• ### Unit 8: Special Relativity

The physical descriptions we have studied to this point were based on a notion of absolute space and time. A model for this point of view was that space is filled everywhere by a continuous medium called the ether. Light and other forms of electromagnetic radiation were waves in this ether, analogous to sound waves in air. All other phenomena were to be understood as various manifestations of Maxwell's electromagnetism, which was originally based on a mechanical model of ether. It seemed reasonable that the 19th Century "theory of everything" could be tied down by measuring the "elastic" properties of the ether.

Toward the end of the 1800s, however, this model became associated with more and more hastily patched cracks. The detailed history of the gradual realization that ether models were not quite right is complex and technical. However, there is one rather clear indication of trouble. In 1887, Albert Michelson and Edmund Morley of the Case Institute (now Case Western University) performed an experiment using an optical interferometer in which they compared the speed of light in two beams traveling at right angles to each other. If the speed of light relative to the ether was always the same, the measured speed of light would be larger or smaller depending on the direction the experiment was traveling through the ether. The motion of the Michelson-Morley experiment was provided by the rotation of the Earth on its axis and the orbital motion of the Earth around the Sun, as well as the absolute velocity (if any) of the Sun relative to the ether.

They expected to see both diurnal changes and yearly changes in the relative velocities of light in the two paths. True, the changes expected by classical ether theory were small (on the order of 0.01% of the velocity of light), but the Michelson-Morley interferometer was able to detect velocity changes about 6-7 times smaller. To the surprise of all, there were no changes whatsoever observed. This experiment was widely repeated, using constantly improving equipment – a new version of the experiment carried out in 2002 established that the velocity of light is constant to better than 1 part in 1,015 – one of the most precise physical measurements ever accomplished.

The explanation of the Michelson-Morley null result was length contraction, as developed by Hendrik Lorentz and George Francis FitzGerald. Length contraction explained the Michelson-Morley result, the idea being that matter is held together by electromagnetic forces (true), and so the actual size of objects will change with motion through the ether (false). In the end, it was Albert Einstein's formulation of the theory of Special Relativity that gave us a consistent explanation of all such phenomena. His primary postulate was to accept that the speed of light and the laws of physics are constant in all reference frames – including reference frames that are in motion. Oddly, despite the fact that Einstein's theory completely explained the Michelson-Morley result, he took no motivation for his theory from that experiment.

Completing this unit should take you approximately 10 hours.

• ### 8.1: Introduction to Relativity

Einstein stated that his motivation for developing the special theory of relativity was Maxwell's theory of electromagnetism – the same theory we learned about as the foundation of electromagnetic waves. Einstein's theory made it possible for physicists to accept the reality of electric and magnetic fields in their own right, whereas the ether theory interpreted those fields as "deformations" of the ether as a medium.

To follow Einstein's thinking, recall that Maxwell had predicted the speed of light to have a universal value called c, and that was done without reference to any material objects – the calculation worked entirely in empty space. Einstein asked what this apparent universality of c meant for material objects that are in motion while they send and receive light pulses. Essentially, Einstein elevated the constancy of c (in vacuum) to the level of a law of nature.

• ### 8.2: Simultaneity, Time Dilation, and Length Contraction

The revolutionary aspect of Einstein's theory is that it translated a fact from electrodynamics to the wider world of physics by re-formulating the foundations of Newton's classical mechanics itself. The biggest contradiction to Newton's worldview concerns the nature of time and space themselves.

• ### 8.3: Relativistic Momentum and Energy

From the point of view of a 19th century physicist, perhaps the most consequential achievement of Newton's classical mechanics was the idea that conservation laws exist. In particular, the quantities momentum and energy would never even have received their own name if it were not for the fact that they obey their own conservation laws: whenever objects interact with each other, they can exchange momentum and energy – but they can never create or destroy either of those quantities.