The Ascent of Gravity

by Marcus Chown

  But we know better. We are certain he is not on the surface of the Earth but far away from the gravity of any planet. When he let go of the hammer and the feather what really happened is they hung motionless in space, and the floor of the cabin accelerated up towards them at lg. It hit the hammer and the feather simultaneously. After all, how could it not?

  What this shows is that, if gravity is acceleration, the explanation of why all masses fall at the same rate is utterly trivial. There is no need for gravity to adjust itself to each mass to make this happen. No wonder Einstein called it the happiest thought of his life.

  Gravity, Einstein realised, is not like other forces. It is an illusion. It is caused by us accelerating and not realising it. Einstein codified the idea that ‘gravity is indistinguishable from acceleration’ in his Principle of Equivalence. It became the foundation stone of his theory of gravity.

  But why do we mistake acceleration for gravity? Because, as Einstein perceived, we have a limited perspective. And our limited perspective, like that of the astronaut in the blacked-out rocket, does not permit us to see the reality of our situation. That reality is that we are living in warped space-time. This takes a little explanation.

  Linear acceleration implies warped space

  The astronaut in the blacked-out rocket – out of boredom or curiosity again – carries out another experiment. This time it involves a laser. He takes the laser and puts it on a shelf 1 metre above the floor of his cabin. He switches it on so that its beam stabs horizontally across the cabin, creating a bright-blue spot on the far wall. He walks across and is puzzled to see that the spot is less than 1 metre above the floor. As it crossed the cabin, the light beam appears to have curved downwards.8

  We of course know that the rocket is accelerating at 1g. So, while the light beam crosses the cabin, the floor accelerates up towards it. It is no surprise to us that the beam strikes the far wall of the cabin at a point less than 1 metre above the floor. The puzzled astronaut, however, believing he is experiencing gravity on the surface of the Earth, concludes that the path of light is bent in the presence of gravity, or, equivalently, gravity bends light.

  But why does gravity bend light? One of the defining features of light is that it always takes the shortest path between two points. Usually, the shortest path is a straight line. But not always, realised Einstein.

  Consider a hiker negotiating a wild and rugged landscape between two hilltops. Being an experienced hill walker, he finds the shortest path. Now say a woman in a microlight is flying high above the landscape. She is able to follow the hiker’s path because of his hi-vis outfit. And the path she sees from her eagle’s vantage point is a winding and tortuous one.

  What this illustrates is that, in a hilly landscape, the shortest path between two points is not a straight line. It is a winding and tortuous path. A curve.

  This has implications for the astronaut who sees his laser beam curve downwards as it crosses his cabin. The only way the shortest path can be a curve is if the space in the cabin is warped, like the hiker’s hilly landscape.

  Gravity therefore bends light because gravity is synonymous with warped space. It is warped space. It is hard to imagine a more profound shift in our picture of gravity from Newton’s view.

  Rotational acceleration implies warped space

  The example of the rocket illustrates acceleration in a straight line. But it turns out that any acceleration is associated with warped space. Imagine, for instance, a spinning roundabout.

  Any body that changes its velocity – that is, its speed or direction or both – is said to be ‘accelerating’. The roundabout is doing just this. Although the natural motion of every element of the roundabout is to travel at constant speed in a straight line, every piece is constantly being dragged away from its desired straight-line path and made to move in a circle.

  Think of laying 1-metre rulers, end to end, around the periphery of the roundabout and across the diameter of the roundabout. If the roundabout is 5 metres in diameter, five metre rulers will be needed to span it and about sixteen metre rulers to stretch around the circumference. This is because, as every schoolchild knows, the circumference of a circle of diameter, d, is given by π-d.

  Now imagine that the roundabout is spinning not just fast but super-fast – so fast that all points along the periphery are travelling at an appreciable fraction of the speed of light. According to Einstein’s special theory of relativity, the rulers shrink in their direction of motion. It may now take twenty rulers or fifty or a hundred to stretch around the circumference, depending on how fast the roundabout is spinning. Contrast this with the rulers spanning the diameter of the roundabout. They are moving perpendicular to their length, not in the direction of their length. So they suffer no relativistic shrinkage, and five 1-metre rulers are still sufficient to span the diameter of the roundabout.

