Einstein Relativity Theory
Einstein in 1905, formulated his special theory of relativity on the basis of following two postulates:
1. The laws of physics are same in all inertial frames. This is the principle of Relativity.
2. The speed of light c in vacuum is constant and same as observed from all inertial frames. This is known as the Principle of constancy of speed of light.
The first postulate implies that not only the laws of mechanics, but also that of electrodynamics and optics should be same for all inertial reference systems. It asserts that all inertial frames are equivalent and there is no place for a privileged frame like Absolute space ether.
The second postulate follows from the fact that Maxwell’s equations relate the speed of light in vacuum to electric and magnetic constants, 
. Hence, if laws of electromagnetism are same in different inertial frames, the value of c too should remain constant. In the words of H. Bondi, “If the spirit of the principle of Newtonian relativity is applied, it follows that this basic feature, the velocity of light, should be independent of the inertial system from which it is observed. The assertion that this is so …. is known as the special theory of relativity.”
The second postulate implies that speed of light does not depend on the motion of its source. The null effect of Michelson-Morley experiment is thus naturally explained. If speed of light is same in all direction, irrespective of the motion of source, no change in phase difference Ø would occur when the arms of the interferometer are rotated by 90˚.
Analyzing the innocent looking postulate about constancy of speed of light, Einstein showed that concepts of both space and time intervals are frame dependent. For example, suppose a light signal is sent from point x1 at time t1, along the x-axis, and reaches the point x2 at time t2, as seen by an observer in frame S. The same events are observed by a second observer in frame S’, moving relative to S with velocity v along x-axis. Observer S’ assigns values (x1’ , t1’) and (x2’, t2’) for the events. Constancy of c demands that,
Since S’ is moving relative to S, x2’ – x1’ ≠ x2 – x1; consequently t2’ – t1’ ≠ t2 – t1. By considering that origins of two frames coincide at t1 = t1’ so that x1 = x1’, it is evident that x2’ ≠ x2 and t2’ ≠ t2. That is, not only space and time intervals, but the space and time co-ordinates as well of an event, are frame dependent. Einstein was thus led to reformulate the concepts of space-time measurements and their frame dependence. Moreover, postulating constancy of c. Einstein demonstrated by a simple thought experiment, that two events occurring simultaneously in one frame are found to be simultaneous from other frame. That is, simultaneity is also relative.
Having examined the concepts of space-time measurements and simultaneity. Einstein asserted the principle of relativity of physical laws, or the equivalence of inertial frames. He thus, derived a set of transformation equations connecting space-time co-ordinates of an event as determined in two in two inertial frames moving relative to each other. Einstein showed that under these transformations, Maxwell equations (and hence speed of light in vacuum) remain invariant. These transformation equations are known as Lorentz transformations.
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