Einstein’s Relativity Explained in 4 Simple Steps

What is relativity? Einstein's mind-bending theory explained

When the theory of relativity appeared in the early 1900s, it upended centuries of science and gave physicists a new understanding of space and time. Isaac Newton saw space and time as fixed, but in the new picture provided by special relativity and general relativity they were fluid and malleable.

Who came up with the theory of relativity?

Albert Einstein. He published the first part of his theory — special relativity — in the German physics journal Annalen der Physik in 1905 and completed his theory of general relativity only after another decade of difficult work. He presented the latter theory in a series of lectures in Berlin in late 1915 and published in the Annalen in 1916.

What is special relativity?

The theory is based on two key concepts.

First, the natural world allows no “privileged” frames of reference. As long as an object is moving in a straight line at a constant speed (that is, with no acceleration), the laws of physics are the same for everyone. It’s a bit like when you look out a train window and see an adjacent train appear to move — but is it moving, or are you? It can be hard to tell. Einstein recognized that if the motion is perfectly uniform, it's literally impossible to tell — and identified this as a central principle of physics.

Second, light travels at an unvarying speed of 186,000 miles a second. No matter how fast an observer is moving or how fast a light-emitting object is moving, a measurement of the speed of light always yields the same result.

Starting from these two postulates, Einstein showed that space and time are intertwined in ways that scientists had never previously realized. Through a series of thought experiments, Einstein demonstrated that the consequences of special relativity are often counterintuitive — even startling.

A page of the original manuscripts of the theory of relativity developed by Albert Einstein on display at the Israeli National Academy of Science and Humanities in Jerusalem on March 7, 2010. Uri Lenz / EPA file

If you’re zooming along in a rocket and pass a friend in an identical but slower-moving rocket, for example, you’ll see that your friend’s watch is ticking along more slowly than yours (physicists call this "time dilation").

What’s more, your friend’s rocket will appear shorter than your own. If your rocket speeds up, your mass and that of the rocket will increase. The faster you go, the heavier things become and the more your rocket will resist your efforts to make it go faster. Einstein showed that nothing that has a mass can ever reach the speed of light.

Another consequence of special relativity is that matter and energy are interchangeable via the famous equation E = mc² (in which E stands for energy, m for mass, and c² the speed of light multiplied by itself). Because the speed of light is such a big number, even a tiny amount of mass is equivalent to — and can be converted into — a very large amount of energy. That’s why atomic and hydrogen bombs are so powerful.

What is general relativity?

Essentially, it’s a theory of gravity. The basic idea is that instead of being an invisible force that attracts objects to one another, gravity is a curving or warping of space. The more massive an object, the more it warps the space around it.

For example, the sun is massive enough to warp space across our solar system — a bit like the way a heavy ball resting on a rubber sheet warps the sheet. As a result, Earth and the other planets move in curved paths (orbits) around it.

This warping also affects measurements of time. We tend to think of time as ticking away at a steady rate. But just as gravity can stretch or warp space, it can also dilate time. If your friend climbs to the top of a mountain, you’ll see his clock ticking faster compared to yours; another friend, at the bottom of a valley, will have a slower-ticking clock, because of the difference in the strength of gravity at each place. Subsequent experiments proved that this indeed happens.

What does relativity look like 'under the hood?'

Special relativity is ultimately a set of equations that relate the way things look in one frame of reference to how they look in another — the stretching of time and space, and the increase in mass. The equations involve nothing more complicated than high-school math.

General relativity is more complicated. Its “field equations” describe the relationship between mass and the curvature of space and dilation of time, and are typically taught in graduate-level university physics courses.

Tests of special and general relativity

Over the last century, many experiments have confirmed the validity of both special and general relativity. In the first major test of general relativity, astronomers in 1919 measured the deflection of light from distant stars as the starlight passed by our sun, proving that gravity does, in fact, distort or curve space.

In 1971, scientists tested both parts of Einstein’s theory by placing precisely synchronized atomic clocks in airliners and flying them around the world. A check of the timepieces after the planes landed showed that the clocks aboard the airliners were running a tiny bit slower than (less than one millionth of a second) than the clocks on the ground.

The disparity resulted from the speed of the planes (a special relativity effect) and their greater distance from the center of Earth’s gravitational field (a general relativity effect).

In 2016, the discovery of gravitational waves — subtle ripples in the fabric of spacetime — was another confirmation of general relativity.

Relativity in practice

While the ideas behind relativity seem esoteric, the theory has had a huge impact on the modern world.

Nuclear power plants and nuclear weapons, for example, would be impossible without the knowledge that matter can be transformed into energy. And our GPS (global positioning system) satellite network needs to account for the subtle effects of both special and general relativity; if they didn’t, they’d give results that were off by several miles.

