89 Einstein’s Postulates

Scientific theories are not collections of unrelated equations. Instead, they are logical frameworks built from a small set of fundamental assumptions called postulates. Once these postulates are accepted, mathematical reasoning is used to derive predictions that can be tested experimentally.

You have already encountered this approach in mathematics. For example, geometry and trigonometry are based on axioms from which more complicated relationships are derived. Every theorem ultimately traces back to these foundational statements.

Physics follows the same strategy, with one crucial difference: the postulates must describe the real world. No matter how elegant a theory may be, it is accepted only if its predictions agree with experimental evidence.

In 1905, Albert Einstein proposed two remarkably simple postulates that became the foundation of special relativity. Although these assumptions appear straightforward, they lead to revolutionary conclusions about space, time, energy, and motion.

Einstein's First Postulate

The first postulate concerns reference frames, which are coordinate systems used to describe the positions and motions of objects.

Every measurement of velocity is made relative to some reference frame. For example:

• The speed of a car is measured relative to the road.
• The trajectory of a baseball is measured relative to the Earth.
• The orbit of a planet is measured relative to its star.

Some reference frames are simpler than others. The simplest are those that move at constant velocity without accelerating or rotating. These are known as inertial reference frames.

Newton's First Law of Motion is valid in every inertial frame. In contrast, accelerating or rotating reference frames require the introduction of additional fictitious forces, such as the centrifugal force or Coriolis force, to explain observed motion.

For example, while riding in an airplane cruising at constant speed and altitude, physics experiments behave almost exactly as they do in a laboratory on Earth. However, during takeoff or landing, passengers feel pushed backward or forward because the airplane is accelerating, making it a non-inertial reference frame.

Einstein recognized that no inertial frame should be considered fundamentally special. The laws of physics should have exactly the same form in every inertial reference frame.

This statement has profound consequences. It means that there is no preferred frame of reference and no experiment performed entirely within an inertial frame can determine whether that frame is "truly at rest" or moving at constant velocity.

Einstein's Second Postulate

The second postulate concerns one of the most familiar yet mysterious phenomena in nature: light.

During the nineteenth century, James Clerk Maxwell developed the equations of electromagnetism, which predicted that electromagnetic waves travel through a vacuum at a speed of

However, Maxwell's equations did not specify the reference frame in which this speed was measured.

Classical mechanics suggested that velocities should simply add together. For example, if you walk forward inside a moving train, your speed relative to the ground equals the speed of the train plus your walking speed.

If light behaved in the same way, observers moving at different speeds would measure different values for the speed of light.

Einstein realized that this possibility created a contradiction with Maxwell's equations. If an observer could travel alongside a light wave at exactly the speed of light, the electromagnetic wave would appear frozen in space. Maxwell's equations do not permit such stationary electromagnetic waves in a vacuum.

Einstein therefore concluded that the problem was not Maxwell's theory—it was the classical rule for adding velocities.

The unavoidable conclusion is that every inertial observer measures exactly the same speed of light in a vacuum, regardless of the motion of the source or the observer.

The Michelson-Morley experiment, performed in 1887, was originally designed to detect Earth's motion through a hypothetical medium called the luminiferous ether. Surprisingly, no such motion was observed. The measured speed of light remained the same regardless of Earth's direction of motion around the Sun.

Although many scientists attempted to explain these results while preserving classical mechanics, Einstein instead accepted the experimental evidence and built a new theory upon it.

Together, Einstein's two postulates require a complete revision of our understanding of space and time. In the following sections, we will see that quantities once thought to be absolute—such as time intervals and distances—depend on the relative motion between observers.