The Ascent of Gravity

by Marcus Chown

  In the brane picture, the large-scale Universe is a threedimensional island, or 3-brane, floating in a space of ten dimensions. In this scenario strings have two possibilities open to them. One end of a string can be anchored to the 3-brane, waving free like kelp attached to the seabed of the Sargasso Sea. Or a string can form a loop which is not attached to the 3-brane. The familiar fundamental particles of the Standard Model are of the former type and so confined to the 3-brane. The graviton alone is a string loop which is free to move off-brane and explore the ten-dimensional ‘bulk’.

  This suggests an intuitive explanation of one of the biggest puzzles in physics: why the force of gravity is weaker than the other fundamental forces of nature by such an extraordinarily large factor. As pointed out before, the force of gravity between a proton and electron in a hydrogen atom is 10,000 billion billion billion billion times weaker than the electromagnetic force between them. In 1999, Lisa Randall of Harvard University and Raman Sundrum of the University of Maryland in College Park discovered that extra dimensions need not be rolled up far smaller than an atom. If they were warped in a particular way, they could be as large as the Universe but have gone entirely unnoticed.22

  In the Randall-Sundrum scenario, the reason the force-carriers of the non-gravitational forces such as the electromagnetic force are relatively strong is that they are confined to our 3-brane. Gravitons, on the other hand, leak out into the full ten-dimensional bulk, and so their effect is diluted.

  Although this is an attractive intuitive explanation for the weakness of gravity, there is no evidence yet of large space dimensions that are hidden from our view. String theory remains big on possible explanations of phenomena in our Universe but small on actual explanations that are capable of spawning precise and testable predictions. .

  If our Universe is indeed a three-dimensional island floating in a ten-dimensional space-time, then an obvious thing to wonder is: Is it the only such island? And if it is not the only island, could our 3-brane collide with another 3-brane? This is actually the basis of a novel explanation for the big bang proposed by a team led by physicist Neil Turok, director of the Perimeter Institute in Waterloo, Canada.

  In the scheme, two entirely empty 3-branes approach each other along a fifth dimension (the fourth being time). Think of them as two slices of bread coming together, flat-side to flat-side. The two 3-branes pass right through each other. But they have enormous energy of motion in the fifth dimension and, at the moment they kiss, that energy has to go somewhere. Where it goes is into creating the mass-energy of subatomic particles on the branes and into heating them to a blisteringly high temperature. In short, it creates a hot big bang.

  In Turok’s scheme, on each brane the fireball expands and cools, galaxies congeal out of the debris and fly apart, eventually diluting the matter to such an extent that each brane is essentially empty again. The vacuum in the fifth dimension acts like a spring, which eventually pulls the branes back together again. They collide and repeat the cycle. Again. And again . . . Our big bang is just one in a long line of bangs, stretching back into the past and forward into the future.

  The ‘cyclic Universe’ is potentially distinguishable from the standard cosmological scenario in which the Universe in its first split-second undergoes a phenomenally violent, exponential expansion known as ‘inflation’. ‘If the Universe sprung into existence and then expanded exponentially, you get gravitational waves travelling through space-time,’ says Turok. ‘These would fill the Universe, a pattern of echoes of the inflation itself.’ The cyclic Universe, on the other hand, lacks the chaotic violence necessary to shake the hell out of space-time and so predicts no such gravitational waves from the early Universe.

  The cyclic Universe is a speculative idea. String theory itself is not a fully fleshed-out theory. It may be only a small part of the deeper theory that will explain the origin of space and time and the Universe. Or it may be a red herring. But string theorists feel encouraged that they are on the right track. One reason is of course that it is the only game in town – despite immense effort, no one has found another ‘theory of everything’ capable of unifying all the fundamental forces. But another reason for the optimism of string theorists is that their theory potentially resolves a paradox involving the most mysterious objects in the Universe: black holes.

