by David Kaiser
Gone are the days when observable quantities are known only to within a factor of ten or two. Ask those same questions that Overbye’s heroes had struggled to answer, and today any cosmologist can rattle off the answers as quickly and confidently as a schoolchild who has mastered the multiplication tables. How quickly are galaxies receding from each other? 67.4 kilometers per second per megaparsec, plus or minus 0.7 percent. How old is our observable universe? 13.80 billion years, plus or minus 0.2 percent. How much matter and energy fills the universe? If one includes the weird and unexpected dark energy in the tally, the total weighs in at precisely the razor-edge critical value, give or take 0.2 percent. When graphing data for some quantities these days, cosmologists must amplify their error bars by a factor of four hundred just so the remaining uncertainties can be seen on the page.3
Figure 17.1. Using instruments on the European Space Agency’s Planck satellite (shown lower right), cosmologists have been able to study subtle patterns in the distribution of energy among photons in the cosmic microwave background radiation, a remnant glow released when the universe was only about 380,000 years old. (Source: D. Ducros, © European Space Agency and the Planck Collaboration.)
Where Overbye had focused on the outsized personalities and human struggles at the heart of cosmology, astrophysicists today often focus on two rather different protagonists: white dwarf stars, especially the type that end their brilliant careers in a particular type of supernova explosion; and the cosmic microwave background radiation, the remnant glow left over from the first formation of stable hydrogen whose pattern has been measured to extraordinary precision by the WMAP and Planck satellites. Since the mid-2000s, several independent lines of investigation—relying on different instruments that are focused on different physical processes—have more or less converged to give one consistent set of answers. For the first time in human history, scientists can date the age of the cosmos.4
Cosmologists thus enjoy an embarrassment of empirical riches these days. We sit immersed in huge data sets bulging with billions of entries, to which experts may devote superlative statistical care. Yet the field has hardly been overrun by stodgy accountants donning green visors. In fact, much of the theoretical activity contributed by professional cosmologists these days looks more bizarre than ever, even absurd; some proposals betray more than a whiff of the circus tent. Sit through a lecture by nearly any cosmologist these days, and before long you are likely to hear phrases like “extra dimensions,” “brane-world collisions,” “variable equation-of-state quintessence,” and “multiverse”—the latter presumed to be an infinitely large container, operating under its own set of physical laws, within which our entire observable universe may be but one tiny bubble.
Of course, neither “bizarre” nor “absurd” imply “incorrect.” The long march of cosmology since the Renaissance has been marked by one seemingly preposterous proposal after another, from Copernicus’s assertion that the Earth whizzes around the Sun (our own sensations of stillness notwithstanding) to Einstein’s suggestion that space and time bend in the presence of matter. Bizarreness, too, is in the eye of the beholder. Even so, cosmologists’ collective imagination in recent years has behaved just like an incompressible fluid: try to constrain it within tight quarters (say, by means of precise measurements of observable quantities), and it will squirt out in other directions.
Roger Penrose’s recent work is emblematic of the latest imaginative excursions. Now that cosmologists have determined the precise age of our observable universe, Penrose has proposed that all the buzzing, blooming confusion since the big bang has been but a trifle, a finger snap in the longer (perhaps infinite) history of our universe. Rather than presume that the big bang of 13.8 billion years ago was the start of everything, in other words, Penrose has crafted an ambitious model that he calls “conformal cyclic cosmology,” or CCC. Penrose suggests that our universe has already passed through innumerable previous instantiations prior to the big bang that started our present epoch, and that it will likely cycle on like this forever more, much as in Friedrich Nietzsche’s “eternal recurrence.”5
The first C in Penrose’s model—“conformal”—is critical. The most familiar example of a conformal map is the Mercator projection of Earth. Although Earth’s surface is roughly spherical, one may represent Earth’s features on a flat, two-dimensional map. During the Renaissance, the Flemish cartographer Gerardus Mercator realized that he could stretch and warp the image of Earth’s landmasses on his flat map in such a way that he could preserve the angles between shipping routes near crowded ports—information of great interest to navigators. The result was a map that preserved angles and shapes of small objects everywhere on the map but that greatly distorted overall length scales. Hence, Antarctica looms large on a Mercator projection, dwarfing Europe and Asia combined, even though on Earth’s actual surface, Europe and Asia together cover nearly four times more area than does Antarctica. More recently, the Dutch artist M. C. Escher featured conformal projections in many of his famous lithographs. (Conformal maps clearly hold special appeal in the Low Countries.)
Physicists and mathematicians have long made use of conformal mappings to simplify a given problem or to view strange solutions from a new vantage point. The technique has proven especially powerful for the study of Einstein’s general relativity, as a means of gaining leverage on the deformations of spacetime. Penrose made his landmark contributions to mathematical physics back in the mid-1960s by brilliant application of conformal techniques. (In fact, as historian Aaron Wright has documented, Penrose was inspired in part by Escher’s playful pictures, which delighted Penrose as a child.)6 Armed with these powerful graphical methods—now known as “Penrose diagrams”—he demonstrated that a black hole must necessarily lead to a genuine rupture in spacetime, or “singularity.” No path, not even a light ray’s, can extend beyond some finite limit in the face of a singularity. Penrose’s conformal maps proved that the singular behavior was no artifact of this or that coordinate system, nor was it restricted to simple, highly symmetric scenarios.
