General Relativity – still ahead of its time

“I cannot find time to write because I am occupied with truly great things. Day and night I rack my brain in an effort to penetrate more deeply into … the fundamental problems of physics.”
— Albert Einstein, in a letter to his cousin Elsa, 1914.

Beethoven spent more than 16 hours a day at his piano, sometimes composing four musical works at once. Immersed in his task, he would become feverish, often dousing himself with water that soaked through the floor into the apartment below.

If we could time-travel to Berlin between 1905 and 1915, we would likely find Albert Einstein at the height of his powers, in a similarly febrile state. Yet he pushed on with his equations knowing, as he hinted in the letter to his cousin, that “great things” were within his reach.

Einstein had already achieved greatness. In 1905 he developed the theory of special relativity that wove space and time together into the fabric of the Universe and gave us E=mc2.

But Einstein was just getting started. He realised gravity needed to be brought into the picture. For several years, he could not see how to do it. “In all my life I have laboured not nearly as hard; compared with this problem, the original relativity is child’s play,” he told a colleague. His eureka moment was to realise gravity worked by warping the fabric of space-time. Towards the end of 1915, Einstein produced his masterpiece: the general theory of relativity.

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Einstein’s maths is hard to follow; metaphors help.
Jeffrey Phillips

This year, physicists are celebrating the centennial of Einstein’s theory. They are looking back on the theory’s origins, its growing pains, how it is holding up. And they are devising experiments to test the theory under ever more exotic conditions, to see if, or where, it may falter. And most of all they are looking ahead, pondering the next theory – one that can reach even further than Einstein’s, by incorporating the other great idea of 20th century physics: quantum mechanics.

But for now, Einstein’s theory reigns supreme. “There’s not a single experiment that has gone against it – at least, not one that’s ever been confirmed,” says Clifford Will, a physicist and general relativity expert at the University of Florida in Gainesville. “It’s passed every test with flying colours.”

The notion of relativity was not invented by Einstein. Scientists as far back as Galileo had pondered the consequences of relative motion. Indeed most of us have experienced relativity – perhaps an unnerving moment on a train when you notice a train on a parallel track and wonder which of you is moving. Suppose you and a friend are riding a train moving at 200 kilometres per hour. You throw a baseball to your friend, who’s further forward in the train, at 100 km/h. How fast is the ball moving relative to the ground? You simply add the two speeds together and get

300 km/h. If your friend throws the ball back, its speed relative to the ground is now 100 km/h.

This is the answer Newton would have given. Like most of us, he imagined space and time were absolute and unchanging – the fixed backdrop against which the events of the Universe unfolded.

However, this common-sense view of the Universe struck a problem concerning light. In 1865 James Clerk Maxwell showed light was really an oscillating electromagnetic wave; moreover he calculated that it travelled at a constant speed of about 300,000 kilometres per second.

A constant speed – but relative to what?

If instead of a baseball, you flashed a torch at your friend on the train, would the speed of the light beam be added to the speed of the train? And would you subtract the speed of the train if you flashed it in the opposite direction?

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Credit: Jeffrey Phillips

One idea – popular in the late 19th century – was that light waves propagated through an invisible “ether”, just as ocean waves propagate through water. If that were the case, the speed of light would vary relative to the Earth’s movement through the ether. In 1887 American scientists Albert Michelson and Edward Morley performed an experiment to see if this was the case. (Essentially, they shone a beam of light in different directions to see if light moving “with the ether” moved faster than light moving “against the ether”. They also tried the experiment at different times of the day and year, to see if the Earth’s rotation and its orbital motion had any effect.) Their result: the speed of light was always 300,000 km/s.

Simply put, you can’t boost or slow a beam of light as you can a baseball: shine a flashlight from a train and its speed – relative to you, relative to the ground, relative to anyone anywhere – will be 300,000 km/s. Similarly, no matter how much you increase your own speed, you can’t catch up to a beam of light.

This vexed the young Einstein. Whether he knew about the Michelson-Morley result, and how much it influenced him, is unclear – but his “thought experiment” about riding a bicycle alongside a beam of light was already leading him away from classical physics. (If you could catch up to the beam of light, it would appear motionless – but what does a motionless wave even mean?)