  So how do we explain that the circumference of the roundabout is now much greater than π×d? A hint comes from the circumference of a circle being π×d only on a flat surface like a piece of paper.

  Think instead of a circle drawn on a sphere. Its circumference is less than π×d. By contrast, a circle drawn on something that curves the opposite way – say, a deep valley in a trampoline -has a circumference greater than π×d. This suggests an explanation of why the circumference of the roundabout is greater than π×d: the space occupied by the roundabout is curved, or warped.

  So, whatever type of acceleration is considered – whether in a straight line or in a circle – the result is the same. Acceleration is associated with curved space. And since gravity is curved space, the acceleration associated with rotation can simulate gravity. This was famously depicted in the movie 2001: A Space Odyssey, where a space station in Earth orbit spins like a giant wheel and those inside can walk around the periphery of the wheel with their feet pinned to the floor by its artificial gravity.

  Actually, gravity is more than simply warped space.

  In the case of special relativity, one person’s space turned out to be another person’s space and time; one person’s time another person’s time and space. It is this realisation that led Herman Minkowski to his key insight that space and time are aspects of a seamless entity: space-time. Gravity, then, is not merely warped space, it is warped space-time.

  Minkowski’s concept of space-time, which Einstein, for all his genius, had not anticipated, proves absolutely crucial to understanding gravity.

  Warped time

  Since gravity is warped space-time, it follows that it not only plays games with space – bending the paths of light beams – but it also plays havoc with time.

  Picture an idealised ‘clock’ that consists of a horizontal laser beam bouncing back and forth between mirrors. Each time the light strikes a mirror, it is detected, creating a ‘tick’. If the clock is on the Earth, then the light does not travel between the mirrors in a perfectly straight line but follows a curved path – because, of course, gravity bends light.

  Now think of two such clocks – one higher above the ground than the other. The lower clock is in slightly stronger gravity than the higher clock since it is closer to the bulk of the Earth. This means that the light travelling between the mirrors in the lower clock follows a more curved path than the light in the higher clock. The more curved the path, the further the light has to travel between the mirrors, and the greater the time between ticks. It follows that the lower clock ticks more slowly than the upper clock. In other words, time flows more slowly in strong gravity.9

  Incredibly, this means that you age more slowly on the ground floor of a building than on the top floor. The reason is that, on the ground floor, you are closer to the mass of the Earth so gravity is marginally stronger. In fact, in 2010, physicists at the National Institute of Standards and Technology in the US were able to show that, if you stand on one step of a staircase, you age more slowly than someone standing on the step above you.10 It is an extremely tiny effect — because the gravity of the Earth is
relatively weak – but it is measurable with two super-sensitive atomic clocks.

  If you think this is an esoteric effect with no relevance to everyday life, think again. SatNavs and Smartphones use data from a constellation of Global Positioning Satellites, which swing round the Earth in highly elongated orbits. GPS satellites carry on-board clocks, and, when they swoop in close to the planet, they experience stronger gravity and their clocks slow down. If your electronic devices did not compensate for this effect of general relativity they would be unable to pinpoint your location relative to the GPS satellites.

  In other words, many of us on a daily basis are inadvertently taking part in an experiment that tests the general theory of relativity. If the theory were false, then the GPS system would get your location wrong by about an extra 50 metres a day. In fact, after ten years, it will still be correct within 5 metres, showing just how accurate is general relativity.11

  There is another way in which the slowing of time in gravity manifests itself. Say a person is in a room on Earth rather than on a spaceship. They shine a blue laser beam up at the ceiling. They discover something odd. The spot on the ceiling is not blue. It is red. The reason is that the light originated closer to the mass of the Earth, where gravity is stronger and clocks tick more sluggishly. The up-and-down oscillation of a light wave is just like the tick of a clock, which means that the light also oscillates more sluggishly. Since ‘colour’ is just a measure of how fast light is oscillating, with red light vibrating less than blue light, the more-slowly-ticking light is red.

