Special Relativity

The Puzzle

By 1900 physics had two magnificent theories that disagreed. Newton's mechanics said that speeds simply add: walk forward on a moving train and you move faster relative to the ground. Maxwell's theory of electromagnetism said that light travels at one fixed speed, $c$, with no mention of who is measuring. Most physicists assumed light moved through an invisible medium, the ether, and that $c$ was its speed relative to that medium. Experiments kept failing to find any sign of it.

The Two Postulates

In "On the Electrodynamics of Moving Bodies," received on 30 June 1905, Einstein took both theories at their word. He assumed:

• The laws of physics are the same in every frame of reference that moves at a steady velocity.
• The speed of light in empty space is the same for all such observers, whatever the motion of its source.

Everything else follows from holding both to be true at once. No ether is needed.

What Follows

Simultaneity is relative. Two events that happen at the same time for one observer can happen at different times for another who is moving. There is no universal "now."

Moving clocks run slow. A clock moving past you ticks more slowly than your own, by the factor $\gamma$. This is time dilation:

Moving objects are shortened along their direction of travel, an effect called length contraction:

At everyday speeds $\gamma$ is so close to 1 that nobody notices. At 87 percent of the speed of light it reaches 2. As a speed approaches $c$, $\gamma$ grows without limit, which is why nothing with mass can reach the speed of light.

How It Was Confirmed

• Particles called muons, created high in the atmosphere, should decay long before reaching the ground. They arrive anyway, because their clocks run slow from our point of view.
• At its design energy, protons in the Large Hadron Collider travel at 99.9999991 percent of the speed of light. The machine would not work if it were designed with Newton's laws.

What People Get Wrong

• "Everything is relative" is not what the theory says. The speed of light and the spacetime interval between events are absolute; that is the whole point.
• Hendrik Lorentz and Henri Poincaré already had the equations. Einstein's contribution was to derive them from two principles and to accept what they mean: time itself is not universal.
• "Special" refers to the special case of steady motion without gravity. Removing that restriction took Einstein another ten years.

Where It Stands

Special relativity is not a hypothesis under test so much as the working language of modern physics. In 1908 Hermann Minkowski, once Einstein's mathematics teacher, recast it as the geometry of a single four-dimensional spacetime, the form in which it is used today.