Figure 19.2. LISA, the Laser Interferometer Space Antenna, which ESA and NASA will jointly build, launch and use to monitor low-frequency gravitational waves (by courtesy of Kip Thorne)
Follow-ups to WMAP, Planck and LISA will be the NASA Einstein Inflation Probe, which will focus on the CMBR, and the Big Bang Observer, which will study gravity waves. The two approaches together may lead finally to something no probes or studies, including the highly successful WMAP, have yet been able to give us: the long-sought understanding of the physical mechanism and energy scales of inflation itself.27 Gravitational waves offer the most direct opportunity we are likely ever to have to probe what the universe was like during the first split second of its existence.
Will this observational evidence show conclusively whether or not inflation actually did happen? Inflation theory makes predictions about what the patterns and characteristics of the gravitational waves should be like. If they turn out to match those predictions, that will be strong evidence. If no gravitational waves can be detected, that would support another model, the ekpyrotic model of the universe in which inflation does not occur but our universe was created by the exceedingly slow collision of two three-dimensional brane worlds moving in a hidden extra (fourth) dimension of space.
Out on a Limb
When it comes to the bigger picture suggested by eternal inflation, it seems such an idea ought to be impossible to test from our blinkered vantage point within our own universe. What evidence could be lying around within our very limited reach?
Stephen Hawking and his colleagues are far from giving up on the possibility of making relevant predictions that can be set against more precise future observations, perhaps by the Planck satellite. In a paper in September 2010, Hawking, Jim Hartle and Thomas Hertog admitted that there is ‘no way the mosaic structure [of universes] can be observed. We don’t see the whole universe but only a nearly homogeneous region [that lies within the range of our observations], within our past lightcone’.28 However, in spite of the possibility that much larger fluctuations are observable only on scales much more enormous than we can study – on ‘super horizon scales’29 – they thought that the no-boundary wave function could come to their aid in calculating small departures from homogeneity within the part of the universe that it is possible for us to observe. The absence or presence of randomness in the spectrum of temperature variations in the CMBR does, they claimed, provide useful information about the bigger picture – and whether there is a bigger picture.
Just as the ‘quantum wave function’ for a particle gives every possible path the particle could follow between two points, the no-boundary wave function represents all the physically possible histories our universe might have had if it began in the way Hartle and Hawking proposed. In a previous paper, in January 2010, they had reported looking at a range of these different universe histories.30 With an infinite number of possibilities, calculating which are more probable was a questionable undertaking. However, Hartle, Hawking and Hertog – without resorting to renormalization procedures of the sort Richard Feynman had called ‘dippy’ when he used them himself to handle infinities – felt confident in coming to some conclusions.31 They divided the universe histories they were studying into two groups.
First, consider universe models in whose histories eternal inflation is not likely to have played a part. In other words, these are probably not part of a larger scheme of universes produced by eternal inflation. If we live in that kind of universe, and if it appears to us to be like the universe we know today, and if Hartle, Hawking and Hertog are correct in thinking they can make valid use of the no-boundary wave function in their calculations, then what do those calculations lead us to expect?
in the CMBR, on scales we can observe, a certain pattern of non-randomness in the spectrum of temperature variations;
beyond our ability to observe, on huge scales, an over-all homogeneity;
only a small amount of inflation in our past.
Observations of the CMBR, though they can’t show us item (2), do not seem to back up those predictions.
So, consider another group of universe models. These universes are likely to be part of an eternal inflation picture. If we live in that kind of universe, and, again, if it appears to us to be like the universe we know today – and if Hartle, Hawking and Hertog are correct in thinking they can make valid use of the no-boundary wave function in their calculations – what do these calculations lead us to expect?
in the CMBR, on scales we can observe, a high degree of randomness in the spectrum of temperature variations;
beyond our ability to observe, on huge scales, a significant amount of inhomogeneity;
a longer period of inflation in our past.
That’s more like it! Or so it seems, so far. The absence or presence of (and the degree of) randomness that we can observe in the CMBR is a key issue.
Hartle, Hawking and Hertog decided, however, to go further out on a limb: their September 2010 paper reported that they calculate that our universe probably ended its inflationary period at the lowest potential value of the field.32 They predict, rather precisely, observations in the area we can observe (within our light cone) – not only that there will be a high degree of randomness in the spectrum of temperature variations in the CMBR, but also the degree and manner in which, if eternal inflation is correct, the distribution and spectrum of the variations will depart from complete randomness.fn3 The departure will be extremely small and not easy to detect.
Now, we wait to see whether Planck and other future probes will be able to produce precise enough measurements to test those predictions, as well as show a specific pattern of slight fluctuations in temperature in the CMBR predicted by Hawking and Hartle’s no-boundary proposal itself. The Planck satellite may also be able to detect paths of light rays that have been bent in specific ways, indicating that our universe has a geometry predicted by some multiverse and eternal inflation models.33
Down-to-Earth Hawking Radiation
While Hawking, Hartle and Hertog had been thinking about what possible evidence might underpin eternal-inflation theory, another group of physicists were working on an experiment that might just possibly create Hawking radiation, not at the border of a black hole or from an event horizon in the early universe but in a laboratory. Daniele Faccio of the University of Insubria, Italy, and his team of researchers reported in a paper accepted by Physical Review Letters in late September 2010 that they had succeeded.34 Their experiment involved firing laser light into a block of glass.