  On the Earth, this ‘gravitational red shift’ of light climbing upwards is extremely small. It is certainly not enough to change the colour of light from blue to red – I was exaggerating. The colour shift is nevertheless measureable in super-accurate experiments. In one such experiment, in 1959, the American scientists Robert Pound and Glen Rebka observed the gravitational red shift of light climbing up a 22.6-metre tower. It was a tour de force because the shift is so tiny over such a short distance. But the effect is relatively easy to see in the light of ‘white dwarfs’, highly compacted stars which have very strong surface gravity.

  Gravity affects time because gravity is not simply warped space but warped space-time. The warped-space part bends the path of light. And the warped-time part slows clocks.

  Warped space-time

  It took Einstein to realise that we are living in warped spacetime and that warped space-time is, in fact, gravity. Nobody else noticed because it is far from obvious.

  Imagine a race of intelligent ants that live on the surface of a trampoline and are confined to its two-dimensional surface. They can wander north and south, and east and west, but they have no perception of a third dimension – that is, above and below the trampoline. Now imagine someone puts a bowling ball on their trampoline. The ants discover that, as they cross from one side to the other, their paths are deflected toward the bowling ball. This peculiar deflection cries out for an explanation. And the ants find one. They reason that the bowling ball exerts a force of attraction on them. Perhaps they even christen the force ‘gravity’.

  But, looking down on the trampoline from the God-like perspective of the third dimension, things look different. It is abundantly clear that the bowling ball has created a depression, or valley, around it. And in taking the shortest path across the trampoline, the ants naturally follow a path that curves around the bowling ball, just as the hiker followed a curved path when negotiating the hilly landscape.12

  We are in much the same situation as the ants on the trampoline. We live in a 3D world and are unable to perceive the full 4D reality in which it is embedded. The Sun creates a valley in the 4D space-time around it just as surely as the bowling ball created a valley in the 2D trampoline. Because we do not see it, we attribute the fact that the Earth’s path through space is deflected in a circle around the Sun — or, strictly speaking, an ellipse – to a ‘force’ which reaches out from the Sun and grabs hold of the Earth. But, in reality, there is no such force – no invisible elastic binding the Earth and Sun – just as there is no force reaching out from the bowling ball.

  The natural motion of a body subject to no other force is to follow the straightest possible trajectory through curved spacetime. Consequently, the Earth circles the Sun like a roulette ball in a roulette wheel. ‘In some sense, gravity does not exist,’ says American physicist Michio Kaku. ‘What moves the planets and the stars is the distortion of space and time.’13

  This reveals the very essence of Einstein’s theory of gravity. The American physicist John Wheeler put it this way: ‘Matter tells space-time how to curve. And curved space-time tells matter how to move.’ It is as simple as that. Actually, it is energy that warps space-time — mass-energy being just one form of energy. But this is just nit-picking. Wheeler’s statement is a masterful distillation of the essence of the general theory of relativity.

  To bring the idea down to Earth – literally – there is a valley in the space-time around the Earth. Our natural motion is to fall to the bottom of the valley – that is, to the centre of the Earth.14 But the surface of the Earth gets in the way. It obstructs our natural motion. The upward force from the ground is how we experience gravity.

  The contrast between Newton’s and Einstein’s theories of gravity is striking. In Newton’s theory, the Earth wants to move uniformly in a straight line because this is what massive bodies naturally do. But the gravitational force from the Sun deflects the Earth from its desired ‘inertial’ motion and causes it to travel in an elliptical orbit around the Sun. In Einstein’s theory, the Sun warps the fabric of space-time around it. The Earth wants to move along the shortest path because this is what massive bodies naturally do. But in the warped space-time this ‘inertial’ motion corresponds to an ellipse.

