Albert Einstein’s general theory of relativity has been called the greatest act of thought about nature ever to take place in a person’s head. It explains gravity, motion, matter, energy, space and time, the formation of black holes, the Big Bang, and possibly dark energy. Einstein developed the theory over more than a decade at the start of the 20th century. It went on to inspire Georges Lemaître, Stephen Hawking, and the LIGO team, which searched for the gravitational waves predicted by the theory.

The theory of relativity arose from a contradiction between the laws of motion described by Isaac Newton and the laws of electromagnetism defined by Scottish physicist James Clerk Maxwell. Newton described nature in terms of matter in motion governed by forces that act between objects. Maxwell’s theories concerned the behavior of electric and magnetic fields. Light, he said, was an oscillation through these fields, and he predicted that the speed of light was always constant, regardless of how fast the source was moving.

Measuring the speed of light is not an easy thing to do. Danish astronomer Ole Rømer tried in 1676 by measuring the time delay in the light arriving from Jupiter’s moons. His answer was 25 percent too slow, but he did show that light’s speed was finite. By the 1850s, more accurate measurements had been made. However, in a Newtonian universe, there must also be changes in the speed of light to account for the relative motion of its source and observer. Try as researchers might, no such differences could be measured.

At the end of the 19th century, many believed that physicists had fully figured out the laws of the universe. All that was now needed were more precise measurements. However, even as a child, Einstein was not convinced that physics had been solved. At the age of 16, he asked himself a question: “What would I see if I were sitting on a beam of light?” In the Newtonian context, young Albert would be traveling at the speed of light. Light coming from in front would reach his eyes at twice the speed of light. When looking back, he would see nothing at all. Even though light from behind was traveling at the speed of light, it could never catch up.

## Annus mirabilis

Einstein’s first job was working as a patent clerk in Bern, Switzerland. It afforded him a lot of spare time to devote to private study. The fruit of this solitary work was the Annus Mirabilis (miracle year) of 1905, when he presented four papers. These included two linked discoveries: special relativity and the equivalence of mass and energy, summed up by the equation E=mc^{2}.

## Special relativity

Einstein used thought experiments to develop his ideas, the most significant of which involved two men—one on a speeding train and the other standing on the platform. In one version (below), inside the train, Bob shines a flashlight at a mirror directly above him on the ceiling. He measures the time the light takes to travel to the mirror and back. At the same time, the train is passing the platform at close to the speed of light. From the platform, the stationary observer Pat sees the light beam shine to the mirror and back, but in the time it takes for the beam to travel, the train has moved, meaning that, rather than traveling straight up and down, the beam travels diagonally. To Pat on the platform the light beam has traveled farther, so, since light always travels at the same speed, more time must have passed.

Einstein’s explanation for this took an enormous leap of imagination, which became the basis of special relativity. Speed is a measure of units of distance per units of time. Therefore, the constancy of the speed of light must be due to an inconstancy in the flow of time. Objects observed to be traveling faster through space are moving more slowly through time. Clocks on the station and on the train are ticking at different rates, depending on the frame of reference from which they are observed. On the moving train, Bob sees his clock ticking away as normal, but to the observer Pat on the platform, the train’s clock is moving very slowly.

The passenger on the speeding train will not notice any slowing of time. The mechanisms by which time is measured—such as the swing of a pendulum, the vibration of a quartz crystal, or the behavior of an atom—are physical phenomena obeying universal laws. According to special relativity, laws remain unchanged within the reference frame—the moving train, or any other set of objects moving together.

**“If you can’t explain it to a six year old, you don’t understand it yourself.**” Albert Einstein

## Energy is mass

The impact of this dilation of time has far-reaching effects, which Einstein gradually pieced together into a single general theory of relativity in 1915. One early breakthrough was the discovery of E=mc2, which states that E (energy) is equal to mass (m) multiplied by the square of the speed of light (c). c2 is a very large number—about 90 million billion—and so a small amount of mass contains a huge quantity of energy. This is evident in a nuclear explosion when mass is converted to free energy.

Returning to the train thought experiment, the two observers now throw tennis balls at each other. The balls collide and bounce back to each person (both Pat and Bob have very good aim). If both observers were in the same reference frame, the described motion of the balls would occur because the balls had the same mass and were thrown with the same force. But in this experiment the balls are in different reference frames—one stationary, the other moving at close to the speed of light. Pat would see Bob’s ball moving much more slowly than his own due to the time dilation, yet when they collide, both balls are knocked back to their owners. The only way this could work is if Bob’s slow tennis ball is heavier, or contains more mass, than Pat’s tennis ball.

Therefore, according to special relativity, when matter moves, it becomes more massive. These mass increases can be measured on the everyday, human scale, but are negligible. However, they have a marked effect when objects are moving very quickly. For example, the protons accelerated by the Large Hadron Collider (LHC) particle accelerator travel very close to the speed of light—within 99.999 percent. Additional energy does very little to this speed, and instead boosts mass. At full power, the protons in the LHC are nearly 7,500 times more massive than they were when stationary.

## THE TWIN PARADOX

A result known as the “twin paradox” is illustrated using a pair of newborn twins. One stays on Earth, while another is taken on a rocket on a journey to a star 4 light-years away. The rocket travels at an average velocity of 0.8c, meaning that it returns from its 8-light-year journey on the 10th birthday of the twin who stayed on Earth. However, to the clock on the rocket, it is only the other twin’s 6th birthday. The clock has been in a moving time frame, so has been ticking more slowly.

Relativity insists that the twin on the rocket is also entitled to consider herself at rest, which seems to lead to a paradox—from her point of view, the twin on Earth had been the one moving. The paradox is resolved by the fact that only the twin in the rocket has undergone acceleration, with its consequent time dilation, both on the way out and to change direction and come back. The twin on Earth has remained in one frame of reference, while the twin on the rocket has been in two—one on the way out and another on the way back. Thus, the twins’ situations are not symmetrical, and the twin who stayed at home really is now four years older than her sister.

