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Relativity Theory

The principle of relativity states that all phenomena in nature should appear the same from all frames of reference. That is, the laws of nature must be (form) invariant as we go from one frame of reference to another. This was first stated by Newton as following: “The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line.”

The above statement restricts the principle of relativity as applicable between inertial frames. This is called principle of special relativity. The principle of relativity, when applied also to non-inertial (or accelerated) frames of reference, is called principle of general relativity.

Galilean transformations are the transformation equations of special (Galilean) relativity. This means that mechanical phenomena, as described by Newtonian dynamics, would give same results when observed from different inertial systems.

However, it turns out that Maxwell equations of electromagnetism are not form invariant under Galilean transformations. That would mean that electromagnetic (or optical) phenomena do not follow relativity principle and would appear different from different inertial frames.

Maxwell equations in particular show that velocity of light c in vacuum is constant Maxwell assumed that light moves in a medium called ether which fills all vacuum and is at rest everywhere. Maxwell’s ether was therefore equivalent to Newton’s absolute space. Consequently, if c is the velocity of light in ether, its velocity in any other inertial frame moving with velocity v relative to ether, according to Galilean relativity would be given by c’ = c – v. This led to the possibility of determining velocity v of an inertial frame (say, earth) with respect to ether by measuring velocity of light c’ with respect to this frame. One of the classic experiments which took up this task performed by A. A. Michelson and E. W. Morley in 1887.