The following is a Letter to the Editor by H. Aspden published in Physics Education, v. 10, p. 327 (1975).


A T Jackson writing about the detection of the ether (Physics Education 1974, v. 9, p. 265) said that:

'The most important fallacy in Fresnel's drift theory would seem to be that he assumed the moving medium dragged both the light and the ether along with it, although the existence of the ether had not been established'.
Yet Fresnel's formula was verified by Fizeau and it was Michelson and Morley who assumed that the ether did not move with the earth and then were surprised to find that the earth's motion through the ether defied detection.

The very astute student may question why Fresnel's analysis involved a fallacy. If the role of the ether in controlling light propagation is analogous to the role of a substance in transmitting sound, the propagation velocity c1 is proportional to (P/d)1/2, where P is a pressure modulus and d is density. Since the speed of light is fixed at c and refractive index n is c/c1, we then find that n2 is proportional to d. Now, Fresnel said that the velocity of light would be increased by u(1-1/n2) due to motion of a disturbing medium at velocity u. If then the ether has structure and its bulk has density dk that moves as a disturbance at velocity u, we may write:

n2 = 1 - k
uk + v(1 - k) = 0
because n equals 1 when k equals zero and the ether exerts no linear force on matter, meaning that its momentum is conserved as k varies.

It is then a simple matter of algebra to show that u(1-1/n2) is simply v. This means that the velocity of light relative to the earth frame is constant, as Michelson and Morley found.