Special theory of relativity

The Newtonian mechanics is considered to be valid in all inertial frames of reference, which are moving at a constant relative velocity with respect to each other. Einstein broadened the scope of this theorem and extended the validity of all physical laws including electromagnetic theory to all inertial frames of reference. Now, constancy of speed of light in vacuum is a core consideration in the electromagnetic theory. Therefore, Einstein postulated that speed of light is a constant in all inertial frames of reference. The speed of light does not depend upon the motion of either the source emitting it or the receiver of the light. This simple assertion about the constancy of the speed of light in vacuum is an epoch making assertion as it contradicts one of the equally fundamental assertion that speed (velocity) is a relative concept and that it essentially depends on the state of motion of observer.

We can comprehend the import of special theory of relativity by a simple example. Let a light pulse is moving in x-direction with its speed “c” and let a space craft is also moving ahead in the same direction with a speed “v”. These motions are observed from a position on the ground. Let us also assume that there is no atmosphere and we are observing motions in vacuum. Now, the speed with which light reaches spacecraft should be the relative speed “c-v”. This is what we deduce classically. Special theory of relativity, however, asserts that the relative speed of light with respect to spacecraft is “c” only – notwithstanding the speed of spacecraft (v).

Motion of a light pulse and a spacecraft

The physical interpretation of the assertion of special theory of relativity is quite unthinkable classically. The constant relative speed of approach by light in the above example is possible only if the constituents of speed (distance and time) are different for observers having different motions. In the instant example, both “distance” and “time” as measured by spacecraft are different than the corresponding measurements by a ground observer which is observing motions of both light and spacecraft. The measurements of “distance” and “time” in two different frames of reference need to be different such that speed ratio for light in vacuum i.e. “x/t” or "x'/t'" in two inertial references (parameters in one reference is denoted by unprimed varibales whereas parameters in other reference is denoted be primed variables) remains a constant.

Motion of a light pulse and a spacecraft

In the figure above, we consider motion of a light pulse and spacecraft which are moving with speed "c" and "v" respectively in x-direction. They are initially at x=0 when t =0. The positions of light pulse and spacecraft are also shown after 1 second. As seen from the reference of ground (coordinate system), pulse and spacecraft travel "c" and "v" meters respectively. The linear distance between spacecraft and pulse after 1 second is "c-v" in ground reference. But according to special relativity, the linear distance between light pulse and spacecraft after 1 second should be "c" in the reference of spacecraft. As "c-v" can not be "c", it is deduced that measurements of distance and time in two references are different. A part of discripancy is due to difference in the measurement of distance and the remaining due to difference in the measurement of time. These diffferences need to be such that ratio of ditance and time is a constant for the pulse of light in all inertial references.