What a Wonderful World (24 page)

The bending of light by gravity provides the vital clue to answering the question: if gravity is acceleration, why do we not realise we are accelerating? Light, recall, always takes the shortest path between two points. Why, then, in the presence of gravity, does it follow a curved path?

Think of a hiker taking the shortest path through a range of hills. From the point of view of a high-flying bird, it is clear that the hiker does not follow a straight-line path. Instead, because of the undulations of the landscape, he pursues a tortuous
curved path.
The shortest path through a curved landscape is therefore not a straight line but a curve. See the parallel? If light follows a curved path in the presence of gravity, then it implies space in the presence of gravity is curved.

In fact, this is all gravity turns out to be: warped space, or, more precisely,
warped space–time.

Nobody, before Einstein, suspected this. And no wonder. Space–time is a four-dimensional thing – it extends in the
directions
north–south, east–west, up–down and past–future. Since we are mere three-dimensional creatures, we are incapable of experiencing a four-dimensional reality directly.

Now, finally, we can understand why we are pinned to the surface of the Earth. There is no ‘force ’ of gravity pinning us there – no invisible elastic holding us to the ground. Instead, space–time in the vicinity of the Earth is warped. We are at the bottom of a shallow valley of space–time. And we are
accelerating
downwards as surely as a ball heading to the bottom of a real valley. Only there is something in the way, stopping us: the ground. It is preventing us from falling. By pushing back, it is giving us the
sensation of gravity.

It is no wonder that nobody before Einstein guessed that
gravity
was acceleration. Not only can we not see the valley of space–time we are in but the Earth’s surface is obstructing our free fall.

Take another familiar example: the Moon, orbiting the Earth, is not held in the grip of the force of gravity as if attached to the Earth by a long piece of elastic. Instead, according to Einstein, the Earth warps the space–time around it, creating a valley. And the Moon flies around the rim of the valley like a roulette ball around a roulette wheel.

We realise none of this because we cannot directly experience the warpage of space–time. It took the genius of Einstein to guess its existence.

This analogy may help. You are a passenger in a car that makes a sharp turn. You feel yourself thrown outwards. And you
attribute
this to a force. If you know any physics, you will call it centrifugal force.

However, from the point of view of someone standing beside the road, no such force exists. You, the passenger, are simply
continuing
to move in a straight line. As the car rounds the bend, it is the
body of the car
that comes towards you. In the rocket example, the astronaut thinks he is experiencing gravity. But, from the point of view of someone outside (admittedly with X-ray eyes), there is no such force. He is just floating motionless. It is the floor of the rocket that comes up to meet him.

So, living on the surface of the Earth, we think there is a force of gravity because we do not realise we are accelerating and have hit something unmovable – the ground. We are accelerating because, unknown to us, space–time is curved.

There is no such thing as the ‘force ’ of gravity. We are simply moving under our own inertia through curved space.

Einstein’s theory of gravity – the general theory of relativity – can actually be encapsulated in a single sentence. It is due to the American physicist John Wheeler, who coined the term ‘black hole ’. ‘Matter tells space–time how to curve,’ said Wheeler, ‘and curved space–time tells matter how to move.’ That’s all there is to it.

The devil, of course, is in the detail. General relativity is notorious for being easy to describe in words – and even in mathematical equations – while its implications in the real world are very hard to tease out.
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Not only that but spotting the hand of general relativity in the outside world is extremely difficult. This is because its predictions tend to diverge from those of Newton’s law of gravity only when gravity is strong. And gravity, on the Earth and in the Solar System, is very weak. If you do not think the Earth’s gravity is weak, hold your arm out straight from your body. The Earth has a mass of 6,000 billion
billion tonnes yet the gravity of all that matter is incapable of pulling your arm downwards.

The general theory of relativity would have been found earlier had the evidence for it not been so subtle. But there was no need for it. Einstein’s motivation was simply to generalise a theory he himself had concocted. This makes the general theory very unusual in the annals of science. Perhaps uniquely, it was not motivated by an observation of the world that did not fit the prevailing theory. Instead, it was one man’s obsession.

Nevertheless, at the time Einstein was devising his general theory of relativity, there
was
an observation that contradicted a prediction of Newton’s law of gravity. Few knew about it, let alone considered it important. It concerned the orbit of the planet Mercury.

Newton had discovered that the force of gravity between two masses weakens in a very particular way: if their separation is doubled, the force becomes four times weaker; if they are moved three times as far apart, it becomes nine times weaker; and so on.
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Newton further showed, in a mathematical tour de force, that the path of a body, under the influence of such an inverse-
square-law
force, is an
ellipse
.
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This explained the observation of the German astronomer Johann Kepler that the orbits of the planets around the Sun are not circular, as the Greeks maintained, but elliptical.

Actually, it is not quite true that each planet moves under the influence of an inverse-square-law force directed towards the Sun. In addition to being tugged by the Sun, each planet is tugged
by
every other planet
, most significantly Jupiter, which is about 1/1000th the mass of the Sun. As a result, its orbit is not an
unchanging
ellipse but one that
very gradually
changes its
orientation
in space, or precesses, tracing out a rosette-like pattern. This is as true of Mercury as it is of any other planet. However,
puzzlingly
, Mercury’s orbit precesses
above and beyond
that expected from the effect of the combined pull of all the other planets.

The mystery of Mercury’s anomalous precession – the planet traces out a rosette that repeats roughly once every 3 million years – is explained by general relativity. According to Einstein, all forms of energy have an effective mass – heat energy, light energy, sound energy, and, crucially, gravitational energy. This means that, like all mass, it gravitates. In other words,
gravity creates more gravity.

