Special Theory of Relativity

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SPECIAL THEORY OF RELATIVITY
Azhar Ali Zafar
Department of Mathematics
GC University Lahore, Pakistan.

Ask a dozen people to name a genius and the odds are that “Einstein” will spring to their lips. Ask that the meaning of relativity and few of them will be able to tell you what it is. (Anonymous)

The special theory of relativity has an undeserved reputation as a difficult subject. It is not mathematically complicated. Perhaps the most challenging aspect of special theory of relativity is its insistence that we replace some of our ideas about space and time which we have acquired through years of comment sense experiences with new ideas.
The essential ideas of special relativity were formally presented in a paper written by Albert Einstein and publish in 1905. In that year he also published his papers on Brownian Motion and on the photoelectric effect. It was for this latter paper (and not specifically for his theory of relativity) that he was awarded the 1921 noble prize in physics. Einstein also proposed a General theory of relativity in 1917. The general theory deals with the effect of gravity on space and time. The special theory of relativity takes its name from its denial of the concept of absolute motion and the consequent recognition that only relative motion has any physical significance. However, it does recognize as preferred class of observers who, are in uniform motion relative to one another, even though it denies that it is meaningful to ask which of them is at rest in any absolute sense. Hence the qualification “special”, the hope being that it would ultimately be superseded by a theory in which all observers are treated as equivalent.
At the time that the special theory was being developed, around the beginning of the 20th century, it was believed that all forces in nature would ultimately be reducible to electro-magnetism and gravitation. With the success of the special theory in resolving the conflicts that had existed between Newtonian Dynamics and Maxwell’s Electromagnetic Theory, it became natural to try to fit gravitation into this new physical frame work. That this proved so difficult seems perhaps more surprising now than it did at that time. It is now realized that the ultimate structure of matter is considerably more complicated than was suspected ninety-three years ago, when the Quantum Theory was still in its infancy and even the Bohr Theory of the atom was still in the future. Although the forces that occur within the atomic nucleus are not yet fully understood, tremendous progress has been made, and underlying it all is the basic framework provided by the special theory of relativity. This is indeed the main strength of the theory. The fact that it predicts modifications of Newtonian Dynamics for particles whose speeds are comparable with that of light is important, but its real achievement has been in providing a foundation on which almost the whole of modern physical theory has been built. However this increasing scope of the special theory has also seemed to increase the apparent perversity of gravitation in refusing to be fitted into this growing structure. James Clerk Maxwell presented the Theory of Electromagnetism. One of the triumphs of the theory was the discovery that light waves are electromagnetic in character. Since all other known wave phenomena required a material medium in which the oscillations were carried, it was postulated that there existed an all-pervading medium, called the aluminiferous ether which carried the oscillations of electromagnetism. It was then anticipated that experiments with light would allow the absolute motion of a body through the ether to be detected. Such hopes were upset by the null result of the famous Michelson-Morely Experiment which attempted to measure the velocity of the earth relative to the ether and found it to be undetectably small. In order to explain this null result, two ad hoc hypotheses were put forward by Lorentz, Poincare and Fitzgerald, namely, the contraction of rigid bodies and slowing down of clocks when moving through the ether. These effects were contained in some simple formulae called the Lorentz transformations. Although this theory was consistent with the observations, it had the philosophical defect that its fundamental assumptions were unverifiable.
In fact essence of the special theory of relativity is contained in the Lorentz transformations however, Einstein was able to derive them from two postulates, and the first being called the Principle of special relativity a principle which Poincare had also suggested independently in 1904 and the second concerning the constancy of the velocity of light. In so doing he was forced to re-evaluate our ideas of space and time and he demonstrated through a number of simple thought experiments that the source of the limitations of the classical theory lay in the concept of simultaneity. Thus although in a sense Einstein found nothing new in that he received the Lorentz transformations his derivation was physically meaningful and in the process revealed the inadequacy of some of the fundamental assumptions of the classical thought.