  Black holes

  It is at the very heart of black holes – where Einstein’s theory of gravity predicts that matter is crushed to infinite density – that known physics well and truly breaks down. But the singularity is not the only location in a black hole that challenges our understanding of reality.

  The ‘event horizon’, as mentioned before, is an imaginary membrane surrounding the singularity that marks the point of no return for in-falling light and matter. When people talk of the size of a black hole, they are implicitly referring to the size of the horizon.

  In 1974, Stephen Hawking shocked the world of physics by announcing that black holes are not actually black. He came to this conclusion after considering quantum processes in the vicinity of a black hole. Remember that the Heisenberg Uncertainty Principle permits particle—antiparticle pairs to be conjured into existence out of the vacuum. Such ‘virtual’ particles have a fleeting existence, annihilating each other and popping back out of existence in a lot less than the blink of an eye. But Hawking realised that, just outside a black hole’s event horizon, something profoundly different can and does happen.

  One member of a newly created particle-antiparticle pair can race outwards, escaping for ever the gravity of the black hole, while the other falls through the horizon into the interior of the black hole. Once trapped inside, it can never re-emerge to annihilate with its birth partner. The escaping particle is elevated from the status of a short-lived virtual particle to a long-lived real particle.

  Hawking realised that processes like this are occurring continually all around the horizon of a black hole. They cause it to glow with ‘Hawking radiation’ as particles stream outwards.

  A defining characteristic of a black hole is, of course, that nothing inside can ever come out. Hawking radiation does not come out of a black hole since it is never in any sense inside. Instead, it is born in the vacuum just beyond the edge of the event horizon.

  The energy to make Hawking radiation real has to come from somewhere. And the only source is the gravitational energy of the black hole itself. As particles continually stream away into space, the gravitational field of the black hole weakens, causing it to gradually shrink, or ‘evaporate’.

  The smaller a black hole the stronger its Hawking radiation.23 For stellar-mass black holes and the supermassive black holes found at the heart of most galaxies, the particle sleet is so utterly negligible that their life expectancy far exceeds the current age of the Universe. But, as a black hole shrinks, its Hawking radiation gets ever stronger. For a tiny black hole – and every black hole reaches a tiny size of course before it finally vanishes – the Hawking radiation is blindingly bright. Black holes, when they end their lives, go out with a bang not a whimper.

  Anything that glows, by definition, has a temperature. And this is the case for a black hole shining with Hawking radiation. At first sight this seems bizarre because a black hole is nothing more than a bottomless well in space-time and so contains no obvious source of warmth. But a black hole is hot not by virtue of any intrinsic property but by virtue of extrinsic quantum processes going on in the surrounding vacuum.

  The tendency of Hawking radiation to cause a black hole to evaporate and eventually disappear creates a serious scientific paradox. It is a fundamental law of physics that information cannot be created or destroyed. Take the Moon. The fact that its location tomorrow can be predicted from its location today by the application of Newton’s laws implies that information about its location tomorrow is contained within its location today. So, as the Moon travels across the sky, information is neither gained nor lost but ‘conserved’. In the evaporation of a black hole, however,
information is lost.

  The precursor of a stellar-mass black hole is of course a star. A vast amount of information is needed to precisely define such a celestial body. The description must include, for instance, the type, location and velocity of every one of the star’s atoms. But, when a black hole has evaporated completely via Hawking radiation, there is literally nothing left. Where does all the information go? This, in a nutshell, is the ‘black hole information paradox’.

  So baffling is the paradox that, for many years, Hawking himself actually entertained the idea that black holes did indeed violate one of the most cherished principles of physics. ‘I used to think information was destroyed in a black hole,’ he said. ‘It was my biggest blunder, or at least biggest blunder in science.’24

  The obvious culprit for a repository of the missing information is the Hawking radiation. Perhaps it somehow spirits away knowledge of the star that spawned the black hole to the four corners of the Universe? But the Hawking radiation – which technically has the spectrum of a ‘black body’ – is characterised solely by its temperature.25 All it carries away from the black hole is this one ultra-trivial piece of information.