The effect of this is tiny and appreciable only where gravity is relatively strong – close to the Sun. Mercury is the planet closest to the Sun. Consequently, it experiences slightly stronger gravity than Newton would have predicted. Since a planet orbits in an exact ellipse only under the influence of a Newtonian inverse-square-law force, general relativity predicts that Mercury should show an anomalous precession, over and above that caused by the pull of the other planets. Einstein calculated the effect. Mercury, he discovered, should trace out a rosette in space that repeats about
once every 3 million years
. Exactly what is observed.

The fact that Einstein’s theory can explain such an esoteric
observation
as the anomalous precession of Mercury was hardly likely to set the world on fire. What did that was the confirmation of the bending of light by gravity during the total eclipse of 1919. The observation – a confirmation by an Englishman of the
prediction by a German, coming so soon after the catastrophe of the First World War – propelled Einstein into the scientific firmament. Instantly, he was hailed as the greatest physicist since Isaac Newton.

Light bending by the gravity of the Sun confirms that energy warps space–time while the anomalous precession of the orbit of Mercury confirms that all forms of energy – including gravitational energy – have gravity. But another prediction of Einstein’s theory is that gravity slows down time. Long before it could be checked on Earth with super-sensitive atomic clocks, the effect was looked for in space – in the light emitted by white dwarfs.

A white dwarf is the endpoint of the evolution of a star such as the Sun. Having exhausted its heat-generating nuclear fuel, such a star continues to shine as its stored internal warmth gradually trickles away into space. A white dwarf packs the mass of the Sun into a volume no bigger than the Earth, making each
sugar-cube
-sized chunk of its matter roughly the weight of a family car. Crucially, such a dense object has a surface gravity about 10,000 times stronger than that of the Sun, which means that, according to Einstein, time should flow noticeably more slowly than on Earth.

For such an effect to be observable, the surface of a white dwarf must possess a clock that is easily visible. Remarkably, it does.

An atom of a particular element, such as sodium or iron, emits light of characteristic colours. These are unique to the element and are essentially its light fingerprint. Colour is merely a
measure of how fast a light wave oscillates up and down. Such a regular oscillation is exactly like the ticking of a clock. And, sure enough, when astronomers observe a white dwarf and the light coming from a particular element on the star, they find that it oscillates
more sluggishly
than it would on Earth. In other words, the clock on the white dwarf ticks
more slowly
. And that slowing is precisely that predicted by Einstein.

Red light oscillates about half as fast as blue light.
Consequently
, the slowing down of the vibration of light shifts the light towards the red end of the spectrum.
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This is why it is called the gravitational red shift.

And this red shift – or red
shirt
, as an article in the science magazine
New Scientist
once referred to it – is observed in other contexts too. For instance, when astronomers observe light from distant galaxies, they find that it too is oscillating more sluggishly than it would on Earth. This is the cosmological red shift. And it has the same cause as its counterpart on a white dwarf.

When we see distant galaxies, we see them as they were when the Universe was younger because their light has taken a long time to travel to us across space. When the Universe was younger, it was
smaller
. This is because the Universe is expanding, its
constituent
galaxies flying apart like bits of cosmic shrapnel in the aftermath of the big bang. Distant galaxies therefore inhabited a Universe where cosmic matter was squeezed to a higher density on average and had correspondingly stronger gravity than today. In such a Universe, time flowed more slowly than today,
according
to Einstein. We observe this in the sluggish oscillation of the light from distant galaxies – the cosmological red shift.

In physics, however, there is often more than one way to skin a cat. Another, entirely equivalent, way of viewing the red shift
of light from distant galaxies and from white dwarfs is to say that, in climbing out of the strong gravity, the light
loses energy
. Since the energy of light is related to how fast it is oscillating, with high-energy light oscillating quickly, light that loses energy oscillates more sluggishly. It becomes
red-shifted.

There remains one prediction of Einstein’s theory of gravity that is yet to be confirmed directly: gravitational waves. In the general theory of relativity, space–time is not merely a passive canvas against which the drama of the Universe is played out. It is an active medium that can be warped by the presence of matter. In fact, it can be jiggled up and down too, creating a wave that propagates outwards like concentric ripples on a pond. This is a gravitational wave.

But space–time is not as elastic as the skin of a drum. It is a
billion billion billion
times stiffer than steel. This makes jiggling space–time to create strong gravitational waves very hard indeed. In practice, it requires some of the most extreme upheavals of matter in the Universe – the merger of two super-dense neutron stars
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or black holes.
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But significant gravitational waves are generated by neutron stars and black holes
long before
they coalesce into one object – in fact, when they are still spiralling together. In 1974, this permitted an ingenious and elegant test of Einstein’s theory. American astronomers Russell Hulse and Joseph Taylor
discovered
a system that consists of two neutron stars in orbit about each other. One is a pulsar, which, as it spins, sweeps a lighthouse beam of radio waves around the sky.

By carefully observing the binary pulsar, or PSR B1913+16, Hulse and Taylor determined that the two neutron stars are spiralling together, getting closer by about 3.5 metres each year. In the jargon, they are losing orbital energy. And, crucially, this lost energy is
exactly
the amount Einstein’s theory predicts they should be radiating into space as gravitational waves. For this
indirect
proof of the existence of gravitational waves, Hulse and Taylor shared the 1993 Nobel Prize for Physics.

The race is now on to detect gravitational waves
directly
. In the beginning, people looked for them with huge suspended metal bars. The theory was that such a bar, when buffeted by a passing gravitational wave, would ring like a bell. But a myriad mundane terrestrial vibrations, such as waves sloshing on beaches thousands of kilometres away, can drown out such a minuscule signal.