The Perfect Theory

by Pedro G. Ferreira

  Peebles stayed above the fray, but in 2002 he did speak out on behalf of Milgrom and his ilk, chiding, “By no means have we ruled out MOND and people who do MOND should be encouraged a little more than they are.” Jacob Bekenstein was more damning in his critique of how those working on MOND have been treated: “One has to take into account that the MOND versus dark matter issue is not just academic. There is a lot of money invested in searching for dark matter. . . . And no way to avoid it; entire careers are vested in dark matter. Obviously if something like MOND gets to be respectable, budgets for dark matter research will suffer and jobs will be fewer.”

  Since MOND’s inception, Bekenstein had been trying to figure out how to make it better. Given his tendency to look at the deep roots of physical theory, he wasn’t happy leaving MOND as it was. He wanted something that could be compared to general relativity and applied on all scales from the Earth all the way up to the universe. “I decided,” Bekenstein said, “that it was time to meet that argument head-on by producing an example of a relativistic theory.” In 2004, Bekenstein published a paper in which he constructed a new theory to rival Einstein’s. He called it TeVeS, for the tensor-vector-scalar theory of gravity. It wasn’t pretty. The name alluded to a jumble of fields that, when combined, led to a completely new set of field equations far more intricate and tangled than Einstein’s general theory of relativity. It was a mess, but Bekenstein’s theory worked. Not only did it behave like MOND when applied to galaxies, but it could be used to work out how the universe evolved and how large-scale structures formed.

  The majority of cosmologists and relativists looked at TeVeS with disdain. They dismissed it as a kludge—a clumsy work-around that didn’t get at the heart of the problem. Yet it was a high-powered kludge invented by a relativist with impeccable credentials. Bekenstein’s black hole entropy was one of the most profound insights of modern general relativity and quantum physics. Yes, there was a tendency for older famous physicists to work on strange ideas, carried away by their own success. But Bekenstein wasn’t like that.

  Bekenstein was also not alone in his assault. While his proposal tackled the problem of dark matter, others tried to do away with the cosmological constant and dark energy. The panorama of rival theories to general relativity became messier but also richer, and the battle over the correct theory of gravity intensified. The stunning observations being made with the new telescopes and instruments developed during the explosion of physical cosmology provided additional ammunition. A pattern emerged whenever the analysis of a new piece of cosmological data was presented as confirming general relativity. The new result was inevitably tied to a press release and ensuing press coverage and, also inevitably, followed by a flurry of papers pointing out that what seemed like incontrovertible evidence for general relativity wasn’t really that solid.

  In January 2008 a paper in Nature signaled yet another quiet shift. In it, an Italian team of observers analyzed the data from a survey of galaxies. It was the kind of thing that Jim Peebles and his followers had been doing for almost forty years. By studying how the galaxies were clustered together, the Italian team was able to measure the rate at which they were falling into each other, attracted by the gravitational field in which they were immersed. This was nothing new. It had been done quite a few times before with different surveys of galaxies. But what was interesting was how they presented their results: on the graph where they presented their data, the Italians superimposed what would be expected from general relativity but also from a few other, alternative models of gravity. Some of the theoretical predictions went straight through the data points, and others missed them completely. It was an obvious thing to do: compare theory and observation.

  The Nature paper heralded a change in spirit and emphasis among the observers in cosmology. The emphasis since the late 1990s had been solely to measure, characterize, and nail dark energy, but this paper instead used cosmological observations to test general relativity. It was a return to testing the fundamental assumptions of physical cosmology.

  In the ensuing years, testing general relativity has been at the heart of observational cosmology. We still want to know if there is dark energy, what it is made of, and how galaxies assemble themselves to become the building blocks of the universe. But again and again, in requests by scientists for funding, in seminars and plenary lectures, testing general relativity has taken center stage.

  Modifying gravity is still frowned upon by many if not all relativists. While tampering with general relativity when it comes up against the quantum is quietly accepted, fixing spacetime to agree with observations is something else. There is still so much to understand and discover in Einstein’s theory, and for relativists, changing it is an unnecessary and inelegant complication. But nature may not agree, and with astronomers taking an interest in Einstein again, we now have an opportunity to explore the fundamental laws of spacetime, looking farther and deeper in the cosmos.

  The ideas of Dirac, Sakharov, and Bekenstein, bolstered by new work in observational cosmology, offer a new way of thinking that is too exciting to ignore and give new purpose to the juggernaut of cosmology. Some of my colleagues at Oxford and Nottingham and I recently decided to write a survey of the field of modified gravity. We felt like jungle explorers uncovering new exotic species. There were dozens of theories, each one odder than the next, proposing quirky modifications to general relativity, often with surprising and realistic results. Our review presented a rich bestiary of gravitational theories, many of which could give general relativity stiff competition. There are so many people thinking about alternatives to general relativity that today’s big general relativity meetings—the successors to the DeWitts’ Chapel Hill conference and Alfred Schild’s Texas Symposiums—offer parallel sessions packed with speakers from all generations and continents trying to take general relativity apart. It is still a fringe activity, but it’s one with many activists.

