The Perfect Theory (33 page)

In loop quantum gravity, spacetime is atomized and there is a minimum size below which it makes no sense to even talk about the concepts of area and volume. Lee Smolin, Carlo Rovelli, and Kirill Krasnov from Nottingham University have each shown how this theory makes it possible to subdivide the area of the black hole into microscopic pieces, each of which stores a bit of information like a screen of digitized information. According to the champions of loop quantum gravity, it all adds up exactly to give the right entropy of the black hole.

The string theorists see things slightly differently. Andrew Strominger and Cumrun Vafa from Harvard have shown that with M-theory, the current incarnation of string theory, it is also possible to derive an exact relationship between the entropy, information, and the area of a black hole. For a particular type of black hole they were able to show how assembling particular types of branes together allows the black hole to store just the right amount of information. The branes gave black holes exactly the right microstructure to solve Hawking's paradox. More generally, they believe that a black hole can be seen as a seething mess of strings and branes, like a tangled ball, with the ends and edges flailing about on the horizon. These bits of branes and string that bounce around on the horizon can be used to reconstruct all the information contained in the black hole. And, again, the numbers add up to give the right entropy.

While radically different, both loop quantum gravity and string theory seem to be on the right track to solve the information paradox. For, if the information actually lives on the horizon, it can feed the Hawking radiation that the black hole gradually emits, releasing information to the outside world as the black hole slowly glows. And so, by the time the black hole finally evaporates, it will have released all the information that it originally sucked in and no information will have been lost.

The string theorists are even bolder and more adventurous and claim that what they have found about Hawking radiation is an even more profound property of physical theories. Black holes seem odd because the amount of information that a black hole can store, while related to its entropy, is actually a function of its area, not its volume as one might naively expect—indeed, Bekenstein and Hawking had already argued that was so in the mid-1970s. But this means that, more generally, the maximum amount of information that can be stored in
any
volume of space will always be bounded. To find what that maximum amount of information is, just take a hypothetical black hole that contains
exactly
that volume of space and work out how much information can be stored on its surface. And so, instead of having to describe physics in a chunk of space, it should be enough to determine what happens on a surface that encompasses it, much as a two-dimensional hologram can encode all the information of a three-dimensional scene. But if this is true for a piece of space, it should be true everywhere, for the whole of the universe. In such a holographic universe, the details of what spacetime is doing at each point in the universe become irrelevant. This property is so striking that it has led Edward Witten and some of his string theory colleagues to argue that spacetime is an
“approximate, emergent, classical concept” that doesn't have meaning at the quantum level. It seems that for any of the approaches to quantum gravity, at the most fundamental level spacetime might not actually exist.

When, in the 1950s, John Wheeler and his students started thinking about spacetime and the quantum, he speculated that if one were able to look really closely at space, with an inconceivably ultra-powerful microscope, one might see that “geometry in the small would seem to have to be considered as having a foam-like character.” He was remarkably prescient, but from what we are beginning to understand, even Wheeler of all people might have been too conservative. Not even a foam begins to capture the complexity of where spacetime comes from.

It looks as if one of the main ideas that underpins Einstein's great theory, the geometry of spacetime itself, needs to be revisited. The quantum seems to push general relativity beyond what it is capable of describing, and a completely new way of thinking may need to be developed. But there are other hints that we may be reaching the limits of what Einstein's theory can tell us about space, time, and even the universe on the whole. It is, as Wheeler pointed out, when a theory is pushed to its extremes that we learn something new and surprising. In those regimes we may get a glimpse of something bigger and better that may in the end supersede Einstein's great discovery.

13

I
HAD JUST GIVEN
my lecture and now stood with the audience in the atrium of the Institute of Astronomy at the University of Cambridge drinking cheap wine out of plastic cups. We gathered in small clusters, shuffling our feet, trying to fan conversation into life. The talk I had been invited to deliver that day had been about modifying gravity, describing a class of theories that proposed to dethrone general relativity as an explanation for some cosmological conundrums. The lecture itself had been uneventful. Early on, I had stumbled in refuting a comment about dark matter but had thankfully recovered. No one had told me I was wrong, nor had the questions dragged, and I was now ready to head home to Oxford.

The institute's director, George Efstathiou, strode up, eyes gleaming, brandishing his white plastic cup like a weapon. “Thank you for coming,” he said. “That was an interesting talk. In fact I would say it was a good lecture about a really crap subject.” I smiled politely as he slapped me on the back. It wasn't the first time I had faced this reaction and I wasn't surprised. Efstathiou had been instrumental in working out the details of how dark matter might have evolved in the formation of large-scale structure. He had also been one of the first to claim that there was evidence for a cosmological constant in the distribution of galaxies. Having risen fast in his career, Efstathiou was successful and confident. “When I took over the institute, I tried to declare it a zone free of modified gravity. And on the whole, I think I have been pretty successful.” He beamed as the small group of people around us looked down at the ground. “Why on earth do you work on it?” he asked me, not really expecting an answer.

A few months earlier, I had attended a small workshop at the Royal Observatory in Edinburgh entirely devoted to discussing alternative theories of gravity. The crowd that day had included a strange mix of astronomers, mathematicians, and physicists. This meeting was different. Whenever a speaker finished a presentation, there was a round of warm applause of a kind common to self-help groups. There was also a buzz in the air, as if all the talks that day were groundbreaking revelations of some divine law of physics. Everyone was a prophet. Everyone was Einstein. The camaraderie reminded me of my brief flirtation with a Trotskyite organization in my youth, when I had experienced a heady sense of community as my fellow agitators and I agreed implicitly with one another on the innate corruption of the world.

