Imagine you are on a smooth, quiet train with the blinds down. Can you tell whether it is moving? Drop a ball and it falls straight down; pour a drink and it lands in the glass. Galileo made the same point in 1632 with a ship's cabin, full of flies, fish and dripping water, all behaving exactly as on dry land. The laws of motion work the same way for everyone moving at a steady speed in a straight line, so no experiment inside can reveal that steady motion. This is the principle of relativity. Albert Einstein's great step was to take it more seriously than anyone before him.

A puzzle about light

Maxwell's equations gave a single speed for light. But a speed relative to what? Most physicists assumed that light traveled through an invisible medium called the ether, as sound travels through air. If so, the Earth's motion through the ether should make light seem slightly faster in some directions than in others, like a headwind and a tailwind. In 1887 Albert Michelson and Edward Morley in Cleveland built a very sensitive instrument to detect the difference. The Michelson-Morley experiment found no difference in the speed of light in any direction. The result puzzled physicists for nearly two decades.

Special relativity

In 1905 Einstein, then a 26 year old clerk at the Swiss patent office in Bern, published his answer. He started from two postulates. First, the laws of physics are the same for all observers moving steadily. Second, the speed of light in a vacuum is the same for every observer, however fast they or the light source are moving. Each statement sounds simple. Together they have startling consequences: if the speed of light cannot change, then measurements of time and space must.

Time dilation means that a moving clock runs slow as measured by an observer it is moving past. Length contraction means that a moving object is measured as shorter along its direction of motion. Neither effect is noticeable at everyday speeds, but both grow large near the speed of light. Even "at the same time" loses its absolute meaning: two events that happen at the same moment for one observer may happen at different moments for another moving past.

None of this is an illusion. Muons are particles created when cosmic rays strike the upper atmosphere. They decay in about two millionths of a second, on average, which at their speed should let very few survive the trip to the ground. Yet many arrive, because their fast motion slows their decay as measured from Earth. Particle accelerators confirm the same effect every day.

In a short paper later in 1905 Einstein showed that mass and energy are equivalent, so a small amount of mass corresponds to an enormous amount of energy. That is the meaning of the famous equation E = mc², where c is the speed of light. Relativity also shows that no object with mass can be pushed all the way to the speed of light, since that would take an infinite amount of energy.

General relativity

Special relativity left out gravity. Einstein worked on the problem for a decade, starting from what he later called the happiest thought of his life: a person falling freely does not feel their own weight. The equivalence principle says that the effects of gravity cannot be told apart from the effects of acceleration. In a windowless rocket speeding up in deep space, you would feel pressed to the floor just as you do on Earth.

In 1915 Einstein completed the general theory of relativity. In it, gravity is not a force pulling across space, but the curving of space and time by mass and energy. Planets and falling apples follow the straightest possible paths through curved spacetime. The astronomy and scientific method courses tell how the theory passed its early tests on starlight and the orbit of Mercury. Another prediction is that clocks run slower deeper in a gravitational field, so a clock on the ground floor ticks very slightly slower than one in the attic. A third is gravitational waves, ripples in spacetime itself. The LIGO detectors in the United States first recorded gravitational waves in September 2015, from two black holes merging more than a billion light years away. The discovery was announced in 2016, a century after Einstein predicted such waves.

Worked example: relativity in your pocket

The Global Positioning System relies on about 30 satellites carrying atomic clocks. Your phone works out where it is by comparing the arrival times of their signals. Both kinds of relativity matter. The satellites move at about 14,000 kilometers per hour, so special relativity makes their clocks lose about 7 millionths of a second per day compared with clocks on the ground. They also orbit about 20,000 kilometers up, where gravity is weaker, so general relativity makes them gain about 45 millionths of a second per day. The net result is a gain of about 38 millionths of a second each day.

That sounds trivial, but radio signals travel about 300 meters in a millionth of a second. Left uncorrected, the errors in position would build up by roughly 10 kilometers a day. Engineers therefore set the satellite clocks to tick very slightly slow before launch. Each time a map app finds you, it quietly confirms Einstein.