His answer was special relativity. Speed is distance divided by time. So if the speed of light isn’t affected by the motion of the observer, then space and time must be. As your speed increases, time expands or “dilates” and distance is shortened in the direction of motion. So moving clocks run more slowly (this is why satellites need to adjust their time). And remember the case of the baseball thrown on the train? Einstein showed that, relative to the ground, the ball isn’t travelling at 300 km/h, but fractionally less.

Special relativity wove space and time together into the fabric of the Universe. It was astounding – yet something was missing. Gravity. In 1907 Einstein had an epiphany that put gravity in the picture. Gravity, he said, warped the fabric of space-time.

Einstein realised the effect of gravity is just like the effect of acceleration. When you accelerate, you feel a force that is indistinguishable from gravity – think of being pressed to the floor in a rising elevator. Moreover objects with different mass respond to gravitational acceleration in the same way. As Galileo showed, heavy and light objects fall at the same rate. The only possible explanation, Einstein realised, is that gravity isn’t a property of matter, but of space-time. For the next eight years Einstein laboured to express the details of the theory in mathematical terms. In November 1915, he captured them in four publications that defined his general theory of relativity.

The mathematical details are complex but, thankfully, we have a useful metaphor. No doubt Einstein would have approved – he made great use of metaphors. Imagine a bowling ball on a rubber sheet. The sagging is most pronounced in the area closest to bowling ball – this is the “warping” of space. Now imagine rolling a marble across the same sheet. As it passes near the bowling ball, its path will curve because of the warping of the sheet – this is reminiscent of how our Earth curves around the Sun. (Gravity actually warps time as well as space – they are connected.)

This seemingly fantastic theory of how gravity curves space-time was first put to the test to explain the strange orbit of Mercury. Since the mid-1800s, astronomers had noticed that instead of tracing an ellipse around the Sun, as predicted by Newton’s laws, Mercury’s orbit shifted slightly with each rotation. General relativity provided the answer: as the closest planet to the Sun, Mercury experienced the greatest warping of space-time, explaining the slight but detectable deviation in its elliptical orbit.

General relativity also predicted that light would be affected by the warping of space-time. British astronomer Sir Arthur Eddington tested that prediction by observing the Hyades star cluster when the Sun’s path took it directly in front of the cluster. Normally, the Sun is too bright to allow such a measurement – but on May 29, 1919, a solar eclipse made it possible. Eddington led an expedition to the island of Principe off the west coast of Africa and sent another team to Brazil (in case Principe had cloudy weather). The relative position of the stars in the cluster was compared to the way they looked several months before, when the cluster was well away from the Sun.

Einstein was proved right; the light from the stars in the cluster was bent as it passed the Sun, shifting their relative positions by the amount predicted by the theory. The British astronomers presented their results at a meeting in London in early November. Back in Berlin, Einstein was perfectly calm. When someone asked him what he would have done had the eclipse measurements not confirmed his theory, he replied: “In that case,

I would have to feel sorry for God, because the theory is correct.”

“I would have to feel sorry for God, because the theory is correct.”

The London announcement, picked up by newspapers in Britain and America, made Einstein a superstar; he would remain a media darling for the rest of his life. Yet at the same time physicists were loathe to ditch Newton for Einstein.

“There was a lot of doubt about the theory, in many quarters, for quite a long time,” says Clifford Will. “The lack of strong experimental evidence, coupled with the fact that no one could see how it would ever be important in astronomy, plus a lack of understanding of what the theory really meant … all of that caused the entire subject to go into decline for almost 50 years.”

The next crucial experiment was not carried out until 1959. General relativity predicted that light and other forms of radiation ought to be stretched in a gravitational field, an effect known as “gravitational redshift”. To put this idea to the test, physicists at Harvard placed a sample of radioactive iron in a basement where the gravitational field is stronger because it is closer to the centre of the Earth. They carefully measured the wavelength of the radiation that reached a detector on the roof (a distance of 22.5 metres), then switched the experiment around, putting the radioactive sample on the roof and the detector in the basement. Sure enough, when the radiation came from the basement the wavelength was ever so slightly longer compared to when it came from the roof. Gravity had indeed stretched the radiation waves.

