by Paul Davies
Four years previously, Albert Einstein had used his general theory of relativity to predict that the sun’s gravity would warp space and shift the apparent positions of the stars. The very idea that gravity can ‘bend starlight’ caught the public’s imagination, and Eddington’s confirmation of the prediction elevated Einstein to international fame. Curiously, the man himself took it all in his stride. He was so convinced that his brainchild, general relativity, was right, that when he was told about Eddington’s measurement he seemed unimpressed. Suppose Eddington had obtained a contradictory outcome, Einstein was asked by an assistant. ‘Then I would feel sorry for the good Lord,’ he replied. ‘The theory is correct anyway.’ Since Eddington’s pioneering expedition, gravitational lensing has matured into an entire branch of astronomy. Dramatic spacewarps occur when one galaxy eclipses another, occasionally producing a complete ring of light (see Figure 6). Black holes produce enormous space-warps, leading to spectacular effects on surrounding light sources.
Figure 5. The bending of light. During an eclipse, stars can be seen near the sun’s location in the sky. Einstein predicted that the sun’s spacewarp should slightly displace the position of the stars, and Eddington confirmed this in 1919. Rather than thinking of the star beam as bent when it passes close to the sun, it’s better to regard light as taking the shortest, straightest path it can through curved space.
Early on, Einstein realized that the warping or curving of space would not only occur around massive objects; it would also affect the shape of the universe as a whole. In 1917, he presented his idea of what he thought the overall cosmic geometry might be. This was pre-Hubble and Einstein assumed the universe was static. He ran into the same conundrum as Newton had, two hundred and fifty years earlier: why didn’t the cosmos collapse under its own unsupported weight?
Figure 6. Gravitational lens in which the spacewarp of a foreground galaxy images a more distant object to produce a ring of light.
The difference was that Einstein came at the problem armed with a totally new theory of gravitation. Perhaps general relativity could provide a means to shore up the universe? He soon found that it could, but only by adding an extra term to his prized gravitational field equations. This he did reluctantly, feeling that the additional term was a fudge, compromising the elegance and simplicity of the original equations. But it seemed to do the job. The fudge factor described a new kind of repulsive force, or antigravity, with the strange property that it would become stronger with distance, whereas normal gravity grows weaker. Einstein picked the strength of the new force to match the combined gravity of all the matter in the universe, to produce a static equilibrium.
A distinctive feature of Einstein’s static universe was its shape: space curves in on itself in such a way that it closes up into a finite volume, but without having any edge or boundary. To understand what this means, imagine that a light beam deflected slightly by the sun goes on to pass close to another star, getting deflected a bit more, then another, and another . . . Is it possible for the light to be bent right around in a closed loop? Einstein’s model universe showed that it was. The entire universe could turn light beams into circles in every direction at once. You could look out into space and, with a big enough telescope, you’d see the back of your own head!
A closed space is difficult to picture in three dimensions, but easy in two. The spherical surface of the Earth is finite but has no edge or boundary. Einstein’s universe is an analogous concept, but with one dimension extra – forming a three-dimensional shape called a hypersphere. Although it’s hard to visualize, the amazing artwork of M. C. Escher attempts to portray the geometry of curved space in aesthetically striking woodcuts. Whether you can imagine it or not, a hypersphere makes perfect sense and can be described mathematically. It’s often asked what’s ‘outside’ the hypersphere. The answer is nothing: there is no outside. All observers are located in the space itself, so any discussion of a bigger space ‘containing’ the hypersphere is pointless.
Gravitational waves
Imagine that by some magic the sun were to disappear at noon. We would not know about it until just after 12:08 when the sunshine abruptly stopped. According to Newton’s theory, in which gravity acts instantaneously across space, Earth’s orbit would cease curving at precisely noon. Our planet would sense the sun had gone even if we couldn’t. But in Einstein’s theory nothing can go faster than light, including changes in gravity. If the sun abruptly dematerialized, the resulting gravitational disturbance would ripple outwards at a finite speed. In 1918 Einstein predicted that ripples of space can indeed exist, and they travel at the speed of light. These gravitational waves will be produced whenever there is a cataclysm, such as the collision of two black holes (see Figure 7). A century passed before tiny vibrations of space from a black-hole merger were finally picked up as disturbances in delicately arranged laser beams. These ultra-sensitive systems are now being used as gravitational telescopes, opening up an entirely new window on the universe and paving the way to study the details of the most violent cosmic events.
Figure 7. Gravitational waves produced by two black holes spiralling together. These ripples in the geometry of space spread out at the speed of light and have been detected on Earth with ultra-sensitive laser devices called interferometers.
If space really is closed up in this manner, would we not notice it? Well, not if it’s big enough. Einstein was able to appeal to general relativity to estimate the total volume of his loopy universe. It all depends on the amount of matter there is: the more matter, the stronger the gravitational grip and the smaller the universe. Using the average density of matter estimated by astronomers, Einstein calculated that his static closed universe would have a total volume of a few thousand billion billion cubic light years, which I figured out to be equivalent to about a trillion trillion trillion trillion trillion trillion gallons, give or take a few pints.
