B00B7H7M2E EBOK (42 page)

When the universe was created, we were not consulted.

Andrei Linde

WHETHER THERE IS
an edge to the universe, and what, if anything, might be beyond, are old questions. German astronomer Heinrich Wilhelm Olbers, who lived from 1758 to 1840, pointed out what is now known as Olbers’s paradox: if space has no edge and is infinite and contains an infinite number of stars, the night sky should be as bright as the Sun. It isn’t. He wasn’t the first to worry about that and certainly not the last. Suppose, instead, space is infinite but the number of the stars is not, and the stars are limited to some sort of system ‘inside’ infinite space. That creates another problem: their system will collapse because of their mutual gravitational attraction. Try to solve that by saying that the star system rotates and its centrifugal force keeps it from collapsing, and someone will surely think to ask: In relation to what is it rotating, since it’s the only thing in an infinite universe?

An expanding universe takes care of some of those problems while introducing other challenges, particularly to non-expert
thinkers
: the balancing act summed up in the formula for omega, such proposals as Friedmann’s first model in
Figure 6.1
– a universe that is not infinite in size but nevertheless doesn’t have any edges or boundaries in space (though it does in time), and the paradox of something that expands but doesn’t expand ‘into anything’. Theorists at the cutting edge of physics and astrophysics try to help us get our minds around these counterintuitive concepts with stories of spheres and balloons, saddles and cones. We’re as hard put as scholars were in the 16th and 17th centuries to decide how literally descriptions and the theories they represent are meant to be taken.

Clearly, all theories are not created equal when it comes to how much they should be accepted as ‘reality’. (‘Reality, whatever that may mean’, quips Hawking.) For example, many physicists think that inflation theory is a description of something that very possibly happened – either that or something like it. Fewer are prepared to give wormhole theories or Hawking and Jim Hartle’s no-boundary universe that much credence, but they do not reject them either. Then there is Hawking’s most recent proposal, that the universe sprang into being from nothing, in the form of a particle of space and time resembling an extremely small, slightly irregular, wrinkled sphere in four dimensions – the ‘pea instanton’. Though he may be right, you aren’t required to salute that yet. None of the theories discussed in this chapter look likely ever to be confirmed from observational and experimental evidence in the way the Big Bang theory has been. Then again, who knows?

In a universe where on the large scale everything is moving further and further from everything else, if we reverse the direction of time and travel back towards the beginning, we will find things getting closer and closer together. In the late 1960s, Hawking and Penrose, taking off from Penrose’s earlier work on black holes, showed that, in Hawking’s words, ‘if general relativity is correct, any reasonable model of the universe must
start
with a singularity’ – that is, a point at which everything we will ever be able to observe in the universe was compressed in a point of infinite density. At the singularity, spacetime curvature would also have been infinite. A singularity is a dead end. Physical theories can’t work with infinite numbers. All the theories of classical physics become useless there. No one can predict what would emerge from the singularity, and it’s no use asking what happened before it. It’s no wonder that when they find themselves locked out like this, physicists, whatever their religious or philosophical persuasion, are extremely ill at ease.

Hawking was disinclined to let the Big Bang singularity lie. He went on tinkering with his own ideas about what happens when things are very compressed, either in the centre of a black hole or in the very early universe. Eventually he and American physicist Hartle decided to employ a device called ‘imaginary time’ that theorists use for working out problems in quantum mechanics.

It isn’t quite accurate to speak of Einstein’s erasing the difference between the space dimensions and the time dimension, leaving four-dimensional spacetime. There remains a basic distinction in relativity theory between the space and time dimensions. That distinction disappears if the time coordinate is an ‘imaginary number’. (See box
here
.) No longer are there three dimensions of space and one of time, or four dimensions of spacetime. In essence, there are four dimensions of
space
.