  When I gave my talk that afternoon in Cambridge, Efstathiou had been dismissive. Yet even Efstathiou, a brilliant mind and one of the pioneers of the current standard cosmological model in which general relativity, dark matter, and dark energy all play their role, would be excited if the new astronomical data pointed at new physics. A new theory of gravity, far-fetched as it may be, would definitely count as new physics. It is now up to the new astronomical data to tell us whether there truly is something new out there.

  14

  Something Is Going to Happen

  I RECENTLY SPENT SOME time advising the European Space Agency. ESA is responsible for sending scientific satellites into space, often cooperating with NASA. One of its most famous experiments is the Hubble Space Telescope, which has been used to take some of the crispest, cleanest images of deep space.

  Satellites are the new outposts of science, unspeakably sophisticated laboratories where virtually unimaginable experiments can take place, floating in space at the boundaries of our reach. And they are expensive, costing anywhere from half a billion to many billions of dollars each. You don’t just chuck these beasts up into the sky. It takes years—sometimes even decades—of planning and design before a firm decision is made on whether sending them up is worthwhile.

  At ESA, we discussed what humanity’s future space missions should be along with various proposals that were being made by large international teams of scientists. During the long, drawn-out meetings in which we were clobbered with PowerPoint presentations, Gantt charts, and costs that made my eyes water, I would often lose the will to live. This science seemed so different from the freewheeling exploration, unbridled creativity, and beautiful mathematics that had pulled me in as a graduate student. It was also shocking that we were discussing such far-reaching, breathtaking missions as if they were corporate enterprises, like opening new factories in some faraway land.

  What struck me forcibly was how, in the middle of the drudgery and technospeak, general relativity was at the heart of the scientific case for so many of the satellite missions pr
oposed. Yes, general relativity was writ large on all the proposals, hovering magnificently above the specifics and technicalities that we were discussing. There and then, we were being asked to fund billion-dollar missions that would either test Einstein’s theory or use it to explore the outer recesses of space and the inner workings of dense, massive objects. It was the future of space science in the twenty-first century. Not all the proposals could be funded, not all the satellites would fly, and the choice was breathtaking.

  One mission proposed to pick out the ripples of space and time, the waves of gravity expelled from the explosive collisions between black holes. It would be the spawn of LIGO and GEO600, a humongous interferometer made up of not one but three satellites orbiting the sun with ultraprecision laser beams bouncing back and forth between mirrors spaced millions of kilometers apart. Called the Laser Interferometer Space Antenna, or LISA, it would mop up after the ground-based experiments that are currently coming online, picking up the faint signals that LIGO and GEO won’t see.

  That wasn’t all. Another mission was proposed to measure the history of the expansion of space back to when the universe was a hundredth of its current age. It would take the methods of physical cosmology and push them to eleven, surveying swaths of the sky to build up catalogues with hundreds of millions of galaxies. Then, by looking at how the galaxies are assembled together into the vast cosmic web, carefully studying how the clusters and filaments of light came together around voids through gravitational collapse, it would be possible to figure out the effects of dark matter and dark energy or whether, indeed, as some now seem to believe, Einstein’s theory breaks down on the largest scales.

  There was yet another proposal for a satellite that would target the inner cores of black holes and look for the powerful x-ray emissions that had opened up such a phenomenal window on the universe in the late 1960s and 1970s. This time, it would be possible to go further and look at how the extremely warped spacetime near their centers would shred matter and light apart, just as Zel’dovich, Novikov, Rees, and Lynden-Bell had claimed it would. For the first time, it might just be possible to measure physical processes that happen close up to the infamous event horizon, the Schwarzschild shroud that had baffled so many for so long.

  During those meetings it became clear to me that general relativity will be at the heart of physics and astronomy in the twenty-first century.

  It’s not going to be easy. The real world of tightened budgets, poverty, and recession make many think twice about spending billions of euros or dollars on a satellite mission. While it’s not surprising that the US government decided to pull out of funding LISA, it’s still devastating.

  LISA was to be the final step in the discovery of gravitational waves. Not only would LISA discover these elusive ripples, it would be a colossal, perfect observatory for using them to look at black holes colliding and neutron stars circling each other. LISA would let us learn so much about all the fantastic exotica that Einstein’s theory of relativity predicts. The first stage of LIGO was a huge success even though it didn’t see anything. It proved that the technology, an insane mishmash of lasers, quantum, and precision engineering, actually works and is gearing up to be made even better. The next stage of LIGO, known as Advanced LIGO, may see something and prepare the way for LISA. But now, with the Americans pulling out, LISA is on the ropes. Who would be willing, in such a time of need, to fund a big beast with such an esoteric goal?

  The quest for gravity waves is just too important to be given up. And so the Europeans, through ESA, will go ahead. The new interferometer will be smaller, but still spectacular. It will still cost billions, just not as many. And the distraught relativists in America have regrouped and refuse to give up. Quietly, a number of groups scattered throughout the country have set to work trying to come up with their own proposal for something cheaper, more compact, and less ambitious that would still be able to look into the far recesses of spacetime. If the Europeans have a change of heart or are further consumed by the financial crisis, there will be a backup plan.

