The Bang Before the Big One

How the fact that the Universe has been essentially non-quantum for most of its history is telling us it must once have undergone a burst of super-fast expansion

‘If you can look into the seeds of time,

And say which grain will grow, and which will not, speak then to me.’

Shakespeare (Macbeth)

‘Many and strange are the universes that drift like bubbles in the foam upon the River of Time.’

Arthur C. Clarke (‘The Wall of Darkness’)

In the everyday world, a cause always precedes an effect. You brake at a pedestrian crossing because moments earlier someone stepped out into the road; you get drenched by the rain because a cloud burst overhead. In the everyday world, things happen with absolute certainty. The Sun will rise tomorrow; Mars will in six months’ time be exactly where Newton’s laws predict it will be, so NASA can be confident its robot space probes will reach the Red Planet. In the everyday world, a Martian space probe – or a football kicked through the air – follows a single, well-defined path towards its destination, not half a dozen separate paths simultaneously.

These statements may appear so ridiculously self-evident as to be unworthy even of mention. But actually the way the everyday world behaves is very surprising. After all, the fundamental theory that orchestrates our Universe is quantum theory. And a central characteristic of quantum theory is that things happen with no prior cause. There is no telling whether a particular photon will bounce off a window or go right through, whether a radioactively unstable atomic nucleus will sit quietly for the next billion years or self-destruct in the next millisecond. What actually happens is irreducibly unpredictable, in common with everything else that happens in the quantum world. And when a photon or any other denizen of the microscopic world flies through space, it does not follow a single path but, in some sense, all possible paths simultaneously.

The most striking feature of our Universe – one hardly ever remarked upon, even by physicists – is that it behaves in a largely non-quantum manner. And not just at this particular moment in time. Because of the finite speed of light, telescopes act as time machines, revealing past epochs of the Universe. And what those time machines tell us is that for the majority of cosmic history, the Universe has been behaving in a pretty non-quantum way.

It is a paradox. We live in a quantum universe that largely looks un-quantum. This is a profound observation about reality. And, remarkably, it may be telling us something about the very birth of the Universe. What is that thing? In its earliest moments, the Universe must have undergone a burst of super-fast explosive expansion.

To understand how it is possible to deduce something so precise about the primordial Universe from the fact that we live in a non-quantum world it is first necessary to say something about the theory of the beginning of the Universe. Our most successful theory of physics, as already mentioned, is quantum theory. Because it describes the microscopic world of atoms and their constituents, it may not be obvious that it has anything to say about the large-scale universe. However, the Universe has expanded from a highly compressed state in the Big Bang. In its earliest moments, therefore, the Universe was indeed smaller than an atom. So if we want to understand the earliest moments of creation, we need a quantum theory of the Universe – a theory of quantum cosmology.

In practice, this means having a quantum theory of gravity, since gravity orchestrates the behaviour of large masses such as the Universe.1 Such a theory is often dubbed the holy grail of physics since it would unite the theory of the very small – quantum theory – with the theory of the very big – Einstein’s theory of gravity, the general theory of relativity. Unfortunately, although physicists have been able to describe the three non-gravitational forces in quantum terms, they have failed, despite many decades of trying, to do the same for gravity.2

Not having a quantum theory of gravity, and so a quantum theory of cosmology, would appear to be a fatal handicap in any speculation about the beginning of time. Remarkably, however, it is still possible to say something about the early Universe. Recall that it is a characteristic of quantum theory that when a particle travels between A and B, it can do so by travelling along every conceivable path, each of which has a certain ‘probability’ of being taken. It is likely, therefore, that a successful theory of quantum cosmology will view the history of the Universe not as a single thread but as a whole bunch of strands all bundled together. The challenge is then to discover why our Universe has followed its own particular history rather than any other.

One way to do this is to use observations of our present-day Universe to rule out a host of possible histories in the hope that the only history we will be left with is one like our own. And the most striking observation about our Universe, as already pointed out, is that for most of its history it has been non-quantum. Consequently, we can discard the myriad possible cosmic histories in which the Universe stays smaller than an atom and dominated by quantum effects such as quantum unpredictability. This naturally leaves only universes that grow big.

The trouble is, there is still a multitude of these non-quantum histories. They are described by predictable, non-quantum laws, of which the most important – because it describes how the large-scale Universe evolves in time – is Einstein’s theory of gravity.

