Cycles of Time 
by Roger Penrose.
Bodley Head, 288 pp., £25, September 2010, 978 0 224 08036 1
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How Old Is the Universe? 
by David Weintraub.
Princeton, 370 pp., £20.95, 0 691 14731 0
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Twenty years ago, the science writer Dennis Overbye published a marvellous book, Lonely Hearts of the Cosmos, in which he traced the development of cosmology – the scientific study of the universe as a whole – during the second half of the 20th century. The cosmologists in Overbye’s book were lonely for two reasons. They included the last remnants of a generation of astronomers who, before large groups of collaborators and automated data collection had become routine, used to sit up all night, alone, under unheated domes, squinting through huge telescopes to catch the faintest glimpses of light from faraway galaxies. And for much of the period that Overbye covered, the field of cosmology hung on the margins of respectability among physicists, a neglected stepchild in the shadow of such flashy fields as high-energy particle physics, with its hulking accelerators and skyrocketing budgets.

Overbye captured the cosmologists’ struggles to measure basic features of our universe. Usually their answers could be trusted only to within a factor of two – that is, each measurement carried roughly 100 per cent uncertainty. Were galaxies receding from each other at such-and-such a speed, or twice that fast? The answer bore directly on how old our observable universe could be – another key quantity that could be pinned down only to within a factor of two. (The instructor on one of my undergraduate courses in the subject merrily informed us on the first day that we could use the equation ‘1 = 10’, since most quantities of interest had comparable uncertainties. We were not, however, allowed to square that equation.) No wonder cosmologists had to suffer for so long: those huge uncertainties appeared downright amateurish when compared with the quantitative triumphs in other branches of physics. For the energy levels of a hydrogen atom, for example, theory and experiment had long since converged, agreeing right down to 14 decimal places.

Since even the basic pace of the universe’s expansion was so difficult to determine, cosmologists often threw up their hands (or argued at length) over follow-up questions, such as whether the expansion was speeding up or slowing down. The answer to that question would reveal how much stuff the universe contained. A densely packed universe, with lots of matter and energy per cubic metre, should eventually halt its expansion and collapse back onto itself, a big crunch at the end to mirror the big bang at the beginning. A universe with less matter and energy stuffed into each unit of volume would expand for ever at a quickening pace, becoming progressively more dilute. Balanced right between, Einstein’s equations predicted a Goldilocks solution: some critical amount of stuff per volume for which the rate of expansion would slowly fade but the universe would never recollapse, gently coasting into oblivion instead. The fate of the universe hung on numbers like the present-day expansion rate and the amount of stuff per unit volume. Yet try as they might – and their efforts were often extraordinarily clever – cosmologists simply couldn’t measure the universe’s basic features with the requisite confidence or precision.

That began to change, and to change fast, soon after Lonely Hearts of the Cosmos appeared. We cosmologists feel a lot less lonely these days. The field is booming, attracting new recruits, using fantastic new instruments, and producing a plethora of exciting new ideas. In the autumn of 1992, my fellow undergraduate physics students and I joined our professors for a champagne study break to mark the first release of data from the Cosmic Background Explorer (COBE) satellite. From its perch high above the atmosphere, the satellite had measured the first light released after the big bang: photons that had been streaming freely through the universe since the moment when electrons first began to combine with protons to form stable, neutral hydrogen atoms, about 380,000 years after the universe began. (Before that moment, ambient temperatures were too high to allow stable hydrogen to form.) From the subtle bumps and wiggles in the distribution of those photons, cosmologists could discern that the temperature of outer space today is just 2.725 degrees above absolute zero, and is consistent across the entire sky to one part in 100,000.

The following year, spacewalking astronauts repaired the Hubble Space Telescope, paving the way for further astronomical inquiry unhindered by the Earth’s atmosphere. Two independent teams used the refurbished Hubble to study supernovae, cataclysmic explosions from self-destructive stars that can temporarily outshine entire galaxies. Their data, first announced in 1998, reversed decades of expectations by suggesting that our universe isn’t just getting bigger; it’s getting bigger faster. To reconcile their robust observations with Einstein’s relativity, cosmologists were forced to consider that empty space had an intrinsic energy – dubbed ‘dark energy’, to signal our deep ignorance of its origin – whose tendency to make the universe expand overwhelms the competing gravitational tendency of matter to clump together. Five years after that came the first data from the Wilkinson Microwave Anisotropy Probe (WMAP), a satellite whose instruments can attain a resolution 30 times greater than those on COBE. Measuring totally different phenomena from the supernova studies, the WMAP data confirmed that nearly three-quarters of the energy content of the universe is dark energy.

