Postulates of Relativity

Einstein based his theory of relativity on two very simple postulates:

What is a reference frame? Any nonaccelerating frame in which an observation can be made.

The first one of these postulates should not raise any objections. In its motion around the Sun the Earth moves through space with a speed of more than 29 km/s (= 2$\pi\cdot$ 149 Million km / year). Since we are moving very nearly in a circle, each 6 month our velocity vector reverses direction. But we still expect that a physics measurement is independent of the season it was made in!

The second postulate explains what Michelson and Morley measured. However, this is not quite so easy to digest. Let's conduct a thought experiment: You fly in a rocket through space with a speed of c/2,directly towards Earth. Now you shine a laser in forward direction. The light of the laser has a speed c, according to Einstein. Naively, and with what we know about velocity addition so far, we would expect that the light of the laser has a speed of c+c/2 = 1.5c when observed on Earth. Not! Einstein's second postulate says that the speed of light as seen on Earth is still c. Quite amazing. This leads to all kinds of interesting and borderline unbelievable consequences. All of them have, however, been experimentally verified by now. And so we now know that this theory is correct. We can never think of space and time the same way again!

The speed of light, c, obviously plays a very special role in the theory of relativity. While we are at it, we define two very useful dimensionless quantities:

$\beta$ is the ratio of the speed of an object, v, to that of light. $\gamma$ is always larger or equal to unity.

A philosophical note: Sometimes people argue that everything is relative, that there is no absolute truth any more. And they justify it with Einstein's theory. Nothing could be more wrong! Instead Einstein introduced a new absolute truth that was previously unknown with his postulates.

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