Special theory of relativity

After many readings of relativity theories, it emerges that it would be futile to follow the conventional approach of studying relativity by explaining the “unthinkable” first and then derive conclusions. No description, however good, satisfies a reader that incidence of time for an event or length of a rod is different in two inertial references. Keeping this aspect of study in mind, we shall attempt a slightly different approach here. Upfront, we shall accept relativistic assertions about distance (space) and time. This is a better approach as it allows us to proceed with the theory and come back to the lingering thoughts when we are equipped with the basic or working knowledge of the theory. After all, electromagnetic theory of light (and hence constancy of speed of light in vacuum) is such an elegant and complete theory that we can only be more than willing to accept assertions which are based on it.

Yet another aspect of the study of relativity is that it relates phenomena which occur over a very large spatial extent. The consideration of motion of light even for 0.1 second involves a linear extent of 30000000 meters. Clearly, there is limitation to pick examples or illustration from our real world. Most of the experiments or illustrations cited in the study of relativity are reasonable as imagined. Conception of special theory of relativity is more an outcome of “experiments in head” than the actual ones, but such experiments are rigorous and subject to direct or indirect scientific verification. This process of performing mental experiments is known by a German term “Gedankenexperimenten”. Einstein used this process often to reach conclusions. Clearly, we shall also be required to do a bit of “Gedankenexperimenten” to understand his theories. In a nutshell, we should be ready to imagine spacecrafts or space objects moving at very high speeds without any inhibition. We may even imagine ourselves sitting in those high speed spacecraft. Similarly, we may imagine a train which is moving at a speed of say 100000 km/hr. Apart form the scientific validity of reasoning, there is no constraint in imagining experiments or examples which otherwise can not be realized in our small world.

What is time ?

We do not know exactly what is time. But we know some of its properties. The closest that we come to define time is about the manner in which we measure it. This measurement is essentially an outcome of the characteristic of time known as “simultaneity”. Einstein wrote "That train arrives here at 7 o'clock", I mean something like this : "The pointing of the small hand of my watch to 7 and the arrival of the train are simultaneous events." Thus, we measure time of an event by way of the simultaneity of two events – one belonging to measuring device and other belonging to an arbitrary event like arrival of a train. This argument clinches the issue of time from the relativistic perspective. If we are able to prove that two events which are simultaneous in one inertial frame of reference but “not” simultaneous in another, then we can be sure that measurements of time in two inertial references could indeed be different.