The days are gone when observable quantities are known only to within a factor of ten or so. Ask the same questions today that Overbye’s heroes had struggled to answer, and any cosmologist can rattle off the answers as quickly and confidently as a schoolchild who has mastered his multiplication tables. How quickly are galaxies receding from each other? 70.4 kilometres per second per megaparsec, plus or minus 1.8 per cent. How old is our observable universe? 13.75 billion years, plus or minus 0.8 per cent. How much matter and energy fills the universe? If one includes the weird and unwelcome dark energy in the tally, the total weighs in at precisely the razor-edge critical value, give or take 0.7 per cent, meaning that the universe should continue expanding for ever. When graphing data for some quantities these days, cosmologists amplify their error bars by a factor of 400 just so that the remaining uncertainties can be made visible on the page.

David Weintraub’s new book, How Old Is the Universe?, captures the spirit of this post-lonely-hearts era. Weintraub, an astronomer at Vanderbilt University, offers a patient tour of the new data-rich landscape. Where Overbye had focused on the outsized personalities and human struggles at the heart of cosmology, Weintraub advances two rather different protagonists: white dwarf stars, especially the kind that end their brilliant careers in a particular type of supernova explosion; and cosmic microwave background radiation, that remnant glow from the first formation of stable hydrogen whose pattern has been measured with extraordinary precision by WMAP. As Weintraub emphasises, only in the last few years have several independent lines of investigation – relying on different instruments that are focused on different physical processes – converged to give one consistent set of answers. For the first time in human history, scientists can date the age of the cosmos.

Cosmologists thus enjoy an embarrassment of empirical riches these days. We have assembled huge datasets, to which experts may devote superlative statistical care. Yet the field hasn’t been overrun by stodgy accountants. Indeed, much of the theoretical activity contributed by professional cosmologists these days looks more bizarre than ever, even absurd. Of course, neither ‘bizarre’ nor ‘absurd’ implies ‘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 are as wobbly as a trampoline. Bizarreness is in the eye of the beholder.

Even so, many proposals today have a whiff of the circus tent. Sit through a lecture by nearly any cosmologist, and before long you are likely to hear such phrases as ‘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, in which our entire observable universe is just one tiny bubble. Cosmologists’ collective imagination behaves like an incompressible fluid: try to constrain it in one direction (say, by means of precise measurements of observable quantities), and it will squirt out in others.

Roger Penrose’s Cycles of Time takes one such imaginative leap. Now that cosmologists have determined the precise age of our observable universe, Penrose proposes that all the proliferating confusion since the big bang has been a mere finger snap in the longer (perhaps infinite) history of our universe. Rather than presume that the big bang of 13.75 billion years ago was the start of everything, in other words, Penrose proposes an ambitious model that he calls ‘conformal cyclic cosmology’, or CCC. The universe, he suggests, had already passed through innumerable previous instantiations before the big bang that started the present epoch, and that it will probably cycle on in this way for ever.

The first ‘C’ in Penrose’s model – ‘conformal’ – is critical. The most familiar example of a conformal map is the Mercator projection of the Earth. Although the Earth is roughly spherical, one may represent its surface on a flat, two-dimensional map. Mercator, the 16th-century Flemish cartographer, realised that he could stretch and warp the image of the Earth’s landmasses on his flat map in such a way as to preserve the angles between shipping routes near crowded ports – information of great interest to navigators. The result was a map that preserved angles and the shapes of small objects everywhere on the map, but greatly distorted scale overall. Hence Antarctica looms large on a Mercator projection, dwarfing Europe and Asia combined, even though in actuality, Europe and Asia together cover nearly four times the area of Antarctica. The Dutch artist Escher featured conformal projections in many of his lithographs. (Conformal maps clearly hold special appeal in the Low Countries.)

Physicists and mathematicians have long made use of conformal mapping to simplify problems or to look at strange solutions from a new vantage point. The technique has proved especially powerful for the study of Einstein’s general relativity, as a means of getting to grips with the warp and weft of space-time. Penrose made landmark contributions to mathematical physics back in the mid-1960s with his brilliant application of conformal techniques. He demonstrated with his ‘Penrose diagrams’ that a black hole must necessarily lead to a rupture in space-time, or ‘singularity’. No path, not even a light-ray’s, can extend beyond some finite limit in the face of a singularity. They are the cosmic equivalent of Shel Silverstein’s ‘where the sidewalk ends’.