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What is theory of relativity?

Albert Einstein's theory of relativity is actually two separate theories: his special theory of relativity , postulated in the 1905 paper, The Electrodynamics of Moving Bodies and his theory of general relativity , an expansion of the earlier theory, published as The Foundation of the General Theory of Relativity in 1916. Einstein sought to explain situations in which Newtonian physics might fail to deal successfully with phenomena, and in so doing proposed revolutionary changes in human concepts of time, space and gravity.

The special theory of relativity was based on two main postulates: first, that the speed of light is constant for all observers; and second, that observers moving at constant speeds should be subject to the same physical laws. Following this logic, Einstein theorized that time must change according to the speed of a moving object relative to the frame of reference of an observer. Scientists have tested this theory through experimentation - proving, for example, that an atomic clock ticks more slowly when traveling at a high speed than it does when it is not moving. The essence of Einstein's paper was that both space and time are relative (rather than absolute), which was said to hold true in a special case, the absence of a gravitational field. Relativity was a stunning concept at the time; scientists all over the world debated the veracity of Einstein's famous equation, E=mc2, which implied that matter and energy were equivalent and, more specifically, that a single particle of matter could be converted into a huge quantity of energy. However, since the special theory of relativity only held true in the absence of a gravitational field, Einstein strove for 11 more years to work gravity into his equations and discover how relativity might work generally as well.

According to the theory of general relativity, matter causes space to curve. It is posited that gravitation is not a force, as understood by Newtonian physics, but a curved field (an area of space under the influence of a force) in the space-time continuum that is actually created by the presence of mass. According to Einstein, that theory could be tested by measuring the deflection of starlight traveling near the sun; he correctly asserted that light deflection would be twice that expected by Newton's laws. This theory also explained why the light from stars in a strong gravitational field was closer to the red end of the spectrum than those in a weaker one.

For the final thirty years of his life, Einstein attempted to find a unified field theory, in which the properties of all matter and energy could be expressed in a single equation. His search was confounded by quantum theory's uncertainty principle , which stated that the movement of a single particle could never be accurately measured, because speed and position could not be simultaneously assessed with any degree of assurance. Although he was unable to find the comprehensive theory that he sought, Einstein's pioneering work has allowed countless other scientists to carry on the quest for what some have called "the holy grail of physicists."

Einstein’s Relativity Explained in 4 Simple Steps

Albert Einstein’s theory of relativity is famous for predicting some really weird but true phenomena, like astronauts aging slower than people on Earth and solid objects changing their shapes at high speeds.

But the thing is, if you pick up a copy of Einstein’s original paper on relativity from 1905, it’s a straightforward read. His text is plain and clear, and his equations are mostly just algebra—nothing that would bother a typical high-schooler.

That’s because fancy math was never the point for Einstein. He liked to think visually, coming up with experiments in his mind’s eye and working them around in his head until he could see the ideas and physical principles with crystalline clarity. (Read “10 Things You (Probably) Didn’t Know About Einstein.”)

To bring his process to life, National Geographic created an interactive version of one of Einstein’s most famous thought experiments: a parable about lightning strikes as seen from a moving train that shows how two observers can understand space and time in very different ways.

Here’s how Einstein got started on his thought experiments when he was just 16, and how it eventually led him to the most revolutionary equation in modern physics.

1895: Running Beside a Light Beam

By this point, Einstein’s ill-disguised contempt for his native Germany’s rigid, authoritarian educational methods had already gotten him kicked out of the equivalent of high school, so he moved to Zurich in hopes of attending the Swiss Federal Institute of Technology (ETH). (Also see “Why the FBI Kept a 1,400-Page File on Einstein.”)

First, though, Einstein decided to put in a year of preparation at a school in the nearby town of Aarau—a place that stressed avant garde methods like independent thought and visualization of concepts. In that happy environment, he soon he found himself wondering what it would be like to run alongside a light beam.

Einstein had already learned in physics class what a light beam was: a set of oscillating electric and magnetic fields rippling along at 186,000 miles a second, the measured speed of light. If he were to run alongside it at just that speed, Einstein reasoned, he ought to be able to look over and see a set of oscillating electric and magnetic fields hanging right next to him, seemingly stationary in space.

Yet that was impossible. For starters, such stationary fields would violate Maxwell’s equations, the mathematical laws that codified everything physicists at the time knew about electricity, magnetism, and light. The laws were (and are) quite strict: Any ripples in the fields have to move at the speed of light and cannot stand still—no exceptions.

Worse, stationary fields wouldn’t jibe with the principle of relativity, a notion that physicists had embraced since the time of Galileo and Newton in the 17th century. Basically, relativity said that the laws of physics couldn’t depend on how fast you were moving; all you could measure was the velocity of one object relative to another.