  Newton did not show the ‘cause’ of the apple falling. He showed only that the same force pulls on an apple and the Moon. ‘I frame no hypotheses,’ he wrote in The Principia. Einstein, however, showed the cause of gravity. The Earth warps the space-time around it and the apple and the Moon respond to that warped space-time.

  ‘That one body may act upon another at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another,’ said Newton, ‘is to me so great an absurdity that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it.’15 It was an absurdity. Action at a distance, according to Einstein, was mediated by warped space-time. Newton would have been pleased to be vindicated.

  Their visions of space and time provide an even more striking contrast between Newton and Einstein. Newton considered space as a passive backdrop against which the cosmic drama is played out, and time the regular ticking of some universal Godlike clock. But, according to Einstein, there is no such thing as absolute space and absolute time. Space and time are stretchy and combined into the seamless entity of space-time. Not only that but matter determines the shape of space-time, which in turn determines how matter moves, which changes the shape of space-time, which changes the way matter moves . . . in the most complex of complex dances. Far from being a passive backdrop to the Universe, space-time is a thing in its own right.

  Almost certainly, Newton’s view of space and time was pragmatic. He recognised that space could be sensibly defined only as the distance between two bodies. That it must be ‘relational’. But he also recognised that, with such a view, it was not possible to make progress with the mathematical tools at his disposal. It was a mark of his genius that he realised that absolute space and absolute time were nevertheless good enough concepts to explain the most obvious features of the Universe.

  The voice of space

  Space-time’s role as an actor in the cosmic drama – as a thing in its own right – gains its most remarkable expression in the phenomenon of ‘gravitational waves’. Space-time can be jiggled by the movement of mass. And this jiggling causes waves to propagate outwar
ds like ripples on a pond. Ripples in the very fabric of space-time.

  Einstein vacillated about the existence of ‘gravitational waves’, thinking they existed in 1916, changing his mind shortly after, and then changing it back in 1936. But on 14 September 2015, almost exactly 100 years after Einstein’s prediction, gravitational waves were picked up for the first time on Earth.

  Imagine being deaf since birth and suddenly, overnight, being able to hear. That is the way it was for astronomers. For all of history they have been able to ‘see’ the Universe. Now, at last, they can ‘hear’ it.

  Our media has a tendency to overhype things. But a good case can be made that the discovery of gravitational waves is the most important development in astronomy since the invention of the telescope in 1608. They are literally the ‘voice of space’.

  The event picked up on 14 September 2015 was an extraordinary one. In a galaxy far, far away, at a time when the Earth boasted nothing more complex than a bacterium, two monster black holes were locked in a death spiral. One was 29 times the mass of the Sun and the other 36 times the mass of the Sun. Each travelling at half the speed of light, they whirled about each other one last time. As they kissed and became one, three whole solar masses were destroyed and converted into gravitational waves. A tsunami of tortured space-time surged outwards, so violent that, for a brief instant, its power output was 50 times greater than all the stars in the Universe put together.

  Space-time is a billion billion billion times stiffer than steel, which is why it can be vibrated significantly only by the most violent cosmic events such as black hole mergers. But those vibrations, like ripples spreading on a lake, die away rapidly. And the gravitational waves that reached Earth on 14 September 2015, having travelled for 1.3 billion years across space, were mind-bogglingly tiny.

  Enter the Laser Interferometric Gravitational wave Observatory (LIGO), in effect a couple of giant 4-kilometre rulers made of laser light – one at Livingston in Louisiana and the other at Hanford in Washington.16 At 5.51 a.m. Eastern Daylight Time on 14 September 2015, first the Livingston, then 6.9 milliseconds later the Hanford, rulers repeatedly expanded and contracted by 100 millionth the diameter of an atom.17 ‘The signals are infinitesimal. The sources are astronomical. The sensitivities are infinitesimal. The rewards are astronomical,’ writes Janna Levin of Columbia University in New York.18