Penrose has returned to these 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, as our observable universe was right after our big bang. When temperatures are much greater than particles’ masses, the particles behave as if they had essentially no mass at all: they zip around at nearly the speed of light, just as photons do. That’s critical, because the behaviour of massless particles involves no inherent reference scale – no baseline unit of length or time, no metre stick or calibration clock against which other measures might compare. As far as a photon is concerned, time simply does not flow. A space-time 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 a cycle, 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 universe would behave as ours does today. Pockets of dust would clump and, fuelled by the energy of gravitational collapse, ignite into the nuclear reactors we call stars. Thousands and soon millions of stars would attract each other gravitationally and form tight-knit galaxies; the galaxies would form clusters and superclusters; and all the cosmic phenomena that our keenest instruments can observe would unfold, just as Weintraub’s book describes: galaxies would recede from each other; some white dwarf stars would go supernova.

So much for the behaviour of the universe after a few tens of billions of years. We know from supernova measurements and WMAP data that our universe will almost certainly never recollapse on itself but continue to expand for ever. So Penrose presses on: what would the universe look like after, say, 10100 years, a timescale equivalent to the current age of our observable universe raised to the tenth power? By that late time, nearly all of the extant matter would be likely to have fallen into black holes. Indeed, swarms of black holes would have swallowed each other, forming supermassive black holes. But even black holes, it turns out, are not foolproof containers. Penrose’s colleague Stephen Hawking demonstrated 35 years ago 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 singularity itself; the radiation is generated just outside the boundary of the black hole, known as the ‘event horizon’.) Black holes behave like cosmic rubbish-compactors: swallowing up massive detritus and ever so slowly seeping energy back out into the cosmos in the form of massless photons. The process might continue inexorably, until the black holes themselves evaporate. A nearly empty universe would be left, containing virtually nothing but massless particles – a space-time governed once again by conformal geometry.

Penrose considers the geometrical similarity of start and end too good to pass up. With more of his mathematical sorcery, he demonstrates how the far future surface of one aeon can be smoothly identified with the starting surface of the next, and so on ad infinitum. This sounds bizarre, no doubt, yet Penrose’s audacious proposal is rather conservative by today’s cosmological standards. For one thing, his model requires just four dimensions of space-time: one dimension of time and three dimensions of space, the same as in Newton’s physics, and Einstein’s. No need for six or more additional dimensions of space, as superstring theory requires, dimensions which, to hear the string theorists tell it, must surely be out there, jutting out at right angles to the height, depth and breadth that we’re familiar with, 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.

Penrose’s model displays none of the bizarreries that mark the 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 in space-time itself. Not only would space-time behave like a wobbly trampoline, as in Einstein’s general relativity, but each minute unit of space and time would wiggle around in a blur, subject to Heisenberg’s uncertainty principle. That might sound exciting, but no one has yet produced a workable quantum theory of gravity that would describe these quantum space-time wiggles. Not to worry, counsels Penrose: space-time at the aeon boundaries in his model would be perfectly smooth and well-behaved, governed by Einstein-like equations. No need to appeal to the wild, woolly and as yet unknown laws of quantum gravity.

Penrose devotes his closing chapter to ‘observational implications’. Like nearly all cosmologists, he trains his eye on the cosmic microwave background radiation as captured by the WMAP satellite. He argues that if his model is correct, then we should be able to see through the boundaries separating aeons. Subtle features of the 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, which would expand 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 last November indicating that a close analysis of the WMAP data did turn up just such families of concentric circles. In early December, three separate groups analysed the data again 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 the origin of fluctuations in the radiation. Penrose and his colleague quickly offered a response, challenging some of the arcane statistical arguments. The timescale between critique and counter-critique shrank from days and weeks to hours. Whether or not Penrose’s concentric circles ultimately withstand the experts’ scrutiny and herald a revolution in cosmology (they could after all fade to oblivion like so many crop circles, as championed by UFO enthusiasts), his zeal to connect his elegant ideas to cutting-edge observations captures just what it’s like to work in cosmology today. Now that so much high-precision data is available, it’s no longer enough to argue on the basis of mathematical elegance or aesthetic beauty alone.

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Vol. 33 No. 7 · 31 March 2011

David Kaiser, in discussing Roger Penrose’s predictions about the cosmos in 10100 years’ time, equates that interval with the current age of the universe raised to the tenth power (LRB, 17 February). While the age of the universe is of the order of 1010 years, and (1010)10 does indeed equal 10100, the units of the latter quantity would be years raised to the tenth power rather than years, making the comparison meaningless. To illustrate this fact, the numbers come out differently depending on the units chosen: if the current age is measured in seconds, its tenth power comes out at more like 10170 seconds10, whereas 10100 years is 10107 in seconds. On the other hand, the error underlines Kaiser’s basic point: 10100 years is an incomprehensibly vast stretch of time.

Mark Taylor
Bristol University

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