh (2003). "Magic Number: A Partial History of the Fine-Structure Constant". Archive for History of Exact Sciences. 57 (5): 395–431. doi:10.1007/s00407-002-0065-7. S2CID 118031104.
5. ^ Eddington (1939), lecture titled "The Philosophy of Physical Science". The sentence appears in Chapter XI, "The Physical Universe". Eddington assumes that neutrons are composed of protons and electrons, and his number includes those as well.
6. ^ Eddington (1946)
7. ^ "2022 CODATA Value: inverse fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.

## Bibliography

1. ^ Eddington, Arthur Stanley (1946). Fundamental Theory. Cambridge: Cambridge University Press.