The Ascent of Gravity
Page 18
This mass limit would not matter if there are no stars heavier than three times the mass of the Sun. But there most certainly are. A few rare ones are more than 100 times as massive as the Sun. Such stars are inherently unstable and prone to violent convulsions that eject large quantities of their mass during their lifetime. But, even taking this into consideration, they are still likely to be more massive than three solar masses when their internal fires finally flicker and go out. Runaway collapse to form a black hole appears unavoidable.
In fact, we know it is unavoidable. In 1971, NASA’s ‘Uhuru’ satellite discovered the first black hole candidate: Cygnus X-1. A couple of dozen stellar-mass black holes are now known in our Galaxy. In addition, NASA’s Hubble Space Telescope has confirmed that pretty much every galaxy in the Universe has a giant black hole lurking in its heart. Some are as big as 50 billion times the mass of the Sun whereas the one 27,000 light years away in the heart of the Milky Way – Sagittarius A* – is a mere 4.3 million times the mass of the Sun. The origin of such ‘supermassive’ black holes is one of the outstanding puzzles of modern astrophysics.
But black holes — which conjure singularities into the very heart of general relativity — are not the only problem for Einstein’s theory of gravity. There is another one: the big bang.
The big bang
The general theory of relativity is a recipe for how matter – or, more generally, energy – warps the fabric of space-time. Einstein was never one to shy away from the really big problems in science. So in 1917 he applied his theory to the biggest collection of matter he could think of: the entire Universe.
Gravity orchestrates the large-scale Universe because mass comes in only one type, which always attracts. So, despite being by far the weakest of nature’s fundamental forces, its effect builds remorselessly with increasing mass and, even on the scale of the planets, becomes irresistible, overwhelming all of nature’s other fundamental forces. ‘Gravity is a habit that is hard to shake off,’ as Terry Pratchett put it.14 By contrast, nature’s ‘strong’ and ‘weak’ nuclear forces have ultra-short ranges, and the electromagnetic force, despite having an infinite range like gravity, is cancelled out on the large scale because of the existence of two types of electric charge which permit it to both attract and repel.
With its desire to pull everything together, gravity, like some cosmic Cupid, continually strives to break the terrible isolation of matter. From the beginning of time, when matter was blasted to the four corners of the Universe by the explosion of big bang, it has truly been nature’s lonely hearts club force. ‘Love’, as Dan Simmons observed, ‘was hardwired in the structure of the Universe as matter and gravity.’15
In applying his theory of gravity to the entire Universe, Einstein created ‘cosmology’, the science of the origin, evolution and ultimate fate of the Universe. But he went a little wrong. Like Newton before him, he believed the Universe was the way it had always been and the way it always would be. The great appeal of such an unchanging, or ‘static’, Universe was that it had no beginning or end so there was no need to waste time worrying about the sticky question of how it all got started.
The trouble was that Einstein’s equations appeared to describe a dynamic space-time that was desperate to be in motion. Einstein fixed this by postulating that empty space contains energy, giving it intrinsic curvature, independent of any matter. This curvature, which he called the ‘cosmological constant’, manifests itself as a repulsion of empty space. So, although all the objects in the Universe pull on each other with the attractive force of gravity, this is perfectly counterbalanced by the repulsive force of empty space. Hey presto: a static Universe.
It was Einstein’s greatest acolyte, Arthur Eddington, who showed in 1930 that Einstein’s static Universe could never have worked. Like a pencil standing vertically on its point, it was unstable, and the slightest disturbance would cause it to veer from its balance point. The Universe envisaged by Einstein teetered on the knife edge between expansion and contraction. The merest of nudges would send it careering one way or the other.