The idea is that as the laser pulse moves through the glass block it changes the speed at which light is capable of travelling there (the ‘refractive index’ of the glass). Light near the pulse is slowed more and more as the pulse passes through and the refractive index changes. If a pulse (call it pulse A) were sent chasing after a slower, weaker pulse (pulse B), it would gradually catch up and that would reduce the speed of light near pulse B. Pulse B would slow down more and more, eventually so much that it would get stuck. The leading edge of pulse A, acting like the event horizon of a black hole, would have sucked it in.
Recall the discussion of Hawking radiation: pairs of particles continually appear. The two particles in a pair start out together and then move apart. After an interval of time too short to imagine, they come together again and annihilate one another. Near the event horizon of a black hole, before the pair are able to meet again and annihilate, the one with negative energy may cross the event horizon into the black hole. The particle with positive energy might fall into the black hole, too, of course, but it doesn’t have to. It’s free of the partnership. It can escape as Hawking radiation. To an observer at a distance it appears to come out of the black hole. In fact, it comes from just outside. Meanwhile, its partner has carried negative energy into the black hole.
Faccio and his team watched just such particles – photons in this case – to see whether, as the pulse passed through the glass, its event horizon would sweep in
one of a pair, allowing the other to escape as Hawking radiation. They set up a camera, focused it on the block of glass, and then fired 3,600 pulses from the laser. The camera recorded a faint glow in exactly the range of frequencies that Hawking radiation predicts. Carefully ruling out other sources of the glow, the researchers decided that they had in fact observed Hawking radiation.
Might this get Hawking a Nobel Prize, which is very seldom given for even the most promising theories if there is no experimental or observational evidence to support them? In November 2010, not long after the announcement of the experiment in Insubria, I asked Hawking whether he thought Faccio and his team had actually discovered Hawking radiation. His reply was enigmatic: ‘I will not get the Nobel Prize.’
fn1 The Nobel Prize is very seldom given for even the most promising theories if there is no experimental or observational evidence to support them.
fn2 WMAP was finally consigned to ‘graveyard orbit’ in October 2010.
fn3 Quoting Hartle, Hawking, and Hertog’s September 2010 paper directly, to give a feel for what all this sounds like in the language of theoretical physics: ‘… an essentially Gaussian spectrum of microwave fluctuations with a scalar spectral index n8 & $126;.97 and a tensor to scalar ratio of about 10%’ (James Hartle, S. W. Hawking and Thomas Hertog, ‘Eternal Inflation without Metaphysics’).
20
‘My name is Stephen Hawking: physicist, cosmologist and something of a dreamer’
HAWKING’S BOOK THE grand design, written with Leonard Mlodinow, appeared in the early autumn of 2010 with a subtitle that sounded rather un-Hawkinglike. New Answers to the Ultimate Questions of Life. Nothing here of the wry humour of previous titles – a ‘brief’ history – the universe in a ‘nutshell’. Apparently this book was going to get serious.
The Grand Design pulled together the thinking and work Hawking has been doing for over half a century, to give us a thorough update on the state of the quest for a Theory of Everything. Here are Feynman’s sums-over-histories, the anthropic principle, the meaning of ‘models’ and ‘reality’, the no-boundary proposal, information loss, the disparagement of modern philosophy (this time on the first page rather than the last), the battle with God. But right from the beginning of the book one dramatic change is clear: the quest for a Theory of Everything has, indeed, fragmented.
Isaac Asimov once wrote that ‘of all the stereotypes that have plagued men and women of science, surely one above all has wrought harm. Scientists can be pictured as “evil”, “mad”, “cold”, “self-centred”, “absent-minded”, even “square” and yet survive easily. Unfortunately they are usually pictured as “right” and that can distort the picture of science past redemption’. Stephen Hawking’s startling about-faces, which you have witnessed throughout this book, shatter that stereotype. Hawking has a robustly healthy history of pulling the rug out from under his own assertions. But, as we’ve seen, what appear to be about-faces have hardly ever actually been steps backwards or reversals. In Hawking’s own version of the game Snakes and Ladders, snakes don’t take him further from his goal. They just lead him off on more promising pathways. Be that as it may, giving up hope of discovering a fundamental Theory of Everything is an enormous shift – one that Hawking would not have made unless faced with truly unyielding evidence that it was warranted, the only way forward.
Another thing that is clear from the start of The Grand Design is that Hawking no longer regards string theory with the suspicion he once did. It’s not easy to pin down precisely when he changed his mind on this issue. Most accounts, not his own, have him still rather anti-strings well into the 1990s. However, he told me in 1990 (Chapter 13) that he thought superstring theory had become the most promising route towards a Theory of Everything. He was right, but … with a twist.
