Einstein's Two Postulates and the Power of Thought Experiments

A teenager chases a light beam

Einstein later wrote that, at about age 16, he wondered what he would see if he could run alongside a beam of light at speed c. The wave would look frozen: electric and magnetic fields varying in space but not changing in time. Yet Maxwell's equations allow no such thing. A frozen light wave is impossible.

So either Maxwell's equations fail for a fast-moving observer, or no observer can ever catch up to light. Ten years later, Einstein built a theory on the second answer. He did it mostly in his head, with thought experiments: imagined situations worked out carefully using physical laws. This lesson is about the two simple statements at the heart of that theory, and why they were so radical.

The magnet and the conductor

Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" opens with another thought experiment. Move a magnet toward a coil of wire and a current flows. Move the coil toward the magnet instead, at the same relative speed, and exactly the same current flows. Yet the physics of the time explained the two cases differently: in one, a changing magnetic field creates an electric field; in the other, the magnetic force acts on moving charges in the wire.

To Einstein, giving two different explanations for one observed result was a sign that something was wrong. Only the relative motion of the magnet and coil seemed to matter. That suggested the principle of relativity should apply to electricity and magnetism too, not just to mechanics.

The two postulates (1905)

Postulate 1, the principle of relativity: The laws of physics are the same in all inertial frames of reference.

Postulate 2, the constancy of the speed of light: Light in a vacuum travels at the same speed, c = 3.00 × 10⁸ m/s, in every inertial frame, regardless of the motion of the source or of the observer.

Postulate 1 extends Galileo's principle from mechanics to all of physics, including Maxwell's equations. Postulate 2 follows from it: if Maxwell's equations hold in every inertial frame, then every inertial observer must measure light at the speed c those equations predict.

Each statement sounds harmless. Together they are explosive, because they contradict the Galilean velocity rule u = u′ + v. If a spacecraft moving at 0.60c sends a light pulse forward, Galileo says Earth measures 1.60c. Einstein says Earth measures c, and so does the crew. Both cannot be right.

What has to give?

Speed is distance divided by time. If two observers moving relative to each other measure the same speed for the same light pulse, then they must disagree about distances, about times, or both. Einstein realized that Newton's assumptions of absolute space and absolute time had never been tested at speeds near c. He dropped them. The consequences fill the rest of this unit:

• Simultaneity is relative: two events at the same time for one observer can happen at different times for another (lesson 4).
• Moving clocks run slow: time dilation (lesson 5).
• Moving objects are shorter: length contraction (lesson 7).
• Velocities do not simply add, and nothing with mass reaches c (lessons 9 and 10).
• Mass is a form of energy: E = mc² (lesson 11).

And the ether? With postulate 2, light needs no special frame, so the ether is unnecessary. Einstein wrote that introducing a 'light ether' would prove superfluous.

Evidence that c is the same for everyone

• Michelson–Morley (1887) and its many repeats: no difference in light speed along different directions as Earth moves (lesson 2).
• Double stars: in 1913 Willem de Sitter argued that if light from an approaching star moved faster than light from a receding one, the images of orbiting double stars would be badly scrambled. Their orbits look regular, so light's speed does not depend on the speed of its source.
• Fast-moving sources: in 1964 at CERN, physicists timed gamma rays given off by neutral pions travelling at more than 0.999c. Galileo would predict nearly 2c. The gamma rays travelled at c.

Today the second postulate is built into the definition of the metre: since 1983, the metre has been defined as the distance light travels in a vacuum in 1/299 792 458 of a second, so c is exactly 299 792 458 m/s.