Albert Einstein is history’s most iconic scientist. His General Theory of Relativity plugged the gaps in Newton’s work and described what gravity is—or, perhaps more accurately, it described what gravity is not: it refuted that it was a force at all. Einstein explained gravity by explaining it away.
Einstein was intrigued by the “ghosts” that had appeared in Newton’s gravitational machinery during the 19th century, as measurements became more precise. Astronomers who charted the positions of the planets watched Mercury and Uranus continually drift from the orbits predicted by Newtonian mathematics. Initially, the astronomers thought that undiscovered planets must be pulling the errant planets out of their orbits, and in the case of Uranus they were correct. On September 23, 1846, Neptune was discovered at almost exactly the position calculated for it by Urbain LeVerrier of the Paris Observatory. This was the first time a celestial object had been predicted to exist from a calculation. In a sense, it was the first time that astronomers postulated the existence of a piece of “dark matter”—something unseen that betrays its presence by the gravitational effect it has on nearby celestial objects. The success of Neptune’s discovery began a flurry of activity to find the planet that was now firmly thought to be pulling Mercury from its path. So certain were astronomers that a planet must exist between Mercury and the Sun they even named it: Vulcan.
However, there is no planet Vulcan. Instead, the movement of Mercury is due to an unexpected facet of gravity that Newton’s theory does not take into account. Only when Einstein set about explaining the nature of gravity did he come across the remarkable reason for Mercury’s motion.
Einstein’s great insight was the concept of the “space–time continuum.” This is a fabric—for want of a better word—that stretches through all space, in all directions, and includes time as the fourth dimension. In Newton’s theory of gravity, both space and time were imagined to be rigid frameworks, absolute and invariant; they were also quite separate concepts. In general relativity, space and time constitute a flexible continuum that can be stretched and warped by the presence of matter and energy. The warping of space–time can affect time as well as space, leading to a number of brain-bending consequences such as time dilation (see Can We Travel Through Time and Space?).
Einstein used the idea of the space–time continuum to explain gravity, stating that it was an effect created by the warping of space–time in the presence of matter. Think of a suspended sheet of rubber onto which is placed a heavy object. The object warps the rubber sheet, forming a curved depression. Any smaller object that is placed nearby will roll down the depression, spiral around the heavy object and eventually collide with it. This is analogous to the way in which gravity acts. In this scenario, the two-dimensional rubber sheet is the equivalent of the four-dimensional space–time continuum.
THE SPACE–TIME CONTINUUM: SPACE AND TIME ARE LIKE A FABRIC THAT WARPS IN THE PRESENCE OF MATTER AND ENERGY
An often-quoted saying is that “matter tells space–time how to curve, and space–time tells matter how to move.” But where is this curvature in our Universe? This is where the concept gets a little tricky—the curvature must be in a dimension of space that we are unable to perceive directly. We are familiar only with our three dimensions of space: up and down, left and right, in and out. Einstein included time as a fourth dimension and, further, asked that we accept that the gravity-generating curvature of space takes place through an additional dimension of space–time. Although we cannot see this other dimension explicitly, we feel it as if it were a force acting upon us, and we call it gravity. This is not as outlandish as it may at first sound. In fact it is very similar to centrifugal force, the rotationally generated effect that we first met in the context of planet formation (see How Did the Earth Form?).
When we are in a car that takes a tight bend, centrifugal force makes it seem as if we are being pulled outward. Although we feel as if a force is pulling us outward, it is actually an illusion brought about because of inertia—our resistance to a change in direction. Our bodies would like to continue traveling forward in a straight line but the car pulls us through a different dimension, and we perceive this change of direction as if it were a force acting on us. Imagine the car is remotely controlled and the windows are blacked out. Now, you have no outside reference against which to gauge your motion. Unbeknownst to you, the car is turned into a bend. Inside, you cannot see that you are turning but you feel the centrifugal force pulling you outward. This is used to great effect in fairground ghost train rides when the cart you are riding suddenly veers off around an unexpected curve. So, too, according to general relativity we feel a “force” of gravity because we are moving through the curvature of space in a dimension that we are unable to perceive directly.