  A clue to the resolution of the ‘black hole information paradox’ came from Israeli physicist Jacob Bekenstein. In 1972, he discovered something unexpected about the event horizon: its ‘surface area’ is related to the black hole’s ‘entropy’.26

  Entropy is a concept that emerges from the theory of heat. ‘Entropy always increases’ is a statement of the ‘second law of thermodynamics’, one of the most important principles in science, which explains why castles crumble, eggs break and people grow old. Bekenstein’s discovery was the first indication of a connection between black holes and heat, pre-dating Hawking’s discovery that such bodies glow with heat radiation. Uniquely in black holes, three of the great theories of physics collide: Einstein’s theory of gravity, quantum theory and ‘thermodynamics’, the theory of heat. This is why gaining an understanding of them is of such key importance in the quest to mesh together quantum theory and the general theory of relativity.

  Entropy is intimately connected to information. It is a measure of our lack of information, or ignorance of the state, of a system. More specifically, it is a measure of the system’s microscopic disorder and is defined as the ‘number of microstates that correspond to a particular macrostate’. In the case of a brick, for instance, it is the number of different ways the atoms in the brick can be arranged and still leave the brick looking like a brick. The fact that the horizon of a black hole has an entropy can mean only that it is not smooth and featureless, as general relativity maintains, but has some kind of microscopic structure.

  In 1993, Dutch Nobel Prize-winner Gerard t’Hooft of the University of Utrecht suggested that the horizon of a black hole, far from being smooth and featureless, is rough and irregular on the microscopic scale. And it is in the lumps and bumps of its Lilliputian landscape that is stored the information that describes the star that gave birth to the black hole. It is as if the horizon is a super-dense DVD, with every region a Planck length on a side – that is, of area about 10-70 square metres – containing the equivalent of a binary ‘0’ or ‘1’ of information. ‘A black hole really is an object with very rich structure, just like Earth has a rich structure of mountains, valleys, oceans, and so forth,’ says Kip Thorne of the California Institute of Technology in Pasadena.

  Shortly after t’Hooft’s proposal that the missing information in a black hole might be encoded in its event horizon, Leonard Susskind of Stanford University showed how it might be implemented in string theory. Think of the event horizon of a black hole as a squirming mass of vibrating strings. Using this picture, in 1997, Andrew Strominger of the University of California at Santa Barbara and Cumrun Vafa of Harvard University were able to predict the exact black hole entropy calculated by Bekenstein.27

  Since Hawking radiation is born in the vacuum just a hair’s breadth above a black hole’s event horizon, it stands to reason that it is influenced by the microscopic undulations of that membrane. Those undulations ‘modulate’ it in much the same way that pop music modulates the ‘carrier wave’ of a radio station. In this way the information that described the precursor star is carried out into the Universe imprinted indelibly on the Hawking radiation. No information is lost, after all. And one of the most precious laws of physics is left intact.

  This proposal for averting the black hole information paradox remains speculative. We still lack the deeper theory that will mesh together Einstein’s theory of gravity and quantum theory. But, if correct, it implies something extraordinary. The information to completely describe a star – a 3D body – is perfectly preserved on the horizon of a black hole – a 2D surface. This makes the horizon similar to the holographic image on a credit card. Say a frog carried around with it a hologram of its previous incarnation as a tadpole. Well, a black hole carries around with it a hologram of its previous incarnation as a star.

  This might be nothing more than a weird curiosity if it applied only to esoteric objects such as black holes. But t’Hooft and Susskind suggested that the holographic idea might have implications not just for black holes. It may say something profound about the whole Universe.

