Arthur Milne | |
---|---|

Born | Kingston upon Hull, Yorkshire, England | 14 February 1896

Died | 21 September 1950 Dublin, Ireland | (aged 54)

Alma mater | Trinity College, Cambridge |

Known for | Milne model |

Scientific career | |

Institutions | Victoria University of Manchester University of Oxford |

Doctoral students | Thomas Cowling |

**Edward Arthur Milne** FRS^{[1]} (/ˈmɪln/; 14 February 1896 – 21 September 1950) was a British astrophysicist and mathematician.^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}

## Contents

## Biography

Milne was born in Hull, Yorkshire, England. He attended Hymers College and from there he won an open scholarship in mathematics and natural science to study at Trinity College, Cambridge in 1914, gaining the largest number of marks which had ever been awarded in the examination. In 1916 he joined a group of mathematicians led by A. V. Hill for the Ministry of munitions working on the ballistics of anti-aircraft gunnery, they became known as ′Hill's Brigands′. Later Milne became an expert on sound localisation.^{[7]} In 1917 he became a lieutenant in the Royal Navy Volunteer Reserve. He was a fellow of Trinity College, Cambridge, 1919–1925, being assistant director of the solar physics observatory, 1920–1924, mathematical lecturer at Trinity, 1924–1925, and university lecturer in astrophysics, 1922–1925. He was Beyer professor of applied mathematics, Victoria University of Manchester, 1924–1928, before his appointment as Rouse Ball Professor of Mathematics and to a fellowship at Wadham College, Oxford, in 1928. Milne's earlier work was in mathematical astrophysics. Much of his research in the 1930s was concerned with the theory of relativity and cosmology. His later work, concerned with the interior structure of stars, aroused controversy. Milne was President of the Royal Astronomical Society, 1943–1945. During World War II he again worked on ballistics.

He died of a heart attack in Dublin, Ireland, while preparing to give a set of lectures. These can be found written down in one of his last published books: *Modern Cosmology and the Christian Idea of God* (1952).

## Research into stellar atmospheres and structure

In the 1920s much of Milne's research was concerned with stars, particularly the outer layers known as stellar atmospheres that produce the radiation observed from the Earth. He considered a grey atmosphere, a simplifying approximation in which the strength of the absorption of light by the hot ionized gas is the same at all wavelengths. This produced predictions of how temperature varies through the atmosphere, including the mathematical expression now known as the Milne Equation. He also calculated how the intensity of light from a star varies with wavelength on the basis of this model.^{[8]}^{[9]}

Milne moved on to consider the more realistic case where the strength of the absorption of light by gas within stars (expressed by the absorption coefficient) does vary with wavelength. Using simplifying assumptions he calculated how for the Sun
the strength of the absorption depends on wavelength. His results could not be explained adequately at the time, but later
negatively-charged hydrogen ions (H^{−}) were shown to be a major contributor to Milne's results.^{[9]}

Milne, working with Ralph H. Fowler, studied how the strengths of spectral lines of stars depend on their spectral type. In doing this they applied the work of Meghnad Saha about the ionization of gases to stellar atmospheres.^{[9]}

Milne worked on the structures and interiors of stars in the late 1920s and early 1930s. He often took opinions opposed to those of Arthur Eddington.^{[9]}

## Research into cosmology and relativity

From the early 1930s, Milne's interests focused increasingly on relativity theory and cosmology.^{[10]}

From 1932 he worked on the problem of the "expanding universe" and in *Relativity, Gravitation, and World-Structure* (1935), proposed an alternative to Albert Einstein's general relativity theory. With McCrea (1934) he also showed that the 3 models which form the foundations of modern cosmology first proposed by Friedmann (1922) using the general theory of relativity, can also be derived using only Newtonian mechanics.^{[11]}

*Relativity, Gravitation, and World Structure*

The main difference between the Milne model of an expanding universe, and the current (Einstein's) model of an expanding universe was that Milne did not assume *a priori* that the universe has a homogeneous matter distribution. He did not include the gravitation interaction into the model either.

Milne argued that under the context of Einstein's special relativity, and the relativity of simultaneity, that it is impossible for a nonstatic universe to be homogeneous. Namely, if the universe is spreading out, its density is decreasing over time, and that if two regions appeared to be at the same density at the same time to one observer, they would not appear to be the same density at the same time to another observer. However, if each observer measures its local density at the same agreed-upon proper time, the measured density should be the same. In Minkowskian coordinates, this constant proper time forms a hyperbolic surface which extends infinitely to the light-cone of the event of creation. This is true even when proper time approaches 0, the time of the creation. The universe is already infinite at the creation time!

Milne's model is, therefore, that of a sphere, with an approximately homogeneous matter distribution within several billion light years of the center which then increases to an infinite density. It can be shown that this infinite density is actually the density of the universe when at the time of the big bang. The spherical distribution is unique in that it is essentially the same after a Lorentz transformation, except that a different stationary particle is at the center. As it is the only distribution that has this property, it is the only distribution which could satisfy the cosmological principle of "no preferred reference frame." Based on this cosmological principle Milne created a model that can be described entirely within Euclidean geometry.