A related concept that is central to general relativity is the “principle of equivalence,” which states that a gravitational field is indistinguishable from acceleration. Even in the 16th and 17th century philosophers were beginning to recognize this equivalence. Galileo Galilei proved that the speed at which an object falls does not depend on the amount of mass it contains. He did this by rolling balls of different masses down inclined slides and noticing that the balls always took the same length of time to hit the floor. He reasoned correctly that a feather takes longer to fall than a lead weight not because of the feather’s smaller mass but because its structure is better supported by the air. Apollo astronaut Dave Scott performed a beautiful demonstration of this on the Moon in 1971 when he dropped a hammer and a feather at the same time. In the absence of air resistance, the feather fell at the same rate as the much more massive hammer, and both hit the lunar soil at the same time. This proved that not only objects of different mass but also objects of different composition are accelerated equally by a gravitational field. Einstein’s extension of this in 1907 to the equivalence of gravity and acceleration is perfectly demonstrated with his famous “thought experiment” involving an elevator.
Imagine that you are in an elevator, totally enclosed with no windows. When the elevator is stationary, at whatever story, gravity pulls you down as you stand on the floor. If someone were to cut the cables, the elevator would fall and you would suddenly feel weightless. Any tiny body movement would result in you floating away from the floor because you would be falling at the same speed as the elevator. This is how astronauts feel when they are in orbit. Inside the elevator, you would continue to float until you hit the ground and your experiment came to a gruesome conclusion.
Now take the same elevator into outer space, well away from any gravitating object. This time, you feel weightless because there are no gravitational forces acting on you and you are floating through space at the same speed as the elevator. This is entirely equivalent to the elevator falling on Earth. If you were trapped inside, you would be unable to distinguish between the two cases.
Finally, imagine strapping a rocket motor to the base of the elevator in space and turning it on. The elevator accelerates but your inertia does not want you to move, so you drop to the floor of the elevator, which then pushes against you to accelerate you to the same speed as the elevator. To you, this feels like the force of gravity experienced when you are standing in the elevator on Earth; the faster the acceleration, the greater the force you feel—it is like experiencing a very great gravitational force. Indeed, in fast-moving jets and rockets, this force is often called the “G-force.”
The principle of equivalence encapsulates the results of the elevator “thought experiment” by stating that acceleration is indistinguishable from a gravitational field. Once Einstein had accepted this, general relativity fell into place. His predictions are identical to those of Newtonian gravity when the gravitational force is weak or, in the language of relativity, when the curvature of space–time is shallow. However, when gravity becomes stronger and the curvature becomes more pronounced, general relativity predicts corrections to the way gravity acts on celestial objects. This is how Einstein explained Mercury’s wayward orbit. Unlike the other planets, Mercury is close enough to the massive Sun for the curvature of space to be an important factor and so general relativity was needed to correctly calculate its movement. It was an early success for Einstein’s theory, but not the final proof. As important as resolving a known problem is for a theory’s credibility, the real test is whether it can predict something totally new. Einstein did not fail in this, either. He saw that, according to his theory, gravity should bend starlight much more than predicted by Newton’s theory. The difficulty was, how he could prove it.
To Newton, gravity could only affect objects with mass and, since light was a massless ray of energy, he considered it should pass through a gravitational field relatively unaffected. However, Einstein predicted that light would have to follow the contours of space–time, just as certainly as did planets and moons. His calculations showed that, when passing through a gravitational field, light would be deflected slightly from its path, in the same way a golf ball is deflected if it just clips the hole.
The concept is called “gravitational lensing,” and further calculations showed that the only object in the Solar System capable of bending starlight by a measurable amount is the Sun. The only time astronomers can see stars close to the Sun is during a total eclipse when the glare is blocked by the Moon. In 1919, Arthur Eddington led an observing party to the African island of Principe in the Atlantic Ocean to take the necessary measurements during the upcoming solar eclipse. Although cloudy in the morning, the weather cleared up in time for the dramatic total phase of the eclipse. In the sudden darkness, Eddington took his photographs, then measured the positions of the stars on the developed plates and compared them to photographs taken when the Sun was nowhere near the same stars. He found that the stars had apparently moved from their expected positions, just as Einstein had said they would if light were deflected by gravity.
