Special Relativity Study Materials

Light cone (Image Credit: Wikimedia Commons)

Introduction:

One of the greatest triumphs of Maxwell's electromagnetic theory (c. 1864) was the explanation of light as an electromagnetic wave. But a question arises; Waves in what? In conformity with the mechanistic view of nature then prevailing, it seemed imperative to postulate the existence of a medium—the ether—which would serve as a carrier for these waves. This led to the most urgent physical problem of the time: the detection of the earth's motion through the ether.

One of the many experiments were devised for this purpose. Michelson and Morley (1887), looked for a directional variation in the velocity of light on Earth. Fizeau (1860), Mascart (1872), and later Lord Rayleigh (1902), looked for an expected effect of the earth's motion on the refractive index of certain dielectrics. And Trouton and Noble (1903) tried to detect an expected tendency of a charged plate capacitor to face the 'ether drift'. All of them failed. The facile explanation that the earth might drag the ether along with it only led to other difficulties with the observed aberration of starlight, and could not resolve the problem. 

In order to explain nature's apparent conspiracy to hide the ether drift, Lorentz developed a theory of the ether that was eventually based on two ad hoc hypotheses: the longitudinal contraction of rigid bodies and the slowing down of clocks ('time-dilation') when moving through the ether at a speed v, both by a factor (1 - v^2/c^2)^{1/2}, where c is the speed of light. This would so affect every apparatus designed to measure the ether drift as to neutralize all expected effects.
In 1905, in the middle of the development, Einstein proposed the principle of relativity which is now justly associated with the name. Actually Poincaré had discussed essentially the same principle during the previous year, but it was Einstein who first recognized its full significance and brilliant use. In it, he elevated the complete equivalence of all inertial frames to the status of axiom or principle, for which no proof or explanation is to be sought. On the contrary, it explains the failure of all the ether-drift experiments, much as the principle of energy conservation explains a priori (i.e. without the need for a detailed examination of the mechanism) the failure of all attempts to construct perpetual motion machines.

(Image Credit: Wikimedia Commons)

At first Einstein's relativity principle seems to be no more than a whole-hearted acceptance of  the null results of all the ether-drift experiments. But by ceasing to look for special explanations of those results, and using them rather as the empirical evidence for a new principle of nature, Einstein had turned the tables: predictions could be made. The situation can be compared to that obtaining in astronomy at the time when Ptolemy's intricate geocentric system (corresponding to Lorentz's 'aetherocentric' theory) gave way to the ideas of Copernicus, Galileo, Newton. In both cases the liberation from a venerable but inconvenient reference frame ushered in a revolutionary clarification of physical thought, and consequently led to the discovery of a host of new and unexpected results. 

Soon a whole theory based on Einstein's principle (and on a 'second axiom' asserting the invariance of the speed of light) was in existence, and this theory is called special relativity. Its programme was to modify all the laws of physics, where necessary, so as to make them equally valid in all inertial frames. For Einstein's principle is really a metaprinciple: it puts constraints on all the laws of physics. The modifications suggested by the theory (especially in mechanics), though highly significant in many modern applications, have negligible effect in most classical problems, which is of course why they were not discovered earlier. However, they were not exactly needed empirically in 1905 either. This is a beautiful example of the power of pure thought to leap ahead of the empirical frontier—a feature of all good physical theories, though rarely on such a heroic scale. With that being said, we present to all of you the necessary course materials found at the WWW domain to study/lean special relativity. 

Lecture Videos:

• A course on special relativity by Prof. Brian Greene, at World Science U.
• Special relativity lectures by Prof. Leonard Susskind, at Stanford University. Lectures are mistakenly labeled as Quantum Entanglements: Part 3.
• Prof. Leonard Susskind's lectures on special relativity from his course; "The Theoretical Minimum".
• Lectures on special relativity by Prof. Shiva Prasad, Department of Physics, IIT Bombay. 

Lecture Notes:

• Virginia Tech's lecture notes and practise problems on special relativity. 
• Some precious lecture notes, example problems, etc., on special relativity.
• 129A Lecture Notes on special relativity. 
• Lecture notes on special relativity based on Prof. Leonard Susskind's lectures.
• A Wikibook on special relativity which is very good.
• "Reflections on Relativity" by Kevin Brown is also very good.
• Lecture notes on special relativity by Prof. David W. Hogg. 

References:

1. Introduction to Special Relativity, Wolfgang Rindler, pp. 1-2