As of 1935, using this model, Milne published a prediction of the cosmic background radiation which appears to be of a much different character than that predicted by Eddington. In fact, many passages in *Relativity, Gravitation and World Structure* are devoted to attacking Eddington's preconceptions.

## Honours

### Awards

- MBE (1918)
- Smith's Prize (1922)
- Gold Medal of the Royal Astronomical Society (1935)
- Royal Society's Royal Medal (1941)
- Bruce Medal (1945)

### Named after him

- Milne, a crater on the Moon
- The E.A. Milne Centre for Astrophysics at the University of Hull (opened 2015)
^{[12]}

## Books by Milne

*Thermodynamics of the Stars*, Berlin: J. Springer, 1930.*The White Dwarf Stars*, Oxford: Clarendon Press, 1932.*Relativity, gravitation and world-structure*, Oxford: Clarendon Press, 1935.*The Inverse Square Law of Gravitation*, London: Harrison and Son, 1936.*The Fundamental Concepts of Natural Philosophy*, Edinburgh: Oliver & Boyd, 1943.*Kinematic relativity; a sequel to Relativity, gravitation and world structure*, Oxford: Clarendon Press, 1948.*Vectorial Mechanics*, New York: Interscience Publishers, 1948.*Modern Cosmology and the Christian Idea of God*, Oxford: Clarendon Press, 1952.*Sir James Jeans: A Biography*, Cambridge University Press, 1952.

## See also

## Notes

**^**McCrea, W. H. (1951). "Edward Arthur Milne. 1896-1950".*Obituary Notices of Fellows of the Royal Society*.**7**(20): 420–426. doi:10.1098/rsbm.1951.0010. JSTOR 769028.**^**O'Connor, John J.; Robertson, Edmund F., "Edward Arthur Milne",*MacTutor History of Mathematics archive*, University of St Andrews.**^**McCrea, W. H. (1951). "Edward Arthur Milne".*Monthly Notices of the Royal Astronomical Society*.**111**(2): 160–170. Bibcode:1951MNRAS.111R.160.. doi:10.1093/mnras/111.2.160a. Retrieved 10 June 2016.**^**Plaskett, H. H. (1951). "Edward Arthur Milne".*Monthly Notices of the Royal Astronomical Society*.**111**(2): 170–172. Bibcode:1951MNRAS.111R.160.. doi:10.1093/mnras/111.2.160a. Retrieved 10 June 2016.**^**McCrea, W. H. (1950). "Edward Arthur Milne".*The Observatory*.**70**(859): 225–232. Bibcode:1950Obs....70..225M. Retrieved 10 June 2016.**^**"Obituary: Edward Arthur Milne".*Journal of the British Astronomical Association*.**61**(3): 75–77. 1951. Bibcode:1951JBAA...61R..75. Retrieved 10 June 2016.**^**Van der Kloot, W.(2011). ″Mirrors and smoke: A. V. Hill, his brigands, and the science of anti-aircraft gunnery in world war I.″ Notes Rec. R. Soc. Lond.**65**: 393–410.**^**Chandrasekhar, S. (1980). "The 1979 Milne Lecture – Edward Arthur Milne: His Part in the Development of Modern Astrophysics".*Quarterly Journal of the Royal Astronomical Society*.**21**(2): 93–107. Bibcode:1980QJRAS..21...93C. Retrieved 12 June 2016.- ^
^{a}^{b}^{c}^{d}Tayler, R. J. (1996). "E. A. Milne (1896–1950) and the Structure of Stellar Atmospheres and Stellar Interiors".*Quarterly Journal of the Royal Astronomical Society*.**37**(3): 355–363. Bibcode:1996QJRAS..37..355T. Retrieved 12 June 2016. **^**Whitrow, G. J. (1996). "E. A. Milne and Cosmology".*Quarterly Journal of the Royal Astronomical Society*.**37**(3): 365–367. Bibcode:1996QJRAS..37..365W. Retrieved 12 June 2016.**^**McCrea, W. H.; Milne, E. A. (1934). "Newtonian universes and the curvature of space".*Quarterly Journal of Mathematics*.**5**: 73–80. Bibcode:1934QJMat...5...73M. CiteSeerX 10.1.1.630.3318. doi:10.1093/qmath/os-5.1.73. This Newtonian derivation is sometimes incorrectly also ascribed to Friedmann.**^**"E.A. Milne Centre for Astrophysics, University of Hull - University of Hull".

## References

- Beating the Odds: The Life and Times of E.A Milne by Meg Weston Smith, in June 2013. Published by World Scientific Publishing Co.
- Gale, George, "Cosmology: Methodological Debates in the 1930s and 1940s," Stanford Encyclopedia of Philosophy. Milne was a major player in the cosmological controversies described in this article.

Preceded by Sydney Chapman |
Beyer Chair of Applied Mathematics at University of Manchester1925–1928 |
Succeeded by Douglas Hartree |