Special theory of relativity

Similarly, we can proceed from the principle of constancy of speed of light in vacuum to the principle of relativity. If we accept constancy of speed of light in vacuum across all inertial references, then we consider that law of propagation of light in vacuum (electromagnetic theory) is valid in them. Now, the laws of motion are already considered to be independent of inertial frames of reference. Addition of electromagnetic theory to this class of invariants suggests that other physical laws in their simplest form are also valid in all inertial references. This is exactly the principle of relativity.

Clearly, two principles are deducible from each other. Yet, we require to state special theory of relativity in terms of two principles. We see that though we are able to deduce second principle from first, but in the process we have narrowed the scope of principle of relativity. The principle of relativity is a very general principle extending to all physical laws - not only to laws of motion and propagation of light. Similarly, the deduction of first principle from second is not direct deduction - rather an extension. For these reasons, it is generally prudent to state both the principles of special theory of relativity.

The important consideration of special theory of relativity is the inclusion of Maxwell’s electromagnetic theory being valid in inertial references. Earlier we limited the scope of validity only to Newton’s laws of motion. We should understand that Newton’s laws of motion are special case of a more general special theory of relativity. Let us have a look at the validity of the Newton’s laws motion in inertial references involving relativistic consideration at higher speed :

1: Newton’s first law of motion of motion is valid in inertial references.

2: Newton’s second law of motion which defines force in terms of time rate of change of linear momentum is valid in inertial references.

3: Newton’s second law of motion which defines force in terms of the product of mass and acceleration is not valid in inertial references, because mass is not a constant in relativistic mechanics. The more general relativistic or modified form of Newton's second law valid in all inertial references, however, reduces to classical Newton's second law of motion at lower speed.

4: Newton’s third law of motion as stated in the form of equal and opposite action and reaction is not valid in inertial references.

5: The conservation of linear momentum, which is the consequence of Newton's third law, is valid in inertial references.

We shall return to these aspects in detail subsequently.

Studying special theory of relativity

The idea of constancy of speed of light in all inertial references shakes up well rooted concepts about distance (space) and time. It raises many questions and makes the study of special theory of relativity a bit difficult. Generally the explanations appear to be inadequate or not very convincing. As a matter of fact, there is a temptation to view the theory with a sense of disbelief. But the fact of life is that relativity (we shall use this term to mean “special theory of relativity” for brevity), there is not even a single “exception of” or “departure from” the predictions of special relativity as on date (spanning a period of more than a century).