The evangelical zeal of the workshop made me deeply uncomfortable, part of a deluded cult. After my own talk, I felt almost sickened by the applause and had to leave the room. I was being unfair; the people in that room had been working on alternative theories of gravity for years, fighting against a mainstream that believed piously in Einstein. These were scientists who would regularly have their papers rejected simply because they were about a deeply unfashionable topic. They were used to facing hostile audiences. At this meeting, their zeal fell on sympathetic ears, and they could freely discuss their goal: to overthrow Einstein's general relativity.

Most of my colleagues are reluctant to change Einstein's grand oeuvre—if it ain't broke, as the saying goes, don't fix it. Especially if you took part in the glorious renaissance of the 1960s, when general relativity had emerged from its murky, stagnant past and stepped into the limelight to become the strange, beautiful theory that could explain everything, from the death of stars to the fate of the universe. That generation of astrophysicists still feels the magical power of Einstein's theory. This depth of loyalty was made clear to me at yet another meeting, this one at the Royal Astronomical Society in 2010. In the same rooms where Eddington had announced the results of the eclipse expedition and had stamped on Chandrasekhar for invoking the specter of gravitational collapse, a gathering of astrophysicists and astronomers were asked who believed Einstein's theory was correct. A few hands went up, and a closer look revealed that these were the pioneering bunch who dragged general relativity into the mainstream in the 1960s. In the opinion of this group, general relativity was too strange and too beautiful to need changing.

No one can deny general relativity's colossal successes throughout the twentieth century, but it is due for a fresh look. Science may benefit from accepting that general relativity is going the way of Newton's theory of gravity. Newton's theory is still alive and well; it remains useful for explaining the mechanics of ballistics on Earth, the motions of the planets, and even the evolution of galaxies. The theory breaks down only in more extreme situations. Where gravity is stronger, Einstein's general theory of relativity has proved more applicable and precise. It may be time to take a further step and look for the theory that surpasses general relativity at its own extremes.

The challenges of applying general relativity on very big or very small scales, or in situations with very strong or even very weak gravity, may be indicators that the theory breaks down in some circumstances. The problematic marriage of general relativity and quantum physics may be a sign that these two theories actually behave slightly differently on the very small scales where they need to agree. General relativity's prediction that 96 percent of the universe is dark and exotic could just mean that our theory of gravity is breaking down. Now, almost a hundred years after Einstein first came up with his theory, may be a good time to reassess its true applicability.

 

History is full of attempts to modify general relativity. From almost the moment he published his theory, Einstein felt that general relativity was unfinished business, part of something bigger. Again and again, he tried and failed to embed general relativity in his grand unified theories. Arthur Eddington also spent the last decades of his life trying to come up with his own fundamental theory, a magical confluence of mathematics, numbers, and coincidences that could explain everything, from electromagnetism to spacetime. Eddington's quest for a fundamental theory was an endeavor that had slowly but surely eroded his prestige.

The Cambridge physicist Paul Dirac thought Einstein's general theory of relativity was the perfect example of how a theory should be. As he said in later life,
“The beauty of equations provided by nature . . . gives one a strong emotional reaction,”
and Einstein's field equations had that beauty. Yet there was something that nagged Dirac, coincidences between numbers in nature that, if indeed the fundamental equations were beautiful, couldn't
really
be coincidences. There were some very, very large numbers in nature that couldn't be there by chance. Compare the electrical force between an electron and a proton with the gravitational force between them. The electrical force is larger than the gravitational force by a factor of one followed by thirty-nine zeros, an inordinately large number, more characteristic of a much bigger quantity, like the age of the universe. Hermann Weyl and Arthur Eddington had also argued that there must be some deep reason for the similarity of these disparate large numbers. Paul Dirac went a step further and conjectured that the strength of gravity, which is determined by a constant of nature, Newton's constant of gravitational attraction, had to evolve in time, counter to the predictions of general relativity.

Dirac proposed his idea in the late 1930s but never really took it forward. During the 1950s and 1960s Robert Dicke, one of his students, Carl Brans, in Princeton, and Pascual Jordan in Hamburg breathed new life into Dirac's idea and created an alternative to Einstein's theory. It was, to some extent, a perfect counterfoil to general relativity. As Carl Brans puts it, “Experimentalists, especially those at NASA, were effusively happy to have an excuse to challenge Einstein's theory, long thought to be beyond further experimentation.” Not everyone saw it that way, and, as Brans recalls, “as time went by, many other theorists seemed also to be offended to have Einstein's theory contaminated by an additional field.”

When Paul Dirac retired, he moved to Florida State University, where he indulged in some of his stranger ideas. He sometimes confided to his colleagues that he was convinced some better, more true-to-nature way of explaining gravity must exist. But he also remained wary of talking too much about his work tampering with gravity, for he felt that it would be seen by some as flaky and speculative.

By that time there had been quite a few attempts to modify general relativity, mostly driven by the problems with coming up with a good, finite theory of quantum gravity. When quantum physics is brought into the game, strange things might happen to gravity, as the Soviet physicist Andrei Sakharov pointed out in the late 1960s.

 

Sakharov had been part of the team, with Yakov Zel'dovich and Lev Landau and many others, that Igor Kurchatov and Lavrentiy Beria had put together to catch up with the Americans in the nuclear race. The son of a physics teacher, Sakharov entered Moscow State University in 1938 at the age of seventeen, worked through the war as a technical assistant, and finally obtained his PhD in theoretical physics in 1947. Like Zel'dovich, Sakharov emerged as a golden boy of the Soviet system. While Landau had bailed out the moment Stalin died, Sakharov had spent almost twenty years, longer than Zel'dovich, working on Soviet nuclear and thermonuclear weapons.