But though Einstein missed the message in his own equations – that the Universe must be in motion – others did not. In order to simplify his equations so that they could be ‘solved’, Einstein had insisted that the density of matter in the Universe remains constant for all time. But the same year he made this assumption, 1917, Willem de Sitter – the Dutch recipient of one of the first smuggled-out copies of Einstein’s theory – also applied the general theory of relativity to the Universe. And in marked contrast to Einstein, he did not insist that the density of matter remain constant but instead kept an open mind. And what de Sitter discovered was a Universe permitted by Einstein’s theory whose space was expanding. If two test particles were put in such a Universe, the general expansion of space would steadily increase the distance between them.
The trouble with de Sitter’s Universe was that it was empty. It was nothing but expanding space-time. It did not describe the Universe we live in. (Also, shockingly, it revealed the genie Einstein had let out of the bottle: space-time is a dynamic thing that can exist entirely independently of matter.)
But, in 1922, a Russian astronomer called Aleksandr Friedmann discovered a whole class of universes permitted by Einstein’s theory that were either expanding or contracting and contained matter. Friedmann’s ‘evolving’ universes were independently discovered five years later by a Belgian Catholic priest called Georges Abbé Lemaître. Most people today know of Friedmann-Lemaître universes by their more common moniker: ‘big bang universes’.16
Friedmann and Lemaitre’s universes were, of course, merely theoretical. But everything changed in the 1920s because of an American astronomer called Edwin Hubble. For his first trick, he discovered ‘galaxies’.
Einstein and others had been handicapped by not knowing the true building blocks of the Universe. At the beginning of the twentieth century, it was known that the Sun belonged to a giant collection of stars called the Milky Way. Scattered about the sky were also myriad other fuzzy ‘spiral nebulae’. The question was: were they clouds of luminous gas within the Milky Way or other islands of suns, or ‘galaxies’, so far beyond the Milky Way that sheer distance had blurred their stars into a fog?
In 1923, using the world’s biggest ‘eye’, Hubble answered the question. He pointed the 100-inch Hooker Telescope on Mount Wilson in Southern California at the Great Nebula in Andromeda. And not only was he able to see individual stars but stars of a special type whose regular brightening and fading revealed their distance. These ‘Cepheid variables’ showed beyond any doubt that Andromeda – and by inference all the spiral nebulae – were far, far beyond the Milky Way.17
Hubble had discovered the fundamental building blocks of the Universe: galaxies. Our Milky Way, with its 100 billion stars, was but one galaxy among about 2 trillion others.18
For his next trick, Hubble began measuring the speed at which galaxies were moving, continuing work begun on Mount Wilson by a former mule driver called Milton Humason.19 By 1929, Hubble had measured the speed of enough galaxies to make an extraordinary discovery. Pretty much all of the galaxies were flying away from the Milky Way, hardly any were approaching. And the further away they were the faster they were receding. Hubble had discovered that the Universe is expanding. Remarkably, the big bang solutions of Einstein’s theory of gravity discovered by Friedmann and Lemaître describe reality.
But it was one thing to discover the expanding Universe and quite another to take on board what it meant. That involved taking the discovery seriously, and scientists always have immense trouble truly believing that their esoteric mathematical equations actually describe the real world.
But, in the late 1930s, and for entirely the wrong reason, the Ukrainian-American physicist George Gamow began thinking about the implications of an expanding Universe. The reason was that he was looking for a furnace to build up nature’s elements. There are ninety-two naturally occurring elements, ranging
from the lightest, hydrogen, all the way up to the heaviest, uranium. Gamow believed the Universe had started out with hydrogen -think of it as nature’s fundamental Lego brick – and all the other elements had been built up, step by step, from hydrogen. But this required a furnace at a temperature of many billions of degrees.20
Gamow believed stars did not fit the bill (he was wrong).21 So he looked for another furnace. And that was when he began imagining the expansion of the Universe running backwards like a movie in reverse. After billions of years – we now know the time to be 13.82 billion years – all the matter of the Universe would be squeezed into the tiniest of tiny volumes. This was the moment of the Universe’s birth: the big bang.
When something is squeezed into a small volume it gets hot, as anyone who has squeezed air into a bicycle pump knows. The big bang was therefore a hot big bang, Gamow realised. It would have been like the fireball of a nuclear explosion.
