Eddington number
Encyclopedia
In astrophysics
, the Eddington number, NEdd, is the number of proton
s in the observable universe
. The name honors the British
astrophysicist Arthur Eddington who, in 1938, was the first to propose a calculation of NEdd, and to explain why this number could be important for cosmology
and the foundations of physics
.
In the late 1930s, the best experimental value of the fine structure constant, α, was about 1/136. Eddington began by arguing, from aesthetic and numerological considerations, that α should be exactly 1/136. He then gave a "proof" that NEdd = 136×2256, or about 1.57×1079. In the 1938 Tarner Lecture
at Trinity College, Cambridge
, Eddington averred that:
This large number was soon christened 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 – a feat for which Punch
dubbed him "Sir Arthur Adding-One."
The best present-day estimate (2008) of the value of the fine structure constant is:
Hence no one maintains any longer that α is the reciprocal of an integer
. Nor does anyone take seriously a mathematical connection between the value of α and NEdd. More defendable estimates of NEdd 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 numbers and sizes of galaxie
s and star
s in the universe.
On possible roles for NEdd in contemporary cosmology
, especially its connection with the large number coincidences
, see Barrow (2002) (easier) and Barrow and Tipler (1986: 224–31) (harder).
Astrophysics
Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties of celestial objects, as well as their interactions and behavior...
, the Eddington number, NEdd, is the number of proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
s in the observable universe
Observable universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...
. The name honors the British
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
astrophysicist Arthur Eddington who, in 1938, was the first to propose a calculation of NEdd, and to explain why this number could be important for cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
and the foundations of physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
.
In the late 1930s, the best experimental value of the fine structure constant, α, was about 1/136. Eddington began by arguing, from aesthetic and numerological considerations, that α should be exactly 1/136. He then gave a "proof" that NEdd = 136×2256, or about 1.57×1079. In the 1938 Tarner Lecture
Tarner Lectures
The Tarner lectures are a series of public lectures in the philosophy of science given at Trinity College, Cambridge since 1916. Named after Mr Edward Tarner, the lecture addresses 'the Philosophy of the Sciences and the Relations or Want of Relations between the different Departments of...
at Trinity College, Cambridge
Trinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
, Eddington averred that:
This large number was soon christened 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 – a feat for which Punch
Punch (magazine)
Punch, or the London Charivari was a British weekly magazine of humour and satire established in 1841 by Henry Mayhew and engraver Ebenezer Landells. Historically, it was most influential in the 1840s and 50s, when it helped to coin the term "cartoon" in its modern sense as a humorous illustration...
dubbed him "Sir Arthur Adding-One."
The best present-day estimate (2008) of the value of the fine structure constant is:
Hence no one maintains any longer that α is the reciprocal of an integer
Unit fraction
A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n...
. Nor does anyone take seriously a mathematical connection between the value of α and NEdd. More defendable estimates of NEdd point to a value of about 1080. These estimates assume that all matter can be taken to be hydrogen
Hydrogen
Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...
, and require assumed values for the numbers and sizes of galaxie
Galaxie
Galaxie is a Canadian multilingual digital pay television audio service owned by Stingray Digital.-Programming:Galaxie consists of 49 commercial-free music based audio channels, each devoted to a particular genre, distributed through digital television platforms. Each channel consists of a...
s and star
Star
A star is a massive, luminous sphere of plasma held together by gravity. At the end of its lifetime, a star can also contain a proportion of degenerate matter. The nearest star to Earth is the Sun, which is the source of most of the energy on Earth...
s in the universe.
On possible roles for NEdd in contemporary cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...
, especially its connection with the large number coincidences
Dirac large numbers hypothesis
The Dirac large numbers hypothesis 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 the present cosmological epoch...
, see Barrow (2002) (easier) and Barrow and Tipler (1986: 224–31) (harder).
See also
- Eddington–Dirac number
- Observable universeObservable universeIn Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...
- Eddington number (cycling)