The Postulates of Relativity

In 1905 Albert Einstein took two simple-sounding statements seriously and followed them wherever they led. They led to moving clocks running slow, moving rods shrinking, and E = mc². Everything in this chapter follows logically from those two statements.

The principle of relativity#

Throughout this chapter, “frame” means an inertial frame: one moving with constant velocity relative to another inertial frame. Drop a stone on a station platform so it lands on your left foot; do the same in a train gliding smoothly at 120 km/h, and it again lands on your left foot. No experiment inside a smoothly moving train can tell you whether it is moving or standing at the platform, as long as it doesn’t speed up, slow down or turn.

For mechanics this follows from Newton’s laws: F = ma holds in the same form in every inertial frame, so identical experiments give identical results. There is no special “at rest” frame: you may call either frame stationary and the other moving.

A problem with light#

Maxwell’s equations predict that electromagnetic waves, including light, travel in vacuum at c = 1/√(μ₀ε₀) ≈ 3 × 10⁸ m/s. If Maxwell’s laws hold in the same form in every frame, then light must travel at c in every frame. Experiments say it does. That leads to a strange bookkeeping problem.

Suppose A, B and a light pulse W start together at t = 0. B moves right at c/2 relative to A; W moves right at c. Each observer writes down distances over time:

Common sense says A-to-W should equal A-to-B plus B-to-W, but here A-to-W equals B-to-W even though B has moved. Something about our measuring tools must differ: perhaps 1 s on A’s clock is not 1 s on B’s, or A’s metre is not B’s metre.

There are only two ways out:

1. Maxwell’s laws hold in every frame, and our ideas of time and length must change; or
2. Maxwell’s laws take different forms in different frames, so experiments with electricity, magnetism or light could reveal whether a train is moving.

Experiments rule out the second. The most famous, by Michelson and Morley (1887), tried to measure the Earth’s motion through the supposed “ether” that carried light waves. It found nothing, one of the most important null results in physics.

Einstein’s postulates#