GRAVITATIONAL LENSING: STARLIGHT IS DEFLECTED BY THE GRAVITY OF THE SUN
“Oh leave the Wise our measures to collate, One thing at least is certain, light has weight. One thing is certain and the rest debate, Light rays, when near the Sun, do not go straight.”
ARTHUR EDDINGTON 20TH CENTURY ASTROPHYSICIST
The conclusion was inescapable: general relativity was correct. As the news spread around the world Einstein became a superstar, but this tremendous success has come at a price to modern physics: we cannot yet, almost a century later, integrate general relativity’s explanation of gravity into our description of the other forces of nature. If we could, we might at last be able to establish the so-called “theory of everything.”
If we include gravity, there are four fundamental forces of nature. First there is the familiar force of electromagnetism; it is responsible for all the electrical and magnetic phenomena that we know of, and has been well-harnessed by science and technology since the late 19th century. Two other fundamental forces came to light in the early 20th century as physicists succeeded in probing the nucleus of the atom. These two nuclear forces are known, rather unimaginatively, as the “strong nuclear force” and the “weak nuclear force.” The strong nuclear force holds an atomic nucleus together and must be overcome in order to split an atom or to fuse two together. Hence, it is the strong nuclear force that allows energy to be liberated by stars and from atom bombs. The weak nuclear force governs certain forms of radioactive decay.
Taken as a force, gravity would be the weakest of all the fundamental forces. An easy way to demonstrate this is to watch an iron nail leap up toward a handheld magnet, proving that the magnetic force generated by the magnet in your hand is able to overwhelm the gravitational force created by the entire Earth. Nevertheless, it is the force of gravity that sculpts the Universe on its largest scales because it acts over vast distances, whereas the other forces are limited in the range over which they act. The two nuclear forces are confined to the width of an atomic nucleus; the electromagnetic force, although longer in range, tends to cancel out over large distances because it has both positive and negative charges, giving rise to repulsion (between like charges) as well as attraction (between opposite charges).
Physicists can explain the force fields associated with electromagnetism and the two nuclear forces as an exchange of tiny short-lived particles, called virtual particles. Gravity, on the other hand, can only be explained as a large-scale curvature of space. Many physicists suspect, and hope, for the symmetry and completeness of their theory, that gravity will eventually be found to be a real fourth force field, exchanging tiny virtual particles called gravitons. If that proves to be so, Einstein’s curvature of space will turn out to be a scientific metaphor, useful for visualizing gravity before the true explanation was found.
The leading candidate for a theory that can unify gravity with the other forces of nature is known as “string theory.” It replaces subatomic particles with minuscule bits of wiggling “string” and uses these to conjure up all the particles of nature, including gravitons. String theory extends Einstein’s ideas about other dimensions by having the strings wiggling through higher dimensions of space–time. We see the strings as point-like particles because we cannot perceive these other dimensions. Yet, for all the confidence in string theory, it is far from proven. The mathematics is so labyrinthine that even experts are having trouble relating the ideas to phenomena that might be observed with experiments and so enable the theory to be tested. Thus, finding a way to join gravity with the other forces of nature remains as difficult as ever; the difference in scale between minute virtual particles and large-scale curvatures of space–time is proving too great. Some new clue is needed to bridge the gap and, in the hope of providing this, physicists and astronomers are looking for any discrepancies between what general relativity predicts and what is actually observed. Such discrepancies would be rather like Mercury’s deviation from Newton’s predictions. They would be the signposts to a new understanding of gravity that can be dovetailed with our understanding of the other forces. The trouble is that no one can yet find any discrepancies.
Einstein himself thought that his theory was likely to fail in extremely strong gravitational fields; in the 1950s, a class of celestial object was found that generated just such a strong gravitational field. That era saw the burgeoning use of radio telescopes, and a Cambridge graduate student, Jocelyn Bell, discovered a pulsating radio signal that was clearly celestial in origin because it appeared in exactly the same place in the sky night after night. It pulsed on and off, as regular as clockwork. She called the source LGM-1, which stood only half-jokingly for Little Green Men. Before long, however, the theoreticians showed that it was most likely to be the spinning superdense remnant of an exploded star. Such a neutron star is even smaller than its cousin the white dwarf (see What Are Stars Made From?).
Whereas white dwarfs are about the size of the Earth and hold as much mass as the Sun, a neutron star is the size of a small asteroid—just 10 to 20 kilometers (6 to 12 miles) in diameter—and contains several times the mass of the Sun. The whole neutron star is packed with matter as tightly as in an atomic nucleus, hence its enormous density and very strong gravitational field. Radio astronomers tend to call them “pulsars” because, as a neutron star spins, it can sweep powerful beams of radio emission through space, and, like a lighthouse beam, the radio signal appears to pulsate on and off as it sweeps over the Earth.
In 2003, a significant discovery was made: a double pulsar—two pulsars in orbit around each other. The pair is remarkable because the stars are separated by just 800,000 kilometers (500,000 miles), almost 90 times closer together than Mercury and the Sun, and speed around each other in just 2.4 hours. Einstein predicted that in such a strong gravitational field, orbiting objects would lose some of their energy and that this would be radiated away as a gravitational wave in the space–time continuum, rather like a ripple in a pond. By timing the contraction of the stars’ orbits around each other, astronomers have calculated the amount of energy the double pulsar is losing. They have found that it is indeed the amount that Einstein’s theory says it should be, at least down to the level that the telescopes can measure. The pulsars are moving closer to one another by seven millimeters every day. As the two get ever closer, so the rate of their energy loss will increase. Eventually, in about 85 million years, the two pulsars will collide, producing a cataclysmic explosion that will bathe much of the Galaxy in gamma rays. The accuracy with which general relativity predicted this energy loss was again great news for Einstein’s theory, but not such good news for physicists hoping for a clue to point them toward fresh ideas about the nature of gravity and how to integrate it with the other forces of nature.
“No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”
ALBERT EINSTEIN 20TH CENTURY PHYSICIST
Most modern tests of general relativity concentrate on testing the principle of equivalence, hoping to find a difference in the way that gravity acts compared with nongravitational accelerations. Only in general relativity is the principle of equivalence exact. In string theory and in other attempts to unify gravity with the other forces the equivalence is only approximately true, which means that with sufficiently sensitive measurements deviations should be found.
One of the most promising experiments has been running for more than 40 years, made possible by the Apollo Moon landing missions. It is known as “Lunar Laser Ranging.” The Moon provides a remarkable gravitational laboratory—a giant test mass close enough to be within reach. During their observing runs, astronomers at the Apache Point Observatory, New Mexico, fire a powerful laser beam at the Moon. They target suitcase-sized reflectors, left on the lunar surface by three of the Apollo missions and two Russian missions. It is a job requiring tenacity and patience because out of every 300 million billion photons of light that the astronomers send to the Moon, just five find their way back to the observatory’s waiting telescope. The rest are lost to the atmosphere of the Earth, or miss the lunar reflectors entirely to be absorbed in the lunar soil or bounced off into a random direction in space. From the tiny numbers returning, the astronomers have been able to measure the movement of the Moon to an accuracy of a centimeter or two, and this has allowed them to calculate that the Moon is moving as Einstein said it should, to within one part in ten trillion. So general relativity still holds.
Recent upgrades in the ground-based equipment have allowed the movement of the Moon to be measured to an accuracy of millimeters. This will place general relativity under even more stringent tests, and there are many physicists anxiously waiting for the results. But for now, Einstein looks remarkably right; one might even say disappointingly right, because the requirements of general relativity prevent progress to what many feel would be a deeper understanding of the cosmos.