The Perfect Theory

by Pedro G. Ferreira

  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.

  While Zel’dovich was creative, expansive, and intuitive, Sakharov was both more technically adept and more interested in abstract problems. The pair spoke admiringly of each other. Sakharov considered Zel’dovich “a man of universal interests,” while Zel’dovich complimented his colleague’s unique and idiosyncratic way of solving problems by saying, “I don’t understand how Sakharov thinks.”

  From 1965, Andrei Sakharov focused on cosmology and gravity, but he worked at his own pace. Zel’dovich produced a torrent of papers laden with new ideas, but Sakharov was more spartan in his output. His collected works make up a slim volume. Among his meager output are some veritable gems on the formation of structure, the origin of matter, and the nature of spacetime. In one short, crisp paper, Sakharov argues that the laws governing spacetime are but an illusion and arise from the complicated quantum nature of reality. He argues that looking at spacetime and how it behaves is very much like looking at water, crystals, or other complex systems. What you think you see is really nothing more than a broad-brush picture of some more fundamental reality. The quantum properties of water molecules and how they loosely bind together are what make water look like water, a clear fluid that sloshes around and behaves the way it does. While the details differ, Sakharov’s broad view proved prescient of how spacetime is perceived now, more than forty years later, as a result of progress in quantum gravity.

  Sakharov looked at Einstein’s theory and conjectured that the geometry of spacetime wasn’t really fundamental, in the same way that the viscosity of water or the elasticity of a crystal wasn’t fundamental. These were properties that emerged from a more basic description of reality. Similarly, gravity emerges from the quantum nature of matter. The surprising result in Sakharov’s simple, three-page paper is that Einstein’s field equations emerged naturally from such an assumption. In other words, the quantum world would naturally induce the geometry of spacetime. Sakharov’s induced theory of gravity looked somewhat like general relativity but in fact led to a more
complicated set of equations. Einstein’s field equations were already a torment; Sakharov’s induced gravity was far worse. The differences from Einstein’s theory would really be visible only when spacetime became very curved, near black holes, or in the very early universe when everything was hot and dense, or on microscopic scales where Wheeler’s quantum foam could come into play. When physical laws were pushed to extremes, they broke down and new laws emerged that encompassed the old ones.

  Andrei Sakharov published his paper in 1967 when he had other things on his mind. His years working on the bomb project had brought him accolades from the Soviet regime. Like Zel’dovich, he was awarded the Hero of Socialist Labour medal three times for his pivotal role. But living up close to the bomb had made him acutely aware of the catastrophic consequences of the nuclear arms race that the Soviets were engaged in with the United States. As Sakharov increasingly objected to nuclear weapons, he also found himself losing his stature and being ignored by the regime. In 1968, he broke ranks, publishing an essay titled “Reflections on Progress, Peaceful Coexistence, and Intellectual Freedom,” wherein he unequivocally declared his objections to one of the Soviet Union’s main defense programs, the development of antiballistic missile defense. It was the end of Andrei Sakharov’s tenure as the model Soviet citizen. The high-profile dissident was stripped of his privileges and awards, banned from working on classified projects, and exiled to Gorky. Zel’dovich frowned at what Sakharov called his “social work,” saying to his closest colleagues, “People like Hawking are devoted to science. Nothing can distract them.” Yet, as Sakharov wrote in his memoir, due the strength of his feelings toward the situation in the Soviet Union, “I felt compelled to speak out, to act, to put everything else aside, to some extent even science.”

  Sakharov may have suffered a personal setback in his scientific career, but his little idea of how the quantum might change general relativity would resurface again and again over the following decades. His paper anticipated a barrage of new quantum ideas that would batter general relativity throughout the 1970s. Some relativists thought correcting the theory in the way Sakharov had suggested would bring it more in line with the quantum world and cure the problems with infinities that plagued the theory. But by the end of the decade, Steven Weinberg and Edward Witten had proved that the infinities in such a theory couldn’t cancel. Tweaking the theory wasn’t enough to fix it—something more substantial had to be done.

  The “super” theories—supergravity and superstrings—were definitely more substantial and seemed promising in their revisions to Einstein’s theory. The fundamental idea behind general relativity remained the same—the geometry of spacetime was still center stage in the understanding of gravity. It just wasn’t the four-dimensional spacetime that Einstein had originally envisaged. In the ten- or eleven-dimensional spacetimes of the super theories, the equations looked similar, but in practice the extra dimensions gave rise to a new realm of extra fundamental particles and force fields affecting the four-dimensional world that we see around us.

  A few lone voices resisted this assault on general relativity, but the overwhelming feeling was that general relativity, when confronted with the quantum and in regions of high density or curvature near singularities or the Big Bang, needed to be fixed.

  Einstein’s theory remained a resounding success if you steered clear of the minefield of quantum gravity and didn’t need to work with the universe right at its beginning, when it was hot, dense, and messy. On large scales, in astrophysics and cosmology, general relativity kept on giving.