Einstein’s theory describes all kinds of possible universes. There are ones that are clumpy or smooth, ones that re-collapse after a short time or expand for ever, ones that expand at breakneck speed or at a snail’s pace, and so on. Our Universe is one universe among this throng, but there appears to be nothing distinctive about it. Nothing to make it stand out from the crowd. Nothing to tell us why we have ended up in our particular Universe rather than any other. What is needed is another plausible reason to thin out the forest of possible cosmic histories. And such a reason has been proposed by physicists Stephen Hawking and James Hartle.

The picture of multiple histories of the Universe all bundled together turns out to be only half the picture. Such histories are properly determined – anchored in reality, if you like – only if the conditions at the beginning of time are pinned down. Unfortunately, physicists are as ignorant of the ‘initial quantum state’ of the Universe as they are of the theory of quantum cosmology itself. At least, they were. In the 1980s, Hawking, of the University of Cambridge, and Hartle, of the University of California at Santa Barbara, noted something interesting about Einstein’s theory of gravity: it can be reformulated in such a way that instead of having three dimensions of space and one of time, it has three dimensions of space and one of ‘imaginary time’.

Imaginary time is a mathematical concept which it is not necessary to understand. The key thing is that it behaves just like space. Using this insight, Hawking and Hartle were able to show that in the initial quantum state, the multiple histories of the Universe, instead of existing in space and time, could have existed in space alone. This allowed them to sidestep neatly the sticky question of what happened before the Big Bang. After all, if the Big Bang happened in space alone – outside of time – asking what happened before the beginning is like asking what it is like north of the North Pole. There is nothing north of the North Pole. It is a question with no meaning.

Remarkably, this means that the initial condition of the Universe could have been that there was no initial condition. Hawking and Hartle have dubbed this the ‘no boundary condition’. It provides a way of further thinning out possible cosmic histories. When possible histories are reformulated in terms of space alone and the no-boundary condition applied, some of those histories turn out to have an extremely small chance of ever occurring. They can therefore safely be discarded. And this is what Hawking and Hartle, together with their colleague, Thomas Hertog, of the University of Paris, did in late 2007. They then looked at the cosmic histories that survived the cull. To their surprise, all of the survivors shared a striking feature: at the outset each underwent a period of super-fast expansion.

This was a very significant discovery. A burst of super-fast expansion is the preferred way that cosmologists fix a serious problem with the Big Bang model. In a nutshell, the basic Big Bang model does not work. It predicts something we do not see when we look out at the Universe. According to the model, the Universe began in a super-dense, super-hot state about 13.7 billion years ago and has been expanding and cooling ever since, with the galaxies and stars congealing out of the debris. However, this simple picture makes a prediction which is dramatically at odds with what we see. It concerns the ‘cosmic background radiation’, the leftover heat of the Big Bang fireball.3 Greatly cooled by the expansion of the Universe over the past billions of years, the afterglow of the Big Bang permeates all of space and comes to us directly from an epoch about 380,000 years after the beginning of the Universe. And herein lies the problem.

If we imagine the expansion of the Universe running backwards to this epoch like a movie in reverse, we find that our currently observable universe was then about 20 million light years across. This means it was impossible for any unevenness in temperature that developed to be ironed out. After all, to even out the temperature, heat would have to flow from warm regions to colder regions. But the Universe was too big. Even at the cosmic speed limit – the speed of light – heat could have travelled no more than 380,000 light years since the Big Bang, and this was only a tiny fraction of the way across the Universe at that time.

A prediction of the basic Big Bang model is therefore that the temperature of the cosmic background radiation cannot possibly be the same in different directions in the sky. The trouble is, it is. To within a tiny fraction of a degree, wherever a telescope is pointed in the sky, it is measured to be 2.7 degrees above absolute zero.

What this contradiction is telling us is that the basic Big Bang model must be an incomplete description of the Universe. Something else is needed. Something new must be bolted on.

One possibility is that there was a long pre-Big Bang era. If this was the case, then the cosmic temperature would have evened itself out automatically. It would be like running cold water into a hot bath. If you wait long enough, the temperature becomes uniform. Another possibility, championed by the physicist João Magueijo, is that the speed of light was much greater in the Big Bang than it is today. This would have enabled heat to have travelled from hot regions of the fireball to colder regions far faster than expected, again evening out the temperature. But there is another possibility, and this is the one that has been embraced by most physicists: that the Universe underwent a phenomenal burst of expansion in its first split second of existence.

