Astronomy:Eddington number

Short description: Number of protons in the observable universe

Arthur Stanley Eddington (1882–1944)

In astrophysics, the Eddington number, N_Edd, 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 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 N_Edd = 136 × 2²⁵⁶, or about 1.57×10⁷⁹. 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 N_Edd point to a value of about 10⁸⁰. 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 15747724136275002577605653961181555468044717914527116709366231425076185631031296 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

As of 2012, the most precisely known value of α⁻¹ was 137.035999174(35).

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 N_Edd.

On possible roles for N_Edd in contemporary cosmology, especially its connection with large number coincidences, see (Barrow 2002) (easier) and (Barrow Tipler) (harder).

See also

• Eddington–Dirac number
• Eddington number (cycling)
• The Sand Reckoner
• Universe

Bibliography

• Barrow, J.D. (2002). The Constants of Nature from Alpha to Omega: The Numbers That Encode the Deepest Secrets of the Universe. Pantheon Books. ISBN 978-0-375-42221-8. https://archive.org/details/constantsofnatur0000barr. 
• Barrow, J.D.; Tipler, F.J. (1986). The Anthropic Cosmological Principle. London: Oxford University Press. 
• Dingle, H. (1954). The Sources of Eddington's Philosophy. London: Cambridge University Press. 
• Arthur Eddington (1928). The Nature of the Physical World. London: Cambridge University Press. https://archive.org/details/in.ernet.dli.2015.23480. 
• Arthur Eddington (1935). New Pathways in Science. London: Cambridge University Press. 
• Arthur Eddington (1939). The Philosophy of Physical Science. London: Cambridge University Press. 
• Arthur Eddington (1946). Fundamental Theory. London: Cambridge University Press. 
• Kilmister, C.W.; Tupper, B.O.J. (1962). Eddington's Statistical Theory. London: Oxford University Press. 
• Slater, N.B. (1957). Development and Meaning in Eddington's Fundamental Theory. London: Cambridge University Press. 
• Whittaker, E.T. (1951). Eddington's Principle in the Philosophy of Science. London: Cambridge University Press. 
• Whittaker, E.T. (1958). From Euclid to Eddington. New York: Dover.