]> 29.6 Invariance Properties

29.6 Invariance Properties

Maxwell's equations have the property that they are unchanged under rotations in space and also under a peculiar kind of transformation that can be considered a rotation in Minkowski space. It is called a Lorentz transformation.

In the late 19 th Century it gradually dawned on physicists that this kind of invariance implies a different form to transformations to moving coordinate systems than were generally used in mechanics.

Sound is known to consist of motions of the air or of whatever other medium it passes through. In a vacuum there are no sounds. Physicists wondered for a long time as to whether there is a similar medium for light.

They postulated an "ether" which were the medium for light in the way that the particles in the air form a medium for sound. If there is such a medium, it would be interesting to know to what extent we are moving with respect to it.

Michelson and later Michelson and Morley attempted to measure our velocity with respect to "the ether" by measuring the velocity of light in different directions in the 1880's. They found the velocity of light the same in all directions even when the source was moving with respect to the observer.

Einstein, in 1905, explained this observation in the basis of the assertion that the laws of nature including Maxwell's equations with the same velocity of light are the same to you whether you are moving or not.

Fitzgerald and Lorentz had shown how to modify the equations of ordinary mechanics to give them the same invariance properties as Maxwell's equations.

We have not discussed the energy associated with electric and magnetic fields nor have we considered their effects on matter.

Even without such discussion it is fairly clear from the structure of Maxwell's equations that the concept of electrons going around in stable orbits around atoms like planets go round the sun is inconsistent with them.

If they did so, being charged particles, they would cause electromagnetic waves which would carry away energy. The orbits could not be stable if energy is conserved unless the electrons have charge density that is independent of time.

Replacing classical mechanics by a formulation that allows electrons to have time independent charge distributions was one of the main triumphs of early 20 th Century physics.

To understand these things you had best learn some physics.