Einstein’s Postulates

The first postulate upon which Einstein based the theory of special relativity relates to reference frames. All velocities are measured relative to some frame of reference. For example, a car’s motion is measured relative to its starting point or the road it is moving over, a projectile’s motion is measured relative to the surface it was launched from, and a planet’s orbit is measured relative to the star it is orbiting around. The simplest frames of reference are those that are not accelerated and are not rotating. Newton’s first law, the law of inertia, holds exactly in such a frame.

The laws of physics seem to be simplest in inertial frames. For example, when you are in a plane flying at a constant altitude, speed, and direction, physics seems to work exactly the same as if you were standing on the surface of the Earth. Galileo illustrated this principle of relativity by imagining observations below deck on a ship: falling drops, swimming fish, and flying insects behave the same whether the ship is at rest or moving steadily in a straight line. Mechanical experiments within the ship cannot distinguish these states of motion. Einstein extended this principle from mechanics to all laws of physics, including electricity and magnetism, in his first postulate of special relativity.

The first postulate does not mean that different observers measure the same values for every physical quantity. An object at rest in one inertial frame can be moving in another, so observers in these frames assign it different velocities, momenta, and kinetic energies. What remains the same is the form of the laws relating these quantities: each observer uses the same laws to describe the motion.

The second postulate of special relativity deals with the speed of light. Late in the 19th century, the major tenets of classical physics were well established. Two of the most important were the laws of electricity and magnetism and Newton’s laws. In particular, Maxwell’s equations predict electromagnetic waves that travel at $c=3.00\times {10}^8\text{m/s}$ in a vacuum. Light is one such electromagnetic wave.

Applying this prediction in every inertial frame contradicts the intuitive results that come from our experience with classical relativity. If a baseball pitcher throws a ball backward from the bed of a moving truck, we on the ground expect to see that ball moving more slowly. For example, if the ball is thrown backward at 60 mph relative to the truck and the truck is moving forward at 20 mph relative to the ground, we would see the ball moving backward at 40 mph. But if Maxwell’s equations apply equally in the spaceship’s frame and Earth’s frame, light from a laser pointed backward aboard a spaceship moving forward at $0.2c$ relative to Earth must still travel backward at $c$ relative to Earth, not $0.8c$. A common approach at the time was to assign light’s predicted speed to a particular frame: that of a proposed light-carrying medium called the luminiferous aether.

Scientists were already familiar with mechanical waves, such as sound, that traveled through a medium. They therefore assumed that light also traveled through a medium. This proposed aether had to pervade even apparently empty space, since light could travel through a vacuum. Light was assumed to travel at speed $c$ relative to the aether. Earth’s motion through a stationary aether should therefore produce differences in light travel times along different directions. In 1881, the American physicist A. A. Michelson used an interferometer to compare light travel times in perpendicular directions. In 1887, he and E. W. Morley repeated the experiment with improved precision. The results of their measurements were startling.

The experiment did not reveal the differences in light travel times expected from Earth’s motion through a stationary aether. For a number of years, scientists tried to reconcile this result with the proposed light-carrying medium while retaining the Newtonian understanding of space and time. The difficulty was explaining why Earth’s motion through that medium could not be detected.

In 1905, Einstein published his first paper on special relativity, “On the Electrodynamics of Moving Bodies”. In this paper, he made the bold assumption that it was not Maxwell’s newer equations of electromagnetism that needed correction, but the assumptions about space and time underlying Newton’s laws. This bold choice was expressed in his second postulate of special relativity.

These two postulates are the starting points from which we derive the results of special relativity. When their consequences conflict with familiar expectations, we retain the postulates and reconsider those expectations. We find that observers in relative motion can disagree about elapsed times and measured lengths, and that mass and energy are related in ways Newtonian physics did not anticipate. The following sections explore these consequences.