General relativity also predicted that gravity stretches time. So a clock at the base of a mountain should run slower than a clock at the peak because the lower clock feels the Earth’s gravity more intensely. Detecting that tiny difference had to await the 1970s, when fleeting time intervals could be routinely measured by atomic clocks. By 2010, physicists were able to measure the discrepancy between two atomic clocks placed one-third of a metre above one another. Each second, the lower clock, being closer to the Earth, lost four-hundred-quintillionths of a second relative to the higher clock.

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Because the Earth’s gravity is stronger at the foot of a mountain than at its peak, a clock will tick more slowly down below than up on top. Credit: Jeffrey Phillips

That may sound trivial, but it has a practical application. For our Global Positioning System (GPS) devices to work, they have to track signals received from an array of satellites to within billionths of a second. The effect from gravity is about 38 microseconds per day. Left uncorrected, the discrepancy would cause our navigation systems to accumulate an error of some 10 kilometres over the course of a day. So the next time you find a bus stop in an unfamiliar city with GPS, thank Uncle Albert.

Probing black holes might get us closer to completing Einstein’s quest to unify the physics of the very small and very large.

Perhaps General Relativity’s most remarkable prediction was the existence of exotic objects that warp space and time so severely that they become cut off from the rest of the Universe. If you saw the movie Interstellar, then you got to see one up close (or at least how we imagine they’d look). We’re talking, of course, about black holes. According to general relativity, a black hole can form when a massive star collapses after exhausting its nuclear fuel supply. If the star is big enough, the collapsed core will have such an intense gravitational field that nothing, not even light, can escape. Anything that crosses the “event horizon” – the boundary of the black hole – is trapped forever.

By definition, black holes cannot be seen directly. We infer their presence from their effect on surrounding matter – either from their effect on the motion of a companion star, or by detecting X-rays given off by matter as it is sucked into the black hole. There’s also mounting evidence that “supermassive” black holes lurk in the centres of most galaxies, including our own Milky Way. Within the next decade, we may get to find out if Insterstellar’s simulation got it right. The Event Horizon Telescope, an array of radio telescopes spread across the globe, will examine the region immediately surrounding the event horizon of the Milky Way’s central black hole.

Black holes stretch space-time; they also stretch Einstein’s theory to its limits. One problem is the so-called singularity said to lie in the centre of a black hole. At a singularity, space and time are infinitely stretched. That’s both mathematically and physically awkward, to say the least. What can “infinite stretching” mean? And it gets worse. In the 1970s, Stephen Hawking applied quantum mechanics to the mathematical description of a black hole, and what he discovered was startling: black holes aren’t so black. Instead, they emit so-called Hawking radiation; given enough time, a black hole should completely evaporate away.

“We still don’t have a terribly good grasp of what’s going on there,” says William Unruh, a physicist at the University of British Columbia in Canada. But probing black holes might get us closer to completing Einstein’s unfulfilled quest to unify the physics of the very small and the very large.

“We might get a little more insight into how quantum mechanics and gravity could be married to each other,” says Unruh.

It’s taken a century, so far, to develop the technology to test Einstein’s predictions. It may take a little longer for the last piece of the relativity puzzle: the existence of gravitational waves. These ripples in space-time should be emitted when massive objects are accelerated. Just as a bowling ball dropped on to a rubber sheet would cause it to ripple – alternately stretching and shrinking the fabric – so too, the waves from massive, accelerating objects should ripple space-time as they pass by. But Einstein predicted the ripples would be so weak it would take cataclysmic events to produce the feeblest wave. He never expected it would be possible to detect them.

Indeed we haven’t yet detected them directly but there is indirect evidence that gravitational waves exist. One piece comes from rotating neutron stars known as pulsars. Barring black holes, neutron stars are the densest objects in the Universe – formed after a massive star explodes into a supernova and its protons and electrons collapse into a core of neutrons. They are so dense that a teaspoon of neutron star material would weigh around a billion tonnes; gravity on their surface is 1011 times that on Earth. Rapidly spinning pulsars emit a narrow beam of radio waves; if the beam happens to be lined up with Earth, we see a periodic flash, as if from some cosmic lighthouse. Pulsars occasionally team up with an ordinary star to form a binary system. As the massive pulsar spins around its companion, stirring up space-time, it should emit gravitational waves.

Since the 1970s, astronomers have been observing a pulsar (with the unpoetic name of PSR B1913+16), that is partnered with an ordinary star. According to general relativity, the gravitational waves emitted by the system should cause their orbit around each other to shrink, something that can be measured by tracking the timing of the radio pulses – and this is exactly what astronomers have seen. This tightening of their embrace could not be explained by the energy radiated away by radio waves alone.