‘Inflation’ was proposed by the Russian physicist Alexei Starobinsky in 1979, and independently by the American physicist Alan Guth in 1981. It has been likened to the detonation of an H-bomb compared with the stick of dynamite of the Big Bang expansion that followed inflation when it ran out of steam. If inflation did occur, then 380,000 years after the Big Bang the Universe would have been far smaller than we deduce from running the movie of its expansion backwards, small enough for heat to travel back and forth easily, ironing out the cosmic temperature.

The trouble with the inflationary idea is that it is untestable practically. The conditions of temperature and density that existed in the first split second of the Universe are so extreme that we could never reproduce them in the laboratory to check what happens. Not only this but, in the three decades since inflation was first proposed, nobody has come up with a compelling explanation of why it happened. The mechanism that underpins it is a mystery. Inflation is simply tagged onto the basic Big Bang model in an unsatisfactory ad hoc manner.

This is why the deduction made by Hawking, Hartle and Hertog is so significant. Simply by taking the mundane observation that we live in a largely quantum Universe and applying their no-boundary condition, they have shown that the most likely possible histories of the Universe involve super-fast expansion. Inflation simply must have happened. It is unavoidable.

But why should the conditions imposed by Hawking’s team on possible universes pick out only those that undergo inflation? The answer is that inflation provides the most likely route for a universe to go from quantum to non-quantum. Quantum tends to be synonymous with small. Non-quantum tends to be big. The quickest way to get from the small to the big is with a burst of super-fast expansion. Unfortunately, there is a problem. Although the team’s analysis shows that inflation was unavoidable, it also shows that it was very short-lived. Too short-lived. The Universe would have doubled its size only a few times over, whereas observations of our Universe reveal that inflation actually doubled its size more than 60 times over, causing it to mushroom by a truly mind-blowing factor.

The inflation deduced by Hawking’s team is short-lived because inflation involves the Universe starting out in an unstable state. Nobody knows exactly what matter ‘field’ is responsible for the instability, although cosmologists commonly talk of a hitherto undetected ‘inflaton’ field whose repulsive gravity inflates the Universe. The point, however, is that anything in an unstable state tends to want to return to stability, and this is more likely to happen quickly than after a long time. Think of a pencil balanced on its tip. Clearly, this is a highly unstable situation. Buffeted by a draught and vibrations, the pencil is far more likely to keel over after a fraction of a second rather than after a day and a half. Similarly, the instability of inflation is far more likely to end after a short time than after a long one.

Fortunately, Hawking’s team has recently realised that there is a way to rescue their idea. It turns on the fact that we see only a tiny part of the Universe that inflated. This is because the Universe is just 13.7 billion years old, so we can see only those objects whose light has taken less than 13.7 billion years to reach us. Light from the rest of the Universe has not arrived yet on Earth. It is beyond the horizon, an imaginary boundary which surrounds us like the surface of a bubble. The bubble is, of course, the observable universe, as mentioned before. But there are other bubbles out beyond the horizon of the observable universe. Somebody else’s observable universes. Astronomers call them Hubble spheres.

There are a large number of Hubble spheres. In fact, the number is roughly equal to e^{[number of doublings during inflation]}.4 And although we find ourselves in this particular Hubble sphere, we could equally well have ended up in the next Hubble sphere. Or the next.

But here is the crucial thing. The more doublings the Universe has undergone, the more possible places we could find ourselves within it. So although universes which undergo more doublings are less likely – because the instability of inflation is more likely to end after a short while than a long while – there are more places in such universes where we could find ourselves. And this effect, it transpires, wins out. So contrary to what Hawking’s team originally thought, it is overwhelmingly likely that we will find ourselves in a universe which underwent a long period of inflation rather than a short one. At long last, we appear to have an explanation for why we find ourselves in a universe which inflated.

Perhaps it is pushing it a little to say that the non-quantumness of the everyday world is telling us that the Universe must have undergone a period of super-fast expansion in the past. But according to Hartle and his colleagues, this is exactly what the non-quantumness of the everyday world combined with the no-boundary idea is telling us. The evidence that inflation occurred is all around you: in the fact that the world is predictable and that, when you walk past a tree, you walk past on one side and not on both sides simultaneously. But although we have come to the end of this chain of reasoning, there is still one loose end. A rather important loose end.