Gamow’s furnace was incapable of building all of nature’s elements.22 But, in being wrong – and this is sometimes the case in science – Gamow was right. That the Universe was expanding implied that it had been born in a searing hot fireball. And when Gamow thought about the big bang fireball, he realised something extraordinary: its heat should still be around today.
The heat and light of a normal explosion – say, the explosion of a stick of dynamite, or even of a nuclear bomb – dissipates into the environment. After an hour, a day, a week, it is completely gone. But the Universe, by definition, is all there is. The heat of the big bang fireball had nowhere to go. It was bottled up in the Universe. Consequently, it must still be around today, greatly cooled by the expansion of the Universe in the past 13.82 billion years. Instead of appearing as high-energy visible light, it should appear as low-energy radio waves. In fact, Gamow’s calculations revealed that this ‘afterglow’ of the big bang would account for 99.9 per cent of the particles of light, or ‘photons’, in the Universe.
But every physicist, be they Einstein or anyone else, gets so far and then makes a mistake. And Gamow’s mistake was to think that the afterglow of the big bang had no features that would make it easy to recognise in today’s Universe. His two students, however, realised that it did. Ralph Alpher and Robert Herman guessed it would have two very striking characteristics: one, it would be coming equally from every direction in the sky, and, two, and somewhat more technically, it would have the ‘spectrum of a black body’.23
Alpher and Herman published their prediction in the international science journal Nature in 1948. But no one took any notice. Even worse, when they asked radio astronomers whether the afterglow of the big bang was detectable, they were told (incorrectly) that it was not.
Fast forward to 1965. Two radio astronomers at the American phone company AT&T had inherited a giant ‘radio horn’ at Holmdel, New Jersey. The horn had been used for pioneering experiments with the first communication satellites, ‘Echo 1’ and ‘Telstar’. Arno Penzias and Robert Wilson wanted to do some astronomy with it. But everywhere in the sky they pointed the horn, they were getting a persistent hiss of static.24
First they thought the source was New York City, just over the horizon, but the hiss remained even when they pointed the horn in the opposite direction. They thought it might be a source in the Solar System but, as the months went by, and the Earth went round the Sun, the hiss did not change as expected. They thought the culprit could be an atmospheric nuclear test that had recently injected electrons high into the atmosphere, which would generate radio waves, but, as time passed, the hiss did not decline as expected.
Eventually, the gaze of Penzias and Wilson alighted on two pigeons which had nested inside the giant radio horn. They had coated the interior with a ‘white dielectric material’, more commonly known as pigeon droppings. Could this be the source of the spurious hiss of radio waves? Penzias and Wilson captured the pigeons and cleaned out the interior of their horn. But, frustratingly, the anomalous hiss remained.
Finally, Penzias learnt from a colleague of a search being made from nearby Princeton University for the heat relic of the early Universe. Incredibly, he and Wilson, totally by accident, had stumbled on the most important cosmological discovery since Hubble’s discovery of the expanding Universe: the leftover heat from the birth of the Universe. They had confirmed the big bang.
It was one of the greatest discoveries in the history of science. The Universe had not existed for ever. It had been born. There was a day without a yesterday. For the discovery of the ‘cosmic background radiation’, Penzias and Wilson would win the 1978 Nobel Prize for Physics.
The arrow of time
One of the mysteries of our Universe is why time flows in the direction it does. Why do people grow old, eggs break and castles crumble but we never see people grow young, eggs unbreak and castles uncrumble? For the answer it is necessary to go back to the big bang.
All the above changes are associated with transformations from order to disorder. But there are many ways an egg can be broken (disordered) and only one way it can be intact (ordered). And since all possibilities are equally likely, it is overwhelmingly likely that an egg will go from being intact to being broken. This is the ‘Second Law of Thermodynamics’, which says that ‘entropy’ (microscopic disorder) can only increase. It is not impossible that an egg will go from broken to intact but it is overwhelmingly improbable.