  If astronomy were an industry, the annual International Astronomical Union meeting would be its annual convention, with just about everyone trying to sell something. At the 2000 meeting in Manchester, UK, over a thousand people gathered to gloat over their recent discoveries and unveil the new projects that were about to be switched on. The cosmologists at that year’s meeting were a triumphant bunch, myself included. The supernova result showing an accelerating universe had been announced a few years before. The measurements of the geometry of the universe had been announced that year. Observations were pointing to a simple yet exotic universe with dark matter and the cosmological constant. There was no more reason for disagreement and debate—personal preferences didn’t matter anymore. It was good, solid science, the data was clear and consistent, and there didn’t seem to be any way around it.

  Jim Peebles was giving one of the plenary talks. This meeting was in some sense a celebration of Peebles’s ideas and how far they had taken us. All the discoveries of the previous few years stemmed, in one way or another, from a field that he had founded with a few others. But Peebles was a staunch avoider of bandwagons, even if he was the one who set them off. In his talk, he reined in the hysteria by asking why we want to make precise measurements of the universe. And he gave his answer: to test our assumptions. He probed every angle of the Big Bang model: Why was it hot in the beginning? Where did the large-scale structure come from? How did galaxies form? In the middle of his talk, Peebles pointed out something obvious. As he later wrote in the proceedings, “The elegant logic of general relativity theory, and its precision tests, recommend GR as the first choice for a working model for cosmology.” But maybe cosmologists shouldn’t jump to conclusions, he warned. While general relativity had been shown to work with utmost precision on the scale of the solar system—the precession of Mercury was a beautiful example—we had no idea if we could apply it with the same level of precision on the scale of the universe. It was, he said, “a spectacular extrapolation.” Peebles was right, although the conference attendees, on the whole, failed to absorb the significance of his assertion.

  The French astronomer Le Verrier had argued passionately that to properly explain the drift in Mercury’s orbit, there had to be a new, undiscovered planet, Vulcan, hovering at the center of the solar system. His faith in Newtonian gravity had led him to predict the existence of something new, exotic, and unseen. Without Vulcan, the Newtonian model wouldn’t work. Of course, Le Verrier had been proved wrong. It wasn’t a new planet but a new theory of gravity that was needed to fix the model.

  Now, in the early twenty-first century, we seem to be in a similar situation, with a wonderful theory of gravity that, to explain cosmology, requires that more than 96 percent of the universe be made up of something we can’t see or detect. Could this be yet another crack in the edifice that Einstein had constructed almost one hundred years before? That general relativity might have to be corrected due to quantum physics had been accepted without too much fuss. But questioning general relativity’s efficacy on large scales was something different. If the dark matter and dark energy of the universe were eliminated from the picture, Einstein’s beautiful theory would have to be modified. The prospect was as unappealing to many astrophysicists as taking a sledgehammer to a classic car just so it would fit in the garage.

  The Israeli relativist Jacob Bekenstein started thinking about modifications to Einstein’s theory in the early 1970s, while he was still a graduate student of John Wheeler at Princeton. At the same time as Bekenstein was thinking about entropy and black holes, he was also puzzled by general relativity and intrigued by the alternative theory that Dirac had proposed. “At some point,” he said, “I felt I did not understand why one did things in general relativity in a certain way, why some issues were important, indeed why one followed the general path to general relativity. I felt the need to compare with a different attempt.”

  The “different attempt” Bekenstein chose to work on was proposed by his compatriot, the Israeli astrophysicist Mordehai Milgrom, in the 1980s. Milgrom’s idea was to take a radically new look at how gravity behaved in galaxies. He pointed out that the evidence for dark matter in the rotation of galaxies seemed to arise out in the edges, where the gravitational force was very weak. If Newtonian gravity was applied in that regime of extremely weak forces, indeed it would make sense to invoke the existence of some unseen matter that could bolster the gravitational pu
ll. But could it not be that the mistake was to apply Newtonian gravity there? So Milgrom made a bold claim, that stars well out in the tails of galaxies felt heavier so that the gravitational pull by the stars at the center of the galaxy on these outer stars would be much more effective than originally assumed. Because the gravitational pull was more effective, this meant the outer stars could move more quickly. This effect could explain what Vera Rubin and others had observed, that the outer parts of galaxies spin around their centers far more quickly than expected. Milgrom called his new approach Modified Newtonian Dynamics, or MOND for short.

  Many astrophysicists thought Milgrom’s proposal went too far in its modification of gravity. It lacked a guiding principle and passed beyond valid speculation into the realm of make-believe. When Bekenstein described the idea at an International Astronomical Union conference in 1982, he said, “Some looked at me as if I told them I have seen a UFO. . . . Almost everybody thought the emerging dark matter notion was important, and almost everybody was very much for dark matter.” For the next two decades, the overwhelming majority of astrophysicists and relativists ignored Milgrom’s idea or tried to shoot it down. Every now and then, a paper would apply Milgrom’s law in a different astrophysical situation and show that it didn’t work. Often these papers were cobbled together and incomplete, yet as long as the paper ruled out MOND, it was deemed good science and easily published. If it defended MOND, it was deemed bad science and getting it into print became an uphill struggle. MOND was, as one astronomer said, “a dirty word.”