  The holographic Universe

  The Universe, in common with a black hole, is surrounded by a horizon. The cosmic ‘light horizon’ is not the edge of the Universe – which plausibly may go on forever – but defines the edge of the ‘observable Universe’. Within the horizon are all the stars and galaxies whose light has had time to reach us since the birth of the Universe 13.82 billion years ago. Outside the horizon are all the stars and galaxies whose light has had insufficient time. Their light is still on its way.28

  T’Hooft and Susskind reasoned that just as the information that describes a 3D star is inscribed on the 2D horizon of a black hole, the information that describes the 3D Universe might be written as a 2D hologram on the horizon of the Universe. The idea is open to several possible interpretations. One is that the Universe, for some unknown reason, can be completely specified using one fewer large dimensions than expected. This is bizarre enough. Another, wilder, interpretation is that we actually live on the surface of the horizon, believing that we occupy its interior. Yet another, even wilder, interpretation is that our 3D Universe is literally a projection of a 2D hologram residing on the horizon that surrounds it, in which case, you and I and everyone else is actually a hologram!

  Reasoning by analogy in such a manner is hardly rigorous physics. And it is a big leap to extrapolate from the properties of black holes to the properties of the entire Universe. But, in 1998, the Argentine physicist Juan Maldacena published a paper which not only shored up the idea that we live in a ‘holographic Universe’ but set the world of physics alight.

  ‘Conformal field theories’ are a class of theories that are compatible both with quantum theory and special relativity (the Standard Model is one such theory). Maldacena pictured a 5D Universe, dubbed ‘the bulk’, filled with fundamental particles that dance to the tune of Einstein’s theory of gravity. He then pictured this Universe’s 4D boundary, which encloses it much as the 2D surface of a balloon encloses a 3D volume of air. It contained fundamental particles dancing to the tune of a conformal field theory.29

  Maldacena’s ‘miraculous’ discovery was that the equations on the boundary contain the same information and describe the same physics as the more complex equations of the bulk. In other words, the effects of gravity in the interior are mathematically equivalent to quantum field theory on its boundary. ‘The duality between a quantum description and a gravitational description appears to reveal a deep and surprising connection between quantum theory and Einstein’s theory of gravity,’ says Berman. ‘Although they appear utterly different, they may in fact be different sides of the same coin.’

  ‘Quantum theory and relativity appear to fight each other,’ says Arkani-Hamed. ‘But, behind the scenes, they actually help each other.�
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  So significant has Maldacena’s paper been deemed by the physics community that it has received almost 10,000 citations in other scientific papers and is widely regarded as a milestone in modern physics. Some physicists believe that the discovery of a link between gravity and quantum theory could turn out to be as important as the discovery by Maxwell in the nineteenth century that a single theory connects electricity, magnetism and light.

  Berman cautions that Maldacena’s result applies only in a simplified, or ‘toy’, model of the Universe known as ‘Anti deSitter’, or AdS. Among other things its space does not expand like normal space. But the hope of physicists is that the result also applies in the real Universe. But nobody has yet been able to prove it.

  What is space?

  The key question posed by Maldacena’s discovery is: how does a quantum field on the boundary produce gravity in the bulk? In an attempt to answer this, in 2015 Mark Van Raamsdonk of the University of British Columbia in Vancouver imagined an even simpler model than Maldacena’s. It was an empty bulk Universe. This corresponds to a single quantum field on the boundary. Like all quantum fields, it was tied together with entanglement – the instantaneous influence Einstein called ‘spooky action at a distance’.30

  Using mathematical tools developed by others, Van Raams-donk was able gradually to remove the entanglement on the boundary. As he did so, he saw that the space-time of his Universe steadily elongated, pulling apart as if made of toffee. Gradually, the very structure of space-time began to disintegrate. Eventually, when he had reduced the entanglement to zero, the space-time shattered into fragments like toffee stretched too far.

  Van Raamsdonk concluded that the long-distance connections which quantum entanglement bestows on space-time are essential to knit it together into a smooth whole. ‘Space-time is just a geometrical picture of how stuff in the quantum system is entangled,’ he says.31