# Special Relativity

Table of Contents

In 1905, Albert Einstein published (among other things) a paper called “On the Electrodynamics of Moving Bodies” in the journal Annalen der Physik. The paper presented the theory of special relativity, based upon two postulates:

**Einstein’s Postulates**

There were two key postulates:

- Principle of Relativity (First Postulate): The laws of physics are the same for all inertial reference frames.
- Principle of Constancy of the Speed of Light (Second Postulate): Light always propagates through a vacuum (i.e. empty space or “free space”) at a definite velocity, c, which is independent of the state of motion of the emitting body.

See Albert Einstein and His introduction to the Concept of Relativity.

The paper presents a more formal, mathematical formulation of the postulates. The phrasing of the postulates is slightly different from textbook to textbook because of translation issues, from mathematical German to comprehensible English.

The second postulate is often mistakenly written to include that the speed of light in a vacuum is c in all frames of reference. This is a derived result of the two postulates, rather than part of the second postulate itself.

The first postulate is pretty much common sense. The second postulate, however, was the revolution. Einstein had already introduced the photon theory of light in his paper on the photoelectric effect (which rendered the ether unnecessary). The second postulate, therefore, was a consequence of massless photons moving at the velocity c in a vacuum. The ether no longer had a special role as an “absolute” inertial frame of reference, so it was not only unnecessary but qualitatively useless under special relativity.

As for the paper itself, the goal was to reconcile Maxwell’s equations for electricity and magnetism with the motion of electrons near the speed of light. The result of Einstein’s paper was to introduce new coordinate transformations, called Lorentz transformations, between inertial frames of reference. At slow speeds, these transformations were essentially identical to the classical model, but at high speeds, near the speed of light, they produced radically different results.

**Effects of Special Relativity**

Special relativity yields several consequences from applying Lorentz transformations at high velocities (near the speed of light). Among them are:

- Time dilation (including the popular “twin paradox”)
- Length contraction
- Velocity transformation
- Relativistic velocity addition
- Relativistic doppler effect
- Simultaneity & clock synchronization
- Relativistic momentum
- Relativistic kinetic energy
- Relativistic mass
- Relativistic total energy

In addition, simple algebraic manipulations of the above concepts yield two significant results that deserve individual mention.

**Mass-Energy Relationship**

Einstein was able to show that mass and energy were related, through the famous formulaE=mc^{2}. This relationship was proven most dramatically to the world when nuclear bombs released the energy of mass in Hiroshima and Nagasaki at the end of World War II.

**Speed of Light**

No object with mass can accelerate to precisely the speed of light. A massless object, like a photon, can move at the speed of light. (A photon doesn’t actually accelerate, though, since it always moves exactly at the speed of light.)

But for a physical object, the speed of light is a limit. The kinetic energy at the speed of light goes to infinity, so it can never be reached by acceleration.

Some have pointed out that an object could in theory move at greater than the speed of light, so long as it did not accelerate to reach that speed. So far no physical entities have ever displayed that property, however.

**Adopting Special Relativity**

In 1908, Max Planck applied the term “theory of relativity” to describe these concepts, because of the key role relativity played in them. At the time, of course, the term applied only to special relativity, because there was not yet any general relativity.

Einstein’s relativity was not immediately embraced by physicists as a whole, because it seemed so theoretical and counterintuitive. When he received his 1921 Nobel Prize, it was specifically for his solution to the photoelectric effect and for his “contributions to Theoretical Physics.” Relativity was still too controversial to be specifically referenced.

Over time, however, the predictions of special relativity have been shown to be true. For example, clocks flown around the world have been shown to slow down by the duration predicted by the theory.