The newest candidate, and perhaps the final claimant for that title of ‘ultimate theory of the universe’, is M-theory. As a theory of everything, in the time-honoured description, it is a little disappointing. M-theory is not simple. You can’t print it on a T-shirt. It doesn’t fulfil the promise of Wheeler’s poem. It doesn’t measure up to the Pythagorean standard, where beautiful clarity is a guide to truth. Does that mean it might be wrong? Hawking’s attitude towards it is not that it is right, or ultimate, but that it is the best we are ever going to do.
M-theory is not a single theory. It is a collection of theories. Hawking describes them as a ‘family of theories’. Each member of the family is a good description of observations in some range of physical situations, but none is a good description of observations in all physical situations. None can account for ‘everything’. The theories may look very different from one another, but all are on an equal footing, and all can be thought of as aspects of the same underlying theory.1 We don’t yet know how to formulate that deeper theory as a single set of equations and arguably never will.
Hawking and Mlodinow compare the situation to a flat map of the Earth. Because the Mercator projection used for such maps makes areas further north and south look larger than they really are in relation to other parts of the world (the distortion becomes more and more pronounced the further north or south on the map you go), and the North and South Poles are not shown at all, the entire Earth ends up much less accurately mapped than it would if we used, instead, a collection of maps, each one covering a limited region, overlapping. Where the maps overlap, they don’t conflict; that bit of the landscape looks the same regardless of which of the overlapping maps you’re consulting. Each map is reliable and useful for the area it represents. But no single flat map is a good representation of the Earth’s surface. Just so, no single theory is a good representation of all observations.2
Today, theorists recognize five different string theories and supergravity, a version of which Hawking had high hopes for in 1980, as the family of approximations of the more fundamental theory, M-theory. The six approximations are like the smaller maps in Hawking’s map analogy.
While this situation may not meet our most idealistic expectations for a complete understanding of the universe, we needn’t sit around too long moaning about our ignorance of the fundamental, comprehensive, underlying theory. There are things we do know about it. There are ten or eleven dimensions of time and space. There are point particles, vibrating strings, two-dimensional membranes, three-dimensional objects, and other objects occupying up to nine (or, in some versions, ten) dimensions of space – in other words, p-branes.
We have already talked about the idea that extra space dimensions beyond the three we experience may be escaping our notice because they are curled up tightly, and that the astounding number of different ways they can curl was at first discouraging to those who were hoping that string theory was going to be the unique theory of everything. Earlier we used the analogy involving a garden hose to help understand the curling up. Hawking and Mlodinow have found a better analogy for it.
They ask us to imagine a two-dimensional plane. It could be, for instance, a piece of paper. It is two-dimensional because two numbers (horizontal and vertical coordinates) are needed to locate any point on it. It may not occur to you that a drinking straw is also two-dimensional. To designate a point on it, you need to show where the point is along its length and also where in its circular dimension. But suppose your straw is very, very thin. You’d hardly feel the need to think about where the point is in its circular dimension. If it were extraordinarily thin, a million-million-million-million-millionth of an inch in diameter, Hawking suggests, you wouldn’t think it had a circular dimension at all. That is the way string theorists encourage us to think about the extra dimensions – curled or curved on a scale so small that we don’t notice them. They speak of them as being curled up into ‘internal space’.
In the early to mid-1990s, theorists were becoming less and less discouraged by the astoundingly many ways dimensions can curl. One change was a new understanding that the different ways of curling up the extra dimensions are nothing but different ways of looking at t
hem from our vantage point in four dimensions. However, as Andrei Linde suggested, the way the extra space dimensions are curled up is crucial. In each universe, it determines the universe’s apparent laws of nature. However many solutions there are in M-theory for the ways internal space can be curled, that is how many different types of universe are allowed, all with different laws. The number is too large to comprehend.
Hawking suggests we think of the emergence of these universes by imagining something like Eddington’s balloon analogy, the balloon with the ant crawling on it, only this time it isn’t a balloon and the ant is missing. In his 2006 lecture at Caltech, he advised his audience to picture the expanding universe as the surface of a bubble. Imagine, then, the formation of bubbles of steam in boiling water. Many tiny bubbles form and disappear. These are universes that expand only a little and collapse before they get beyond microscopic size. No hope of galaxies, stars, or intelligent life in them. Some, however, start out just as tiny but grow large enough so that they are out of danger of collapsing, at least for a long, long while. These expand at first at an ever-increasing rate, undergoing what we have come to call ‘inflation’.
The Grand Design revisits Richard Feynman’s idea that a particle travelling from one point to another in quantum physics has no definite position while it is getting to its destination. That has been taken to mean that it takes no path. As we’ve seen, Feynman realized that it could just as easily be said to take every possible path simultaneously. In this light, consider the possibility of a great many universes, the sort of situation we have in eternal inflation. It doesn’t suffice only to say that each universe has a different history. In fact, thinking of sums-over-histories, each universe has many possible histories and also many possible states later in its existence. Most of those states are totally unsuitable for the existence of life of any sort. There are only a minuscule few of the universes that would allow creatures like us to exist.
Stephen Hawking, His Life and Work Page 33