Figure 17.2. A conformal diagram, developed by mathematical physicist Roger Penrose, to study the causal structure of spacetime. Time runs vertically, and light travels along 45-degree diagonals. In this diagram, matter has collapsed into a black hole. A distant observer may send light signals to the infalling matter and receive a response only up until the time when the matter crosses the “event horizon”; from there, as Penrose clarified with diagrams like this, the matter will eventually reach the “singularity” within the black hole, a rupture in spacetime itself. (Source: Illustration by Viktor T. Toth.)
Penrose has returned to these conformal techniques, now turning them loose on the universe as a whole. He argues that the end of one cosmic epoch, or “aeon,” may look quite a lot like the beginning of another—so much so that perhaps they might be stitched together, end on end, into an infinite tower of repeating aeons. During the earliest moments of one aeon, the universe would be hot and dense, just as our observable universe had been right after our big bang. When temperatures are much greater than particles’ masses, the particles behave as if they have essentially no mass at all. They zip around at nearly the speed of light, just like photons do. That’s critical, because massless particles betray no inherent reference scale—no baseline unit of length or time, no meter stick or calibration clock against which other measures might compare. As far as a photon is concerned, time simply does not flow. A spacetime filled with massless particles would have no inherent scales by which to measure length or time. It would be governed, in other words, by conformal geometry: shapes and angles would have meaning, but overall distances would not.
Remarkably, the end of an aeon might behave in much the same way. As the universe expands and cools after the beginning of one of these cycles, the ambient temperature would drop—looking, for observers within that epoch, just as our own big-bang universe does to us. Massive particles like electrons, protons, hydrogen atoms,
and all the rest would gradually lose energy; they would no longer zip around as fast as massless photons do. In that regime, length and time scales would emerge; the symmetries of conformal geometry would be suppressed. The world would behave as ours does today. Pockets of dust would clump and, fueled by the energy of gravitational collapse, ignite into the nuclear reactors we call stars. Eventually, billions of stars would attract each other gravitationally and form tight-knit galaxies. Galaxies themselves would form clusters and superclusters. All the cosmic phenomena that our keenest instruments can observe would unfold: galaxies would recede from each other; certain white dwarf stars would go supernova.
So much for the behavior of the universe after a few tens of billions of years. We know from the supernova measurements and the WMAP and Planck data that our universe will almost certainly never recollapse upon itself; it should continue to expand forever. So Penrose presses on: what would the universe look like after, say, 10100 years, a timescale that makes the present age of our observable universe (not much more than 1010 years old) seem positively minuscule? By such late times, nearly all the extant matter would likely have fallen into black holes. Indeed, swarms of black holes would likely have swallowed each other, forming supermassive black holes. But even black holes, it turns out, are far from foolproof containers. Penrose’s colleague Stephen Hawking demonstrated in the mid-1970s that black holes should radiate, slowly but surely emitting energy in the form of low-energy light. (This “Hawking radiation” is compatible with Penrose’s earlier proofs about singularities. No radiation leaks out from the vicinity of the singularity; the radiation is generated just beyond the boundary of the black hole, known as the “event horizon.”) Because of Hawking radiation, black holes behave like cosmic trash compactors: swallowing up massive detritus and ever so slowly seeping that energy back out into the cosmos in the form of massless photons. The process might continue inexorably, until the black holes themselves evaporate. What would be left? A nearly empty universe containing virtually nothing but massless particles—a spacetime, that is, governed once again by conformal geometry.
Penrose, that master of conformal geometry, considers the geometrical similarity of start and end too good to pass up. With more of his mathematical sorcery, he demonstrates how one can smoothly identify the far-future surface of one aeon with the beginning surface of the next, and so on ad infinitum. Sound bizarre? No doubt. Yet Penrose’s audacious proposal is in fact rather conservative by today’s cosmological standards. For one thing, his model requires just four dimensions of spacetime: one dimension of time and three dimensions of space, the same as in Einstein’s physics, let alone Newton’s. No need for six or more additional dimensions of space, as superstring theory requires—dimensions that, to hear the string theorists tell, must surely be out there, jutting out at right angles to the height, depth, and breadth that we know and love, yet somehow remaining hidden from view, either because they have mysteriously curled up on themselves and shrunk down to submicroscopic size or because, as luck would have it, we inhabit some strange sausage-like slice (a membrane, or “brane”) on which gravity just happens to behave as if there were only three spatial dimensions.7
The boundaries between aeons in Penrose’s model would betray none of the bizarreries that mark today’s ongoing quest for a quantum theory of gravity. Ordinarily, cosmologists expect the superhot, high-energy regimes surrounding a big-bang event to excite quantum fluctuations of spacetime itself. Not only would spacetime behave like a wobbly trampoline, as in Einstein’s general relativity, but each tiny unit of space and time would presumably wiggle around in some blur, subject to Heisenberg’s uncertainty principle. That might sound exciting, except for the nagging fact that no one has yet produced a workable quantum theory of gravity that might describe the behavior of such quantum-spacetime wiggles. Not to worry, counsels Penrose: spacetime at the aeon boundaries in his model would be perfectly smooth and well behaved, governed by Einstein-like equations. No need to appeal to wild and as-yet-unknown laws of quantum gravity, be it string theory or some other contender.