But if the direction of time is associated with the Universe becoming more disordered, it implies that the Universe must have been very ordered in the past – that is, in the big bang. This poses a problem for physicists since an ordered state is an unlikely state. This is where gravity may come to the rescue, according to Larry Schulman of Clarkson University in New York.25
Initially, the Universe was a fireball in which matter was spread uniformly. This was a disordered state. But around 380,000 years after the moment of creation, the fireball had cooled enough for electrons to combine with nuclei to make the first atoms. Free electrons interact strongly with photons whereas electrons in atoms do not – and there were about 10 billion photons for every electron. Consequently, before the formation of atoms, matter was blasted apart by photons and gravity could not pull it together into clumps. Afterwards, it could. It was as if gravity had suddenly ‘switched on’ in the Universe. Those clumps grew and grew and, ultimately, became the clusters of galaxies we see around us today.
For material experiencing gravity, the most likely state is with it clumped into objects like galaxies and stars. But, as pointed out, when the Universe was 380,000 years old, the matter of the Universe was spread uniformly in a very unlikely state. But the ‘switching on’ of gravity instantly transformed the Universe into an unlikely, special state, exactly as required if the arrow of time is to go the way it goes.
What is remarkable about this explanation is that the Universe looked pretty much the same just before and just after 380,000 years – the ‘epoch of last scattering’. All that happened was that gravity went from being impotent to all-powerful. But from the point of view of gravity, the Universe went from being in a likely state to an unlikely state. A similar argument to Schulman’s has been proposed by the British physicist Roger Penrose.
Penzias and Wilson’s discovery of the afterglow of the fireball of the big bang created problems – lots of problems. If the Universe had begun in a big bang, what was the big bang? What had driven the big bang? And what had happened before the big bang? Nobody had wanted to face such questions, which was why most astronomers, including Penzias and Wilson, had subscribed to an eternal Universe known as the ‘Steady State’ theory.
But there was one difficulty that went to the very heart of general relativity. If the expansion of the Universe were imagined running backwards, as Gamow had pictured it, it would get ever denser, ever hotter and the space-time would become ever more curved. In fact, everything would skyrocket to infinity. It was another monstrous singularity. A singularity in time rather than in space, as in a black hole, but a singulari
ty nonetheless.
So now there were two places where Einstein’s theory broke down, not just one. General relativity, far from being a perfect garment, was revealing itself to be a moth-eaten cloak.
But all hope was not lost for Einstein’s theory.26 Its singularities were not inevitable. One way out remained.
Singularity theorems
When relativity turns a dying star to marshmallow, the marshmallow is unlikely to be perfectly smooth. There is bound to be a lump here, a lump there. And as the star is crushed ever smaller by gravity, this unevenness will be magnified. In other words, the star will not shrink perfectly symmetrically. What this means is that different parts of the collapsing star may not, in the end, all pile up at one impossibly dense point. They may miss each other. There will be no singularity. And Einstein’s theory of gravity will live to fight another day.
And what is true of black holes might also be true of the big bang. If the matter of the Universe is spread unevenly, this unevenness would become magnified as the backward-running Universe shrank ever smaller. Different parts of the collapsing Universe, instead of all piling up at one point, would miss each other and so not create a catastrophic singularity. Since Einstein’s theory of gravity would not break down, it would be possible to use the recipe to follow the history of the Universe to an earlier time before the big bang. Perhaps, for instance, the Universe had contracted down to a big crunch from which it had then bounced in the big bang.
Enter English theorists Stephen Hawking and Roger Penrose. Between 1965 and 1970, the question of whether the singularities in the big bang and in black holes could be avoided became the focus of their research work. And the pair proved a range of powerful ‘singularity theorems’. The most important of them showed that under a wide range of general and highly plausible conditions the singularities in the big bang and black holes were unavoidable. They formed no matter how the backward-running movie of the Universe went, no matter how a star shrank to make a black hole.