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In astrophysics, the Eddington number, , is the number of protons in the
In astrophysics, the Eddington number, , is the number of protons in the observable universe
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these ob ...
. Eddington originally calculated it as about ; 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 and to explain why this number might be important for physical cosmology
Physical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of f ...
and the foundations of physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
.
History
Eddington argued that the value of thefine-structure constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between el ...
, ''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 1.57×1079. 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
Numerology (also known as arithmancy) is the belief in an occult, divine or mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value, via an alphanumeric system, of the letters in ...
considerations, that ''α'' should be exactly 1/137.
Current estimates of ''N''Edd point to a value of about . These estimates assume that all matter can be taken to be hydrogen
Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic ...
and require assumed values for the number and size of galaxies and stars in the universe.
Attempts to find a mathematical basis for this dimensionless constant have continued up to the present time.
During a course of lectures that he delivered in 1938 as Tarner Lecturer at Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any college at either Cambridge or Oxford. ...
, Eddington averred that:
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 most precise value of ''α'' (obtained experimentally in 2012) is: Consequently, no reliable source any longer maintains that ''α'' is thereciprocal
Reciprocal may refer to:
In mathematics
* Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal''
* Reciprocal polynomial, a polynomial obtained from another pol ...
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 and Tipler (1986: 224–31) (harder).
See also
*Eddington–Dirac number
The Dirac large numbers hypothesis (LNH) is an observation made by Paul Dirac in 1937 relating ratios of size scales in the Universe to that of force scales. The ratios constitute very large, dimensionless numbers: some 40 orders of magnitude in ...
* Eddington number (cycling)
*''The Sand Reckoner
''The Sand Reckoner'' ( el, Ψαμμίτης, ''Psammites'') is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the unive ...
''
*Universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...
References
Bibliography
* * * * * * * * * * * {{Large numbers Large integers Proton Astrophysics Physical cosmology