Amid such delightful flights of cosmological theorizing—bizarre to some, conservative to others—Penrose, too, sits immersed in today’s cornucopia of data. Like nearly all cosmologists, he trains his eye on the cosmic microwave background radiation as captured by satellites like WMAP and Planck. Penrose argues that if his model is correct, then we should be able to see through the boundaries separating various aeons. Subtle features from the previous aeon, before the big bang that started our own, might be imprinted in the cosmic radiation. Those signals would show up as concentric circles in the sky (yet another cyclic feature of his model). For example, a massive black hole might have undergone repeated collisions with comparable objects during the late stages of the previous aeon. Each of those encounters would have generated tremendous bursts of energy, expanding in circles outward from the collision zone. Those ripples would cross the boundary to our own aeon, ultimately appearing as concentric circles of anomalously uniform temperature amid the tiny fluctuations of the cosmic microwave background radiation.
With a collaborator, Penrose released a paper in November 2010 indicating that a close analysis of the WMAP data did indeed turn up just such families of concentric circles. Within the space of three days that December, three separate groups reanalyzed the data in the light of Penrose’s claim and found no statistical significance. The circles, if really there, were just as likely to show up by chance given the usual understanding of fluctuations in the radiation. Penrose and his colleague quickly offered a response, challenging some of the arcane statistical arguments. The time lag between critique and countercritique shrank from days and weeks to hours. Like the supermassive black hole collisions, Penrose’s papers generated an explosive outburst of activity.8
Penrose’s concentric circles seem not to have withstood the experts’ scrutiny and heralded a revolution in cosmology; they are more likely to fade into oblivion like so many UFO enthusiasts’ crop circles. Even so, a larger conclusion seems clear. Penrose’s zeal to connect his elegant ideas to exacting details of cutting-edge observations captures just what it’s like to work in cosmology today. With the field swimming (drowning?) in high-precision data, no longer does it suffice to argue on the basis of mathematical elegance or aesthetic beauty alone. Terabytes of precision data and sophisticated statistical algorithms have become a cure for all those lonely hearts—a Match.com for the cosmos.
18
Learning from Gravitational Waves
A billion years ago (give or take), in a galaxy far, far away, two black holes concluded a cosmic pas de deux. After orbiting each other more and more closely, their mutual gravity tugging each to the other, they finally collided and rapidly merged into one. Their collision released enormous energy—equivalent to about three times the mass of our Sun, if all the Sun’s mass were converted to raw energy. The black holes’ inspiral, collision, and merger roiled the surrounding spacetime, sending gravitational waves streaming out in every direction at the speed of light.
By the time those waves reached Earth, early in the morning of 14 September 2015, the once-cosmic roar had attenuated to a barely perceptible whimper. Even so, two enormous machines—the kilometers-long detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) in Louisiana and Washington State—picked up clear traces of those waves.1 In October 2017, three longtime leaders of the LIGO effort—Rainer Weiss, Barry Barish, and Kip Thorne—received the Nobel Prize in Physics for this accomplishment.
The discovery was a long time in the making, in human terms as well as astronomical ones. Einstein predicted such waves a century ago, a consequence of general relativity, his elegant theory of gravitation as the warping of spacetime. Yet Einstein’s first calculation of gravitational waves was marred by some arithmetic errors (not uncommon, even for Einstein). Before long Einstein and most of the world’s experts fell into a decades-long debate over whether such waves should really exist a
t all. The theorists twisted themselves up in knots: gravitational waves must exist; they might exist; they could not exist; no, indeed, they must exist. Around and around they went. Their spirited arguments—which Daniel Kennefick charts in his fascinating book Traveling at the Speed of Thought (2007)—came to sound like the famous vaudeville act: “I can’t pay the rent”; “you must pay the rent.”2
Consensus among theorists emerged slowly over the course of the 1960s. The experts came to agree that gravitational waves really should exist according to the equations of general relativity, and the waves should have specific characteristics. But that still left many questions open. Was general relativity itself a correct description of nature, and could gravitational waves ever be detected?
The question of detection grew at least as murky as the theorists’ debates had been. In 1967, physicist Joseph Weber published results of an experiment in which he claimed to have detected such waves—indeed, detected them with a strength about a thousand times greater than what theorists had come to expect. Exciting, puzzling, and quickly controversial, Weber’s announcement helped to draw more attention to the topic at a time when gravitation remained a side issue for most physicists. After greater scrutiny, however, most experts concluded that Weber’s early results, and a series of his follow-up experiments, had not actually detected gravitational waves.3