But when Einstein applied this principle to his thought experiment, it produced a contradiction: Relativity dictated that anything he could see while running beside a light beam, including the stationary fields, should also be something Earthbound physicists could create in the lab. But nothing like that had ever been observed.

This problem would bug Einstein for another 10 years, all the way through his university work at ETH and his move to the Swiss capital city of Bern, where he became an examiner in the Swiss patent office. That’s where he resolved to crack the paradox once and for all.

1904: Measuring Light From a Moving Train

It wasn’t easy. Einstein tried every solution he could think of, and nothing worked. Almost out of desperation, he began to consider a notion that was simple but radical. Maybe Maxwell’s equations worked for everybody, he thought, but the speed of light was always constant.

When you saw a light beam zip past, in other words, it wouldn’t matter whether its source was moving toward you, away from you, or off to the side, nor would it matter how fast the source was going. You would always measure that beam’s velocity to be 186,000 miles a second. Among other things, that meant Einstein would never see the stationary, oscillating fields, because he could never catch the light beam.

This was the only way Einstein could see to reconcile Maxwell’s equations with the principle of relativity. At first, though, this solution seemed to have its own fatal flaw. Einstein later explained the problem with another thought experiment: Imagine firing a light beam along a railroad embankment just as a train roars by in the same direction at, say, 2,000 miles a second.

Someone standing on the embankment would measure the light beam’s speed to be the standard number, 186,000 miles a second. But someone on the train would see it moving past at only 184,000 miles a second. If the speed of light was not constant, Maxwell’s equations would somehow have to look different inside the railway carriage, Einstein concluded, and the principle of relativity would be violated.

This apparent contradiction left Einstein spinning his wheels for almost a year. But then, on a beautiful morning in May 1905, he was walking to work with his best friend Michele Besso, an engineer he had known since their student days in Zurich. The two men were talking with about Einstein’s dilemma, as they often did. And suddenly, Einstein saw the solution. He worked on it overnight, and when they met the next morning, Einstein told Besso, “Thank you. I’ve completely solved the problem.”

May 1905: Lightning Strikes a Moving Train

Einstein’s revelation was that observers in relative motion experience time differently: it’s perfectly possible for two events to happen simultaneously from the perspective of one observer, yet happen at different times from the perspective of the other. And both observers would be right.

Einstein later illustrated this point with another thought experiment. Imagine that you once again have an observer standing on a railway embankment as a train goes roaring by. But this time, each end of the train is struck by a bolt of lightning just as the train’s midpoint is passing. Because the lightning strikes are the same distance from the observer, their light reaches his eye at the same instant. So he correctly says that they happened simultaneously.

Meanwhile, another observer on the train is sitting at its exact midpoint. From her perspective, the light from the two strikes also has to travel equal distances, and she will likewise measure the speed of light to be the same in either direction. But because the train is moving, the light coming from the lightning in the rear has to travel farther to catch up, so it reaches her a few instants later than the light coming from the front. Since the light pulses arrived at different times, she can only conclude the strikes were not simultaneous—that the one in front actually happened first.

In short, Einstein realized, simultaneity is what’s relative. Once you accept that, all the strange effects we now associate with relativity are a matter of simple algebra.

Einstein dashed off his ideas in a fever pitch and sent his paper in for publication just a few weeks later. He gave it a title—“On the Electrodynamics of Moving Bodies”—that spoke to his struggle to reconcile Maxwell’s equations with the principle of relativity. And he concluded it with a thank you to Besso (“I am indebted to him for several valuable suggestions”) that guaranteed his friend a touch of immortality.

September 1905: Mass and Energy

That first paper wasn’t the end of it, though. Einstein kept obsessing on relativity all through the summer of 1905, and in September he sent in a second paper as a kind of afterthought.

It was based on yet another thought experiment. Imagine an object that’s sitting at rest, he said. And now imagine that it spontaneously emits two identical pulses of light in opposite directions. The object will stay put, but because each pulse carries off a certain amount of energy, the object’s energy content will decrease.

Now, said Einstein, what would this process look like to a moving observer? From her perspective, the object would just keep moving in a straight line while the two pulses flew off. But even though the two pulses’ speed would still be the same—the speed of light—their energies would be different: The pulse moving forward along the direction of motion would now have a higher energy than the one moving backward.

With a little more algebra, Einstein showed that for all this to be consistent, the object not only had to lose energy when the light pulses departed, it had to lose a bit of mass, as well. Or, to put it another way, mass and energy are interchangeable.

Einstein wrote down an equation that relates the two. Using today’s notation, which abbreviates the speed of light using the letter c, he produced easily the most famous equation ever written: E = mc2.