Maxwell's electromagnetic theory of light

1865 Light and sky theory

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A theory in which light is identified with an electromagnetic disturbance propagating in the field. On the design of the theory, the whole of space is filled by the field, and the ether was regarded as the carrier of the field.

It was built by the Scotsman James Clerk Maxwell. In the article 'Ether' for the 9th edition of Britannica (1878) he asserted that interplanetary space is occupied by a material medium. In 1879, in a letter to D. P. Todd (published in Nature in 1880), he discussed measuring the Earth's velocity relative to the ether and pointed out that terrestrial experiments give only a second-order effect.

This is what pushed Michelson toward the interferometer.

Why this date

the 1878 article "Ether" in Britannica. exact

What it grew from

• The analytical theory of heat and Fourier series

  influenced · Confidence: medium

  The mathematical form of Fourier's heat conduction equations, through Thomson's 1842 analogy between the flow of heat and attraction, gave Maxwell the template for a field description of electricity.

  Link sources

  • James Clerk Maxwell, On Faraday's Lines of Force, Transactions of the Cambridge Philosophical Society (1856) Verified 20 Sep 2026

    Yet we find that the mathematical laws of the uniform motion of heat in homogeneous media are identical in form with those of attractions varying inversely as the square of the distance.

  • T. N. Narasimhan, Fourier's heat conduction equation: history, influences and connections, Proceedings of the Indian Academy of Sciences (Earth and Planetary Sciences) 108 (3), 117-148 (1999)

    Later, he demonstrated the similarities between the mathematical structures of Fourier's heat conduction equation and the equations of electrostatics stemming from the works of Laplace and Poisson (Thomson 1842).

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

What grew out of it

• The Michelson-Morley experiment

  influenced · Confidence: high

  Maxwell's remark on measuring motion relative to the ether (letter to Todd, 1879) was the immediate motive for Michelson's 1881 experiment.

  Link sources

  • Michelson 1881, Am. J. Sci. 22 (1881)

    Clerk Maxwell pointed out that [the velocity difference] could be calculated by measuring the velocity of light by means of the eclipses of Jupiter's satellites ... but that for this purpose the observations of these eclipses must greatly exceed in accuracy those which have thus far been obtained.

  • Haubold, Astronomische Nachrichten (arXiv:2111.12176) (1982) Verified 20 Sep 2026

    The incitement for undertaking such a crucial experiment Michelson had found in ideas of J.C. Maxwell.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

• Vector analysis and the vector form of the field equations

  improved · Confidence: medium

  In 1884-1885 Heaviside recast Maxwell's electromagnetic theory in vector notation, removing the potentials and keeping only the fields, and it is out of that notation of his that the form of the field equations familiar today grew.

  Dispute: Both the count of the original equations and the question of who produced the canonical set of four are contested. Hunt assigns twenty equations to the 1873 Treatise, Rautio speaks of twenty equations in twenty variables, Donaghy-Spargo of twenty-two, and Wheeler describes them as scattered over more than twenty pages. The short formula that Heaviside gave the equations their modern form comes mainly from popular accounts (Rautio); Arthur's detailed study shows that Heaviside never gathered the four into one group, that he reserved the name 'duplex' for the pair of curl formulas, that Hertz reached the same form independently and conceded priority to Heaviside, and that the four were first given as a single fundamental set by Lorentz in 1902. The role of quaternions is disputed separately: Brezov (2025) writes that Maxwell derived his equations using Hamilton's quaternion differential calculus, whereas Crowe, Hunt and Wheeler hold the opposite, that the main notation was Cartesian component form and that Maxwell was nearly indifferent to the quaternion expressions.

  Link sources

  • James C. Rautio, The Long Road to Maxwell's Equations, IEEE Spectrum 51 (12), 36 (2014) Verified 20 Sep 2026

    It was Heaviside, working largely in seclusion, who put Maxwell's equations in their present form.

  • Oliver Heaviside, quoted in James C. Rautio, The Long Road to Maxwell's Equations, IEEE Spectrum 51 (12), 36 (2014) Verified 20 Sep 2026

    I never made any progress until I threw all the potentials overboard

  • Bruce J. Hunt, Oliver Heaviside: A First-Rate Oddity, Physics Today 65 (11), 48-54 (2012) Verified 20 Sep 2026

    In 1884–85 Oliver Heaviside rewrote the 20 fundamental equations of Maxwell's Treatise on Electricity and Magnetism into a new and more compact form that by the late 1890s had become standard.

  • John W. Arthur, The Evolution of Maxwell's Equations From 1862 to the Present Day, IEEE Antennas and Propagation Magazine 55 (3) (2013) Verified 20 Sep 2026

    nor did he even put the four main equations together into a single group as we know them now, but what he produced did contain four familiar looking equations

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

Links under review

• Wave optics of Young and Fresnel and the luminiferous ether

  influenced · Confidence: medium

  The only source (Michelson 1881) describes the ether of the wave theory, not its inheritance by Maxwell; no historian (Buchwald, Hunt, Darrigol) is cited.

  Maxwell's electromagnetic theory of light inherited from wave optics the idea of the ether as the carrier of waves.

  Dispute: No direct statement by a historian on the continuity of the ether from Fresnel to Maxwell could be found; it is visible in the texts themselves (Maxwell 1878, Michelson 1881). Encyclopedia.com stresses: "the formalism of the theory did not stand or fall with a particular interpretation" of the ether.

  Link sources

  • Michelson 1881, Am. J. Sci. 22 (1881) Verified 20 Sep 2026

    The undulatory theory of light assumes the existence of a medium called the ether, whose vibrations produce the phenomena of heat and light, and which is supposed to fill all space.

  "Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong.

Node sources

• Michelson A. A. «The Relative Motion of the Earth and the Luminiferous Ether», Am. J. Sci. 22, 120-129 (1881) Verified 25 Sep 2026, quotation assembled from fragments

  In a letter, published in "Nature" shortly after his death, Clerk Maxwell pointed out that...could be calculated by measuring the velocity of light by means of the eclipses of Jupiter's satellites at periods when that planet lay in different directions from earth...In the same letter it was also stated that the reason why such measurements could not be made at the earth's surface was that we have thus far no method for measuring the velocity of light which does not involve the necessity of returning the light over its path

"Verified" means that on that day the quotation was found at the address given, word for word. No date means we have not been able to open the source yet, not that the quotation is wrong. "Assembled from fragments" means the words do not stand together on the page: we found each fragment separately and joined them with an ellipsis.

Further reading

Not evidence: these carry no quotation and support nothing we wrote. They are books and scans to read next.

• Maxwell J. C. «A Dynamical Theory of the Electromagnetic Field», Phil. Trans. 155, 459-512 (1865)
• Maxwell J. C. «Ether», Encyclopaedia Britannica, 9th ed., vol. 8 (1878)
• Harman P. M. (ed.) «The Scientific Letters and Papers of James Clerk Maxwell», vol. 3, 1874-1879, CUP (2002)

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