  We don’t have to wait for the satellites to go up. Fantastic things are already happening. We’ve seen the checkered history of the singularity and how repugnant it was to so many great minds, from Albert Einstein and Arthur Eddington to John Wheeler (until he saw the light). With the discovery of quasars, neutrons stars, and x-rays and the phenomenal burst of creativity from the likes of Wheeler, Kip Thorne, Yakov Zel’dovich, Igor Novikov, Martin Rees, Donald Lynden-Bell, and Roger Penrose, black holes became firmly cemented in our consciousness. By the end of the period in the 1960s and 1970s that Kip Thorne called the Golden Age of General Relativity, black holes had become real things, as much a part of astrophysics and physics as stars and planets.

  On my shelf I have two textbooks on general relativity that came out at the end of the golden age. They are very different. One of them, Gravitation, was written by John Wheeler and two of his brilliant ex-students, Charles Misner and Kip Thorne. It is over a thousand pages long, big with a black cover like a gothic phone book, exquisitely illustrated and packed with just about everything you might want to know about spacetime. MTW, as it is known, has all the odd stuff in it, the Wheelerisms that Wheeler kept on coming up with in his talks and conferences. The other textbook is by Steven Weinberg, one of the fathers of the standard model of particle physics. While Weinberg has established himself as one of the towering intellects of the quantum, he also dabbled in general relativity, and his book Gravitation and Cosmology is a careful, considered introduction to Einstein’s theory. It has much of what MTW has but without the madness. And, given the exciting discoveries of the decade that preceded it, Weinberg’s book doesn’t have much on black holes. In fact, black holes are cautiously mentioned toward the end of a subsection in the middle of the book as something to watch out for, as if black holes come from pushing general relativity just a bit too far.

  You can see why some people were still cautious. Yes, all the evidence seemed to point at dense, heavy objects both far and near. And it was difficult to explain them any other way if not as black holes. But truly, no one had actually seen a black hole. To look at black holes directly is a bit of a paradox. There is nothing there to see—black holes are invisible behind the Schwarzschild shroud. Just because we can’t see them doesn’t mean they aren’t worth looking at. In fact, we have a gigantic black hole sitting right in the middle of our galaxy, the Milky Way. It weighs about a hundred million times more than the sun and has a radius of about 10 million kilometers. It is big. But it is also tens of thousands of light-years away, which means that it takes up only about a hundred-millionth of a degree in the sky, making it tinier than a pinprick from our point of view, far smaller than we are able to resolve with our current telescopes. It is only through the cleverness and perseverance of astronomers that we can be assured a black hole is there.

  Two research groups, one based in Munich and another in California, have patiently followed the motion of a few stars that are hovering close to the center of the Milky Way. Over more than a decade they have been able to track the motion of that group of stars as they swoop around and around, and they have found that the stars move in incredibly curved orbits, clearly being pulled in by some gigantic gravitational force. By carefully measuring the orbits of these stars, they are able to figure out not only how strong gravity is in that region but also where all that gravitational pull is coming from. Combining these observations, the two groups are able to measure the mass of the black hole with exquisite precision and to pin down where the singularity in spacetime should be.

  There is more. Astronomers and relativists are mobilizing to build the telescope that will actually see the black hole. Called the Event Horizon Telescope, it will have a resolution of a billionth of an angular degree, a fraction of the size the black hole takes up in the sky, so that it will actually be able to see Schwarzschild’s shroud, the surface of the black hole that Oppenheimer and Snyder showed is a snapshot frozen in time.
It will be a dark shadow surrounded by the swirling mess that Zel’dovich and Novikov conjectured would surround the black hole, the accretion disk of stars, gas, and dust being shredded by the gravitational pull of the singularity.

  The accumulating evidence is very compelling. While Weinberg’s reticence was understandable, it is now difficult to find anyone who would argue against there being a black hole in the center of the Milky Way. And just like the Milky Way, all the other galaxies should have black holes firmly in their centers like massive engines surrounded by gargantuan spirals of stars.

  The media find anything to do with general relativity and Einstein’s great ideas both enticing and newsworthy. Images of the center of our galaxy lead to headlines like “Black Hole Confirmed in Milky Way” on the BBC, and “Evidence Points to Black Hole at Center of the Milky Way” in the New York Times. On the day I am writing this, the BBC news website features a comment from an Oxford colleague of mine on a recent observation of a quasar now shown to be a super-massive black hole with a mass of a billion suns. What stuns me is that almost fifty years after Maarten Schmidt’s measurements and the first Texas Symposium, black holes can still create such a stir.

  Not a month goes by without something in the news about cosmology or black holes, about the beginning of the universe or echoes of other universes, signatures of the mysterious multiverse. Words like black holes, Big Bang, dark energy, dark matter, multiverse, singularity, and wormholes have penetrated the farthest recesses of popular culture, from Broadway plays and songs to comedy shows and Hollywood movies. And then there are the countless ways in which general relativity has been folded into science fiction, from novels to TV shows to movies. They have surpassed even Wheeler’s wildest dreams in terms of imagination and creativity. Everyone seems to consider himself or herself an expert on general relativity.