The more cataclysmic the event, the better our chances of detecting gravitational waves. So it is no surprise physicists have been trying to detect the ripples created by the Big Bang itself. Last March, a team of astronomers training their radio telescope at the radio-friendly skies of the South Pole, thought they detected the signature of gravitational waves in the faint echoes of Big Bang radiation – the so-called Cosmic Microwave Background. But on closer scrutiny that signature was lost in the dust of the Milky Way.

It’s one thing to try and see the evidence of gravitational waves in the heavens. But if gravitational waves are rippling through the fabric of space-time, perhaps radiating out from a binary pulsar, we might be able to detect them directly on Earth.

Work on gravitational wave detectors has been in train for some 20 years now. The largest of these projects, known as LIGO (Laser Interferometer Gravitational Wave Observatory), has been operating since 2002. LIGO consists of two L-shaped detectors, four kilometres on each side. Both are in remote areas, one in a shrubby expanse near Hanford in Washington state; the other 3,000 kilometres away in the swamps west of Baton Rouge, Louisiana. Two sets of detectors are crucial to rule out rogue signals. A truck rumbling by in Hanford will set off the detector but if a real gravitational wave rolls by, it will set off Hanford, and then a 100th of a second later, Louisiana.

The passing gravitational wave will stretch and shrink space-time, causing each of LIGO’s arms to stretch and shrink alternately by a vanishingly tiny amount (about one 10,000th the size of a proton). Laser beams mounted at the far end of each arm bounce back and forth between mirrors. Their light waves intersect at the corner of the “L”. Normally they are perfectly out of phase – the peaks of one line up with the troughs of the other – so the signals cancel each other out. As soon as one arm changes length, the perfect cancellation is lost and you get a signal.

Other countries are also in the hunt. Italy, for instance, has the VIRGO detector, Australia is constructing AIGO (the Australian International Gravitational Observatory) in Western Australia and India is planning to build its INDIGO detector. There are also plans for a space-based satellite array: the pilot mission, LISA Pathfinder, is set for launch this September (LISA stands for Laser Interferometer Space Antenna).

This May, LIGO was upgraded to Advanced LIGO with its sensitivity increased 10-fold. Excitement is building, as physicists sense that Einstein’s final prediction will soon be confirmed. LIGO spokesperson and physicist Gabriela González anticipates snagging a gravitational wave as early as 2017. Champagne won’t suffice for that celebration, she says. “I think we’ll want something more.”

“General relativity is so … beautiful and simple.”

Yet for all its triumphs, general relativity faces a couple of big challenges. Einstein wrestled unsuccessfully with one of them: reconciling the theory with its great nemesis, quantum mechanics. Each theory has been outstanding in its own domain – relativity in the cosmos, quantum mechanics in the subatomic world. But occasionally the domains overlap. To understand the Universe’s earliest moments, as well as the insides of black holes, we still need a theory that bridges the very large and the very small.

No one knows what the resulting theory might look like. One candidate is string theory, based on the premise that the fundamental building blocks of the Universe are tiny strings. An alternative, “loop quantum gravity” views space-time as granular. As with string theory, however, its proponents have yet to come up with an experiment to test it.

And then there’s the problem of dark energy. Discovered in the late 1990s it appears to be a force that acts in opposition to gravity, causing our Universe to expand at an accelerating rate. The Universe, it seems, obeys two masters – gravity and dark energy – and it may take another Einstein to make sense of the latter.

Will all this require a modification of Einstein’s masterpiece?

No, says Clifford Will. Fiddling with general relativity, he believes, would be tantamount to changing the Fifth Symphony. “General relativity is so unbelievably beautiful and simple – it’s in some ways the most perfect gravitational theory that you could possibly imagine,” he says. All of the alternatives he’s seen so far are “horrendously ugly by comparison”.

And so Einstein’s theory, like a Beethoven symphony, remains with us, 100 years on. We want to go further, but that would mean adding a violin theme here or dropping a few cello notes there; perhaps even writing a whole new movement – and that would mean messing with perfection.

“My personal view,” says Will, is that “whatever’s going on with black holes or dark energy – at the end of the day, I think general relativity will survive”.

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