Intriguing though it was, Einstein’s closed static universe had a rather brief shelf life: within a few years, astronomers had accepted that the universe was expanding – a point that would take Einstein several years to concede. The poignancy of this episode is that the static equilibrium that Einstein strove to capture in his fudged equations is actually unstable; as with Newton’s infinite universe, it’s like trying to balance needles on their tips. Had Einstein acknowledged this he would surely have predicted that the universe could not possibly be static, that it must either collapse or expand. When he eventually learned, to his chagrin, about the expansion of the universe, he abandoned the fudge factor as ‘his greatest blunder’. As we shall see, there is a double irony here: decades later, astronomers would find that Einstein’s fudge factor was needed after all, in a somewhat different context.
Though Einstein invented the idea of a closed universe for the wrong reason, the concept of a hypersphere also works for an expanding universe. But in that case, there is another possibility, which is negative curvature – space curving ‘out’ instead of ‘in’ (see Figure 8). According to general relativity, the shape of an expanding space depends on how much matter is present: a high-density universe curves space positively (i.e. inwards) and a low-density universe curves it negatively (outwards). In between these two geometries is a space with zero curvature, meaning that the rules of geometry are the standard ones you learn at school. It arises if the universe has a certain critical density, equivalent to about six hydrogen atoms per cubic metre on average. So there are three possibilities.
Figure 8. Curved space depicted in two dimensions. Einstein’s ‘hypersphere’ universe – closed with no boundary – is represented by the top picture. Beneath it is a negatively curved space, and at the bottom a flat space.
For many decades, astronomers, Hubble included, tried to measure which of these three was the right one. It’s easy enough in principle: you just have to estimate how many galaxies there are out to greater and greater distances. If space has zero curvature, then the number of galaxies should increase like the
cube of the distance. If space is curved, that relationship changes. The observations are not that easy to do, and in practice, the best estimate for the curvature of space has come from measuring the splodges in the CMB. When this is done the answer comes out as zero – the special, intermediate case. Cosmologists often express this result by saying that space is ‘flat’. They don’t mean it’s like a pancake. They just mean that the geometry of space (on average, over a cosmological scale) obeys the same rules of geometry as Euclid assembled over two millennia ago – the rules you use on a whiteboard or a flat sheet of paper – and not the rules you would apply, for example, to the curved surface of the Earth.
All of which leaves us with a big question: why?
9. Explaining the Cosmic Big Fix
A trained marksman can hit a bullseye from a thousand metres, but if most of us took a potshot we would be well wide of the mark. The same laws of physics are at work, but the marksman has a sharper aim. To hit a bullseye a thousand metres away requires precision and skill. But hitting the same target a thousand light years away defies imagination. Yet that’s how precisely the cosmos seems to have been set up at the beginning. Let me illustrate. If the universe began with a little bang, it would have quickly fallen back on itself under the weight of all its material. The bigger the bang, the longer it could endure before collapsing. For the universe to last for billions of years, the bang had to be exactly big enough given the gravitational pull of all the cosmological material. And an exact match is precisely what the flatness of space indicates, according to general relativity. But that’s not all. The afterglow of the early universe comes to us from about 380,000 years after the big bang. At that time, light can have travelled no more than 380,000 light years in any direction, which, viewed from our perspective 13.8 billion years later, covers a region of the sky only about 1o across. But the CMB is uniform across the whole sky – even regions on opposite sides of the universe have the same temperature. If no physical process can operate faster than light, why are these regions, which have seemingly never been in contact or able to influence each other, equally hot? There was nowhere near enough time for heat to flow between these regions to even out the temperature. It’s another of those balanced pins problems: to achieve such an exquisite degree of orchestration, the initial conditions at the big bang would have to be arranged with nuanced perfection by the Great Cosmic Marksman. It looks like a fix.
Scientists, being instinctively wary of Cosmic Marksmen or any other form of Fixer, have long sought to find a physical mechanism to explain the apparently contrived nature of the universe. In the 1970s, cosmologists looked to the kitchen for inspiration. If you pour hot water willy-nilly on gravy powder it forms a lumpy, inhomogeneous mess. But if you pour carefully and stir vigorously, the gravy is homogenized by frictional effects. Perhaps the universe exploded into being in a mess, then smoothed itself out by friction? Detailed calculations showed that friction helps, but not much. No Cosmic Spoon is big enough or fast enough to do the job.
That was pretty much the way things stood in the 1970s. But then along came a completely new theory in 1980. Suppose the initial explosion was indeed shambolic, but a split second later the universe abruptly leapt in size by a huge amount, as if it had taken a sudden deep breath. As a result, all the irregularities would be quickly smoothed out, just as inflating a balloon removes all the crinkles. No mixing would be necessary. To distinguish this sudden dramatic burst from common-or-garden expansion the former was dubbed inflation. Inflate for long enough and space will flatten out in the same way that the curvature of a balloon decreases with size.