How exactly do histories that are non-quantum at late times – the only ones we considered – become non-quantum? It is all very well to say that bigness is associated with a universe being non-quantum. But how exactly does a universe make the transition from being quantum to non-quantum? This is one of the most fundamental questions in science. After all, we live in a universe orchestrated by quantum theory and yet nowhere – at least in the everyday world – is quantum behaviour obviously apparent.

The key to resolving the paradox is a process called ‘decoherence’. For quantum behaviour to manifest itself, it is fundamental that the quantum probability waves representing the possibilities open to an object mingle with each other, or ‘interfere’. This is because interference is at the very root of quantum weirdness. If quantum waves do not interfere with each other, there is no quantum weirdness. Waves that can interfere with each other are said to be ‘coherent’, which is why the process by which they lose this ability – and lose their quantumness – is called decoherence.

In the early Universe, decoherence occurred in the following way. Quantum uncertainty – Heisenberg again – caused the properties of things to fluctuate wildly.5 Take space–time itself. Close up it resolved itself into violent contortions like a choppy, storm-tossed sea. The enormous expansion of inflation stretched, or magnified, this choppiness. It turned space–time into a landscape with gently sloping hills and valleys. The valleys were places that particles of matter gradually fell into, and the hills were places they avoided. By this process, the structures of today’s Universe, such as giant clusters of galaxies, began to grow. And it was this process – the clustering of matter – that triggered the transformation from a quantum to a non-quantum universe.

Focus for a moment on a valley at a particular location. Such a valley is a quantum entity – magnified by inflation but a quantum entity nonetheless. And like all quantum entities it has many possibilities open to it. For instance, in one possible history of the Universe, the valley is present. And in another, it is not. But, crucially, both possibilities can exist simultaneously, rather like Schrödinger’s eponymous cat being dead and alive at the same time. Which means the quantum waves representing the possibilities can interfere with each other.

Now imagine a particle of matter that falls into the valley. The same particle exists in the alternative history in which there is no valley, so it has nothing to fall into and stays put. Therefore, the particle is in slightly different locations in the two possible universes. The quantum wave representing one case does not quite overlap with the quantum wave representing the second case. Say, for the sake of argument, there is only a 50 per cent overlap.

Now consider a second particle joining the first in the valley. Again, this means the particle is in different locations in two possible universes. Say the quantum waves for the two cases overlap by 50 per cent again. This means that the overlap between the quantum waves representing the two particles in the valley and not in the valley is ½ × ½ = ¼. With a third particle falling into the valley, the overlap is ½ × ½ × ½ = . See where this is going? With each successive particle that falls into the valley, the quantum wave representing the history where the valley is there overlaps less with the wave representing the history where the valley is not there. Once we get to trillions upon trillions of particles, there is essentially no overlap. There can be no interference. And so the Universe has become non-quantum.

It was the growth of clumps of matter, leading to galaxies and you and me, that therefore caused the transition from quantum to non-quantum. But this still leaves one big mystery. Merely talking of fluctuations in space–time assumes the pre-existence of space–time, a smooth entity like a glassy sea that could be ruffled by Heisenberg uncertainty. Where did this smooth non-quantum space–time come from? That is indeed the big question. Clearly, it must have arisen from something totally quantum, something so turbulent and chaotic that space and time were meaningless concepts. This thing was the quantum precursor of space–time. It must have undergone a transformation to the non-quantum space–time we see around us today. How this happened nobody yet knows. There are no shortcuts to understanding the origin of space–time. It will require a true quantum theory of the Universe.

Notes - CHAPTER 8

1. It does this because, despite being the weakest force in nature by a very large factor, it has an infinite range and cannot be screened out. So the more matter there is, the greater its gravity. The gravitational force between a proton and an electron in an atom is 10,000 trillion trillion trillion times weaker than the electric force which keeps matter stiff. So gravity dominates in all bodies which have more than 10,000 trillion trillion trillion atoms, which corresponds to a body about 10 kilometres across. This, incidentally, is why all objects in the Solar System smaller than this are like irregular potatoes, while all objects bigger – like the Earth and the Moon – are crushed by gravity into neat spheres.

2. Quantum theory explains forces as due to the exchange of force-carrying particles. For instance, the electromagnetic force between charged particles arises from the exchange of photons. Think of two tennis players batting a tennis ball back and forth. A force is transmitted to each player by the impact of the tennis ball on their racquet.

3. See Chapter 7.

4. Something that increases exponentially – or is raised to the power of e (about 2.718281828 …) – doubles, then doubles in the same time again, and doubles in the same time again, and so on.

5. See Chapter 2.