Electromagnetism and Newtonian Relativity
Consider two frames of reference in relative motion. Here we consider two frames F and F', with F' having a velocity of v relative to F. Events in F have co-ordinates and times denoted by x, y, z and t. Events in F' have co-ordinates and times denoted by x', y', z' and t'. We choose the x and x' axes to be parallel to v, the y and z axes to be at right angles to each other and x, and y' and z' to be parallel to y and z respectively. We choose t=t'=0 to be when the sets of axes coincide. Diagramatically:
The transformations of Newtonian Relativity allow co-ordinates and times in F to be converted to co-ordinates and times in F':
- x'=x-vt
- y'=y
- z'=z
- t'=t
The laws of classical mechanics (Newton's laws) are the same in F and F', but the laws of classical electromagnetism are not.
Consider a charge a distance from an infinitely long wire with a uniform charge (that is, the same in any two sections of the same length). If the wire is at rest in frame F, the charge experiences an electric field in frame F. In frame F' the charges in the wire are moving with speed v, so the charge experiences the same electric field, and an additional magnetic field. The charge experiences different forces in the two frames, but the transformations of Newtonian Relativity predict the same acceleration.
The Ether
The incompatibility of Newtonian Relativity with classical electromagnetism implies that frames cannot be in relative motion. In this case, there must be an 'ether', so that frames are stationary in relation to the ether.
The wave theory of light implies that light travels at a fixed speed relative to the ether. Optical phenomena will therefore be affected by the motion of the optical equipment through the ether - for example, the focal length of a telescope moving towards a star would be lengthened.
Arago and Airy looked for such effects, but failed. This led Fresnel to propose, in 1818, that moving transparent objects drag the light with them. He showed that all effects on refractive phenomena would be prevented if a moving transparent object of refractive index n added to the velocity of the light the fraction 1-1/n2 of the velocity of the object. In 1851 Fizeau showed that in a moving column of water, light is dragged to the degree predicted by Fresnel. Fresnel assumed that the ether was dragged with the moving object, but when, in 1895, Lorentz created his electomagnetic theory with the assumption of a stationary ether, Fresnel's formula was a consequence of the theory.
Fresnel and Lorentz showed there should never be any first order effects on optics, but second order effects were still possible. These effects would be very small, but after Michelson invented his interferometer, he and Morley used it in 1887 to see if the second order effects existed.
The physics and mathematics involved are too complex to discuss here - if the reader wishes to know more, the famous experiment is discussed in any good book on modern physics (there is also a brief summary on this Michelson-Morley experiment page).
No motion of the Earth through the ether was detected (the experiments were conducted again six months later with the Earth on the other side of the sun, in case it had been temporarily stationary relative to the ether for the first set of experiments). Three possible classical explanations were considered.
- Firstly, it was suggested that the Earth drags the ether with it, in which case the Earth never moves relative to the ether. However, the ether nearer the Earth would be in motion relative to the ether further away, and light from the stars would be deflected.
- Secondly, it was suggested that a moving light source had its own velocity added to the velocity of the light it emitted. This, however, conflicts with the wave theory of light, in which the speed of light is dependent only on the medium it passes through.
- Thirdly, Fresnel and Lorentz suggested that motion through the ether might cause the material to shorten in a direction parallel to the motion. A shortening in the ratio of (1-V2/c2)1/2 would account for the observed effect. In 1932 Kennedy and Thorndike showed this explanation was inadequate in a modifed version of the experiment.
Further reading
"Relativity: Special, General, and Cosmological", by Wolfgang Rindler: