Gravitational Field
Curvature of Spacetime
The Weakest Force Rules the Sky
Lay a steel paper clip on a table, and the whole Earth holds it there. Bring a magnet close above it, and the clip leaps up off the table and hangs in the air, held down only by a thread. A small magnet outpulls the entire planet. Magnetism is part of the electromagnetic force, and gravity is by far the weakest of the forces. Between two protons, the electric push is about 10³⁶ times their gravitational pull. Between two electrons it is about 4 × 10⁴² times.
Yet gravity shapes planets, stars and galaxies, because it only ever pulls. Every bit of matter pulls on every other bit, and the pulls add up. Electric charges come in two kinds that cancel, and in ordinary matter they cancel almost perfectly. Set two bottles holding a kilogram of water each a meter apart. If one proton in about 600 million billion in each bottle lost its electron, the electric push would cancel their gravity. So few are needed, roughly the square root of 10³⁶, because the push grows with the charge of both bottles at once. Atoms are far more even than that: a proton’s charge and an electron’s match to better than one part in 10²¹.
Weak as it is, gravity was measured between objects in a room more than two centuries ago. A rod with a small lead ball at each end hung from a thin wire, and two large lead balls were set beside them. Their pull turned the rod a little, and that faint twist was enough to work out how heavy the Earth is. Even now, the strength of gravity is known only to about two parts in 100,000. Among the classic constants of physics, such as the electron’s mass, it is the least precisely known.
What Falling Cannot Hide
Everything falls at the same rate, whatever it is made of. A satellite that carried titanium and platinum round the Earth found them falling alike to within a few parts in 10¹⁵. So anything falling freely feels no weight. That is why astronauts float: they, their spacecraft and everything in it fall together. In a closed room, no experiment can tell falling freely from floating far from any planet. Einstein’s theory of gravity is built on that idea.
But only in a small room. How fast falling things gather speed drops with the square of the distance from the planet’s center, and everything falls toward that center. So a cluster of falling things does not quite fall as one. The side nearer the planet falls a little faster than the far side, and things side by side close in as they head for the same center. The stretch along the line to the planet is twice the squeeze across it. The squeeze acts in both directions across, and in empty space the two squeezes exactly balance the stretch, so a falling cloud at first changes its shape but not its volume. This leftover is the tide. No way of falling removes it, and it is what physicists mean when they say spacetime is curved.
Near Earth’s surface the tide is tiny. Two balls falling side by side two meters apart drift together by about three millionths of a meter per second every second. Near a giant planet it can tear things apart. Comet Shoemaker–Levy 9 once passed about 1.3 times Jupiter’s radius from the planet’s center. Jupiter’s tide broke it apart, and the pieces kept splitting into a string of some 21, which struck Jupiter one after another two years later.
Time Runs Slower Below
Put two identical clocks at different heights, and the lower one runs slower. Gamma rays sent up and down a tower 22.5 meters tall showed the shift that Einstein’s theory predicts. The height needed has shrunk ever since. Two atomic clocks have shown it across just 33 centimeters. Raise a clock that much and it gains about 90 billionths of a second over a 79-year life. More recently, a single clock found it across a cloud of atoms a millimeter tall.
This is not a side effect of gravity. For anything moving slowly, it is nearly all of gravity. Left alone, a body takes the straightest path it can through space and time together. Where time runs at different rates, that straightest path bends toward where time runs slower, and the bend is what we call falling. A ball thrown up and the Moon going round Earth are both moving as straight as they can. Of all the paths between leaving your hand and landing back in it, a thrown ball takes the one on which its own clock ticks the most. Higher up its clock runs faster, but climbing higher takes more speed, and speed slows a clock too: the arc it follows is the best trade between the two. The weight you feel is the ground pushing you off that path.
The Global Positioning System (GPS) has to allow for it every day. The satellites’ clocks, 20,000 kilometers up, run fast by about 45 millionths of a second a day because they are higher. They run slow by about 7 because they move so fast. Left alone, they would gain 38 millionths of a second a day, a timing error as large as the time light takes to cross 11 kilometers. So they are built to tick slightly slow before launch. On the surface of a neutron star, where gravity is more than a hundred billion times Earth’s, a clock runs about a fifth slower than one far away. Squeeze the same mass to a third of the width, and nothing can hold it up: it falls in on itself and becomes a black hole. A clock falling in ticks on as usual by its own count, but to a watcher far away it seems to slow toward a stop and fade from view.
Space Bends Too
For slow things, curved space hardly matters. Light is not slow, and for light it matters as much as slowed time. So starlight passing the Sun bends twice as much as Newton’s gravity alone would bend it: 1.75 seconds of arc at the Sun’s edge. Stars photographed beside the Sun in a total eclipse showed it, roughly. Radio signals from a spacecraft, passing near the Sun, were delayed by just as much as Einstein’s theory predicts. Half of that delay is the extra distance of curved space, and that half was confirmed to within two parts in 100,000.
A galaxy bends light by about as much as the Sun does, a second or two of arc. But across the vast distances between galaxies, so small a bend is enough. When a heavy galaxy lies almost exactly in front of a farther one, light from the far galaxy comes round it on every side. From Earth, the far galaxy appears as a ring, or as arcs and repeated images, round the near one.
The Einstein Cross is one such sight. A quasar, the blazing core of a young galaxy whose light has traveled for about 10 billion years, shows up four times round a galaxy much closer to us. Each image lies about one second of arc from that galaxy’s center. Because bent light weighs everything in its way, it has become a way to map matter that gives off no light at all.
Ripples in Space and Time
If mass bends space and time, masses that whirl round each other should send the bends out as ripples. The two detectors of the Laser Interferometer Gravitational-Wave Observatory, in the United States, have caught them. The first came from two black holes merging about 1.3 billion light-years away. Each detector has two arms four kilometers long, at right angles. A passing ripple stretches space one way while it squeezes it the other, so one arm grows as the other shrinks. This one changed the difference between their lengths by about 4 × 10⁻¹⁸ meters, a few hundred times less than the width of a proton.
Once, ripples from two colliding neutron stars arrived together with their light. Changes in gravity travel at the speed of light, to within about one part in 10¹⁵. Nearly 400 mergers have now been cataloged, almost all of black holes, which give off no light, and more from the latest observing run are still being studied.
Where Gravity Stops Making Sense
Einstein’s theory of gravity has passed every test made of it so far. Quantum theory describes the other three forces. The two do not fit together. Treat gravity the way the other forces are treated, and endless corrections appear that no handful of measured numbers can absorb. All energy is a source of gravity, and the closer one looks, the more energy the corrections carry, so each makes the next one larger. Calculations show this both for gravity acting on matter and for gravity alone. The theory still works wherever gravity is gentle. It fails at the center of a black hole and at the start of the Big Bang, where gravity and quantum effects matter at once.
Gravity’s weakness makes this hard to test. Its pull has been measured between gold spheres of just 90 milligrams. The rule that it fades with the square of the distance has been checked down to 52 millionths of a meter. Neither comes anywhere near a quantum effect. One experiment could go far toward settling the main question: hold two tiny masses each in one state that combines two places, close together, with only gravity acting between them. If gravity links them in the quantum way, most physicists would take it as proof that gravity is quantum, though some argue a classical gravity might do it too. Nobody can do it yet: it needs masses some thirty million times heavier than the largest whose wave has yet been split between two paths and brought back together.