The inflationary universe scenario explains a lot, and soon became adopted as the party line among professional cosmologists, a status it retains to this day, but it is not without its problems. Chief among these is deciding what drove the frenetic inflationary burst. A huge pulse of antigravity would explain it, like the fudge factor that Einstein invented, but enormously stronger, and transitory, operating for just a brief moment. Cosmologists have invoked an ‘inflaton’ field to do the job, but nobody is sure what it is – it’s just a made-up answer beyond the reach of known physics.
There’s also an exit problem. How did inflation – runaway accelerating expansion – slow down and morph into the traditional hot big bang picture in which the explosively expanding universe slams on the brakes and decelerates? The theory says the energy pent up in the inflaton field was dumped into the universe as heat, the remnant of which we see today in the CMB. But getting the exit phase to work properly is hard, and some of the suggestions look almost as much of a fix as simply positing an ultra-smooth big bang from the outset.
Cosmologists are all agreed on this point: inflation enables a universe to balloon into existence without the need for any input energy. Alan Guth, the originator of the inflationary theory, described the universe as ‘the ultimate free lunch’. Over time, it became popular to say that, with inflation, the universe can come into being from nothing, and therefore its origin is fully explained. But this exaggerated claim rests on obfuscation around the word ‘nothing’. As we shall see in Chapter 20, there is a great deal else required to give a complete account of cosmic existence.
10. Most of Our Universe is Missing
Twinkle, twinkle little star,
How I wonder what you are.
Every schoolchild learns this ditty, and for the greater part of human history nobody knew the answer. In 1835, the French philosopher Auguste Comte claimed we would never know what stars are made of because they are so far away. But even before he said this, astronomers were on the case. In 1814 Joseph Fraunhoffer had found dark lines slashing across the spectrum of sunlight – the rainbow of colours made by a prism. The lines resemble supermarket barcodes. And barcodes are pretty much what they are, each pattern made by a specific chemical element: one barcode for carbon, another for oxygen, and so on. Because astronomers see these distinctive patterns everywhere, we know the whole universe is made of more or less the same material.
Stars are composed mostly of hydrogen and helium, the two main elements that were coughed out of the big bang. The heavier elements we observe across the universe – like carbon, oxygen, nitrogen and iron – were produced by nuclear reactions inside stars, built up step by step starting with hydrogen, in a form of serial alchemy. The sun, the star on our doorstep, is the easiest for us to study, and we now know that its core is a gigantic thermonuclear bomb going off at 100 billion megatons every second. The reason we’re not blown to smithereens is that the explosion is smothered by the weight of half a million kilometres of overlying gas. This controlled nuclear explosion continues day after day, year after year, in an astonishingly steady outpouring of energy. It’s an arresting thought that a mere 1 per cent reduction in solar output would plunge Earth into an ice age and make global warming a distant memory.
The lifetime of a star depends on its mass. Massive stars live fast and die young, gobbling up their resources greedily. The first stars were like this – superstars of a hundred solar masses or more, burning out in a few million years, then exploding, lacing the surrounding space with their chemical products. When our solar system formed four and a half billion years ago, it scooped up a potpourri of this stellar detritus, which is why astronomers are fond of saying our bodies are made of stardust. More prosaically, we are made of nuclear ash.
Working out the life cycle of stars and the origin of the elements was a decades-long research project linking astronomy to chemistry and life. Just when it seemed scientists had finally explained the complete inventory of cosmic material, things began to go wrong. It now seems that all the chemical elements, from hydrogen to uranium, make up only a tiny fraction of the mass of the universe. The rest is Something Else.
Astronomers can tell this mystery matter exists by following a method that dates back three and a half centuries. When Newton discovered the law of gravity, only five other planets were known. That changed on 13 March 1781, when William Herschel,
a German musician turned British amateur astronomer, inadvertently discovered a sixth planet – Uranus – using a home-made telescope. The discovery of Uranus was a milestone in the history of astronomy, as it was the first planet to be discovered with the aid of man-made technology, rather than observed by the naked eye. But by the middle of the nineteenth century it was apparent that something wasn’t quite right. The movement of Herschel’s planet across the sky was being disturbed by the gravitational force of an unseen object. Astronomers scrambled to calculate where in the sky the interfering object might be located. On the night of 23–24 September 1846, Johann Gottfried Galle of the Berlin Observatory found it where predicted; it was the planet we now call Neptune.
Detectives use the dictum ‘follow the money’ to track down shadowy criminals. Astronomers follow the luminous material to trace shadowy matter. Neptune was the first in a long list of unseen, unseeable, or just plain dim entities that were discovered from the way they tug on their more visible neighbours. And there’s a lot of dark matter out there: in fact, it outweighs visible matter by a factor of five. The Milky Way is embedded in a vast blob of the stuff, and there’s even more lurking between the galaxies. There’s no agreement on what the majority of the unseen material is. Apart from the gravity it exerts, there seems to be no obvious detectable effect when dark matter runs into normal matter. It’s almost as if it’s ghost matter, gliding through solid objects without a murmur.