The twin paradox has been a popular theme in science fiction. In the film The Planet of the Apes, astronauts return to Earth to find that thousands of years have elapsed, and the planet is now ruled by apes. In the film Interstellar, physics consultants were employed to ensure that the time elapsed for each character was correct according to relativity.

*“Each ray of light moves in the coordinate system “at rest” with a definite, constant velocity independent of whether this ray of light is emitted by a body at rest or a body in motion.”**Albert Einstein *

## Speed limit

With the relationship between speed and mass, relativity highlights another basic principle: the speed of light is the upper limit of motion through space. It is impossible for an object with mass—a nuclear particle, spaceship, planet, or star—to travel at the speed of light. As it approaches light speed, its mass becomes almost infinite, time slows nearly to a stop, and it would take an infinite amount of energy to push it to light speed.

To generalize his theory, Einstein linked gravity to his ideas about energy and motion. Taking an object in space and removing all reference points, it is not possible to tell if it is moving. There is no test that can be done to prove that it is. Therefore, from the point of view of any object, or reference frame, it stays still while the rest of the universe moves around it.

## Einstein’s happiest thought

This is easiest to picture if everything is moving at a constant speed. According to Newton’s first law of motion, an object maintains its motion unless a force acts to accelerate it (change its speed or direction). When Einstein included the effects of acceleration in his theory, it led to an insight that he called his “happiest thought”: it was not possible to differentiate why an object accelerated—it could be because of gravity, or it could be another force. The effect of both was the same and could be described by the way the rest of the universe moved around the reference frame.

Einstein had described motion in terms of the links between mass, energy, and time. For a general theory, he needed to add space. It was not possible to understand the path of an object through space without considering its path through time. The result was that mass moves through spacetime, which has a four-dimensional geometry, as opposed to the usual three dimensions (up, down, and side to side) of the everyday concept of space. When an object moves through spacetime, the time dimension dilates, and the space dimensions contract. From the point of view of Pat back at the station, the speeding train’s length is compressed, making it look very squashed and stubby. However, it is all normal to Bob; anything he measures on board will have the same length as when the train was stationary. This is because his means of measurement, such as a ruler, has contracted along with space.

**“The theory of relativity cannot but be regarded as a magnificent work of art.”** Ernest Rutherford

## Warping spacetime

In Einstein’s universe, gravity is recast not as a force but rather the effect of warps in the geometry of spacetime caused by the presence of mass. A large mass, such as a planet, bends space, and so a smaller object, such as a meteor, moving in a straight line through space nearby, will curve toward the planet. The meteor has not changed course—it is still moving along the same line in space; it is just that the planet has bent that line into a curve.

Warps in spacetime can be visualized as balls deforming a rubber sheet, making depressions or “gravity wells.” A large “planet” ball makes a well, and a smaller “meteor” ball will roll into the well. Depending on its trajectory, speed, and mass, the meteor might collide with the planet or roll back up the other side of the well and escape. If the trajectory is just right, the meteor will circle around the planet in an orbit.

The warps created by matter also bend time. Two distant objects—for this explanation, a red star and a blue star—are not moving in relation to one another. They are in different points of space, but at the same point in time, the same “now.” However, if the red star moves directly away from the blue, its passage through time slows compared to the blue star’s. That means the red star shares a “now” with the blue star in the past. If the red star travels directly toward the blue one, its “now” is angled toward the blue star’s future. Consequently, events that are observed simultaneously from one reference frame may appear to occur at different times in another.

## Proof of relativity

Einstein’s physics were initially met with bafflement from most of the scientific community. However, in 1919, the English astronomer Arthur Eddington demonstrated that this new way of describing the universe was indeed accurate. He traveled to the Atlantic island of Principe to observe a full solar eclipse and specifically to look at the background of stars near to the sun. Light from stars travels to Earth along the most direct route, known as the geodesic. In Euclidean geometry (the geometry of Newtonian physics), that is a straight line, but in the geometry of spacetime, a geodesic can be curved. So, starlight shining very close to the edge of the sun passes into the warp created by the star’s mass and follows a bending path. Eddington photographed the stars revealed by the absences of the solar glare. These images showed that the apparent position of the stars had indeed been shifted due to the warping of space, an effect now known as gravitational lensing. Einstein was proved right.

Einstein’s general theory of relativity allows astronomers to make sense of what they observe, everywhere from the very edge of the visible universe to the event horizon of a black hole. Today, the time dilations of relativity are taken into account in GPS technology, while the wavelike contractions of space predicted by relativity have recently been discovered in the LIGO experiment. Other ideas from relativity are also being used in the search for possible answers to the mystery of dark energy.

**“Everything must be made as simple as possible. But not simpler.”** Albert Einstein

**“Time is an illusion.” ** Albert Einstein

## ALBERT EINSTEIN

Einstein was born in Germany but spent his formative years in Switzerland. He was an average student, and then struggled to find teaching work, ending up at the patent office in Bern. After the success of his 1905 papers, Einstein took university posts in Bern, Zurich, and then in Berlin, where he presented his general theory in 1915. With the rise of Nazism in 1933, Einstein moved to the United States, where he settled at Princeton University. There he spent the rest of his days trying to link relativity with quantum mechanics.

He failed to do so, and no one else has succeeded yet either. A leading pacifist voice for many years, in 1939 Einstein was instrumental in alerting Allies to the dangers that Germany might build a nuclear weapon. He declined to be involved in the Manhattan Project that built the first atomic bombs. An avid violinist, Einstein stated that he often thought in music.