## Special Theory of Relativity

Einstein gave two postulates to explain the negative result of the Michelson-Morley experiment. Thus they form the basis of the special theory of relativity. These postulates are:

- The laws of physics take the same form in all inertial frames.

According to the first postulate all inertial frames are equivalent. However, It is meaningless to talk of absolute motion. Only the motion relative to the frame of reference has any physical meaning.

- The velocity of light in vacuum has the same value c and is independent of the relative velocity of the source and the observer.

The second postulate simply expresses the result of Michelson Morley experiment.

## Consequences of Postulates of Relativity

The first postulate requires that Maxwell equations should be valid in all inertial frames. But we know that these equations are not Galilean invariant. Thus postulate 1 rejects the validity of the Galilean transformation.

There must be some other transformation under which Maxwell’s equations are invariant. But Newton’s laws are Galilean invariant and cannot be invariant under the transformation which makes Maxwell’s equations invariant. Also, this means that laws of Newtonian mechanics are not really valid. We must have a new set of mechanical laws which together with Maxwell equations are invariant under a new transformation which is not Galilean.

This requires a revision of the fundamental concepts of space and time. These are the absolute quantities in Newtonian mechanics. The absoluteness of these quantities need to be discarded in order to preserve the Einstein postulates which are necessary to explain the negative result of Michelson Morley experiment. The new transformation to replace the Galilean transformation was first derived by H.A. Lorentz in the year 1890 and is known as the Lorentz transformation.

Postulate 2 explains the negative result of the Michelson-Morley experiment. This postulate implies that the velocity of light is unaffected by the ether wind and is *c* for both the beams. Thus there is no path difference between the two beams and there is no question of any fringe shift. Moreover this hypothesis renders the ether hypothesis redundant,

Thus we need a transformation between two inertial frames which

- Preserves the velocity of light.
- Keeps the forms of laws of physics invariant.

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