Hartle and Hawking’s use of imaginary numbers and imaginary time is subtly different from the way others have employed them. They don’t merely use this mathematical trick to solve a problem and then return to the more familiar concept of time. In their ‘no-boundary’ model, imaginary time is something that actually shapes the universe. They point out that imaginary time is a device used in quantum theory, and that is the theory dealing with the very small – atoms and elementary particles. In the early universe, everything was that small. The principles and concepts of quantum mechanics can be expected to apply there.

Hartle and Hawking’s suggestion is that if we were able to travel back towards what we have been assuming was the ‘beginning’ (the singularity) we would find, just short of reaching it, that (in imaginary time) it becomes meaningless to talk about ‘past’ at all. In a situation where there are four space dimensions and no time dimension, chronological time – with its well-defined past, present and future – would not exist, and with it would go all the vocabulary for describing chronological time. No more ‘yesterday’, or ‘always’, or ‘past’. Discussions about a ‘beginning’ or ‘before the beginning’ would also have no meaning.

Hawking asks us to imagine travelling south on the face of the Earth. We can speak of ourselves as travelling south until we reach the South Pole, but there the concept of ‘south’ is meaningless. No one asks what is south of the South Pole. This is also a good analogy because there is no edge or boundary or beginning at the South Pole. Similarly there are no boundaries or edges or beginning in the Hartle-Hawking no-boundary universe – none in space and none in time. Does it follow that in this model time and space stretch to infinity? No. Just as is true of the surface of the Earth (it is finite in size), space and time are not infinite in the no-boundary universe. Hartle and Hawking’s proposal doesn’t compete with Big Bang theory, for
in
real time – the time in which we live – it would still appear to us that there was a singularity at the beginning of the universe.

Hawking refers to the idea as a proposal, not a theory. There are no direct observational data to support it. It is a wild but not illogical leap of imagination. In the 1980s and 1990s Hawking and others proceeded to ask what sort of universe would result from this no-boundary situation and to explore its connections with the observable universe of today. Needless to say, the calculations are extremely complex and so far they’ve been carried out only in simple models. However, until the late 1990s they seemed to indicate that there was no mathematical inconsistency between this proposal and the universe as we observe and experience it, or with well-accepted theories of modern physics.

Now comes a new challenge: the expansion rate seems to be speeding up. Could that happen in a no-boundary universe like Hartle and Hawking’s? Or does it rule out their model? An accelerating expansion rate might mean the universe is ‘open’ and will go on expanding forever. A no-boundary universe that is analogous (though in more dimensions) to the shape of a sphere – like the Earth –
won’t
go on expanding forever. It is a ‘closed ‘ universe, one that recollapses finally to a ‘Big Crunch’.

But Hawking and Neil Turok, a colleague at Cambridge University, have thought of a way to look at the no-boundary universe as
either
spherical and closed and finite
or
open and infinite (shaped like the bell of a tuba). It depends on how you slice it. To demonstrate their new idea in fewer dimensions: it’s like slicing a cone several ways. Cut through it horizontally, and the slice is a circle or a closed universe; vertically, and the slice is a parabola, an open universe. See
Figure 9.1.

Inflation theory doesn’t see the universe as self-contained in the way that Hartle and Hawking’s no-boundary universe is. In fact, it makes suggestions about how our universe may relate to a much larger context.

Figure 9.1 Several Ways to Slice a Cone

In order to demonstrate how inflation theory solved some of the problems in Big Bang theory, we inflated an imaginary balloon a little to represent the expansion of the universe before the inflationary period, paused to mark a tiny red dot on the surface of the balloon, and then inflated the balloon to a truly remarkable size. The tiny red dot itself became huge. It was the red dot, not the balloon, that represented the entire observable universe. Our ‘universe’ turned out to be only a very small fraction of everything there is. Draw a great number of red dots on the balloon, and when the gravitational repulsive force comes, each dot may respond differently. Some may not respond at all. Perhaps only one dot will expand. If so, that dot
is
our universe. What happened to the other dots? Are they universes too?

It is frankly unlikely that anyone will ever be able to discover whether our dot is unique. If the observable universe derived from a minuscule part of the initial conditions for the entire universe, it will be impossible to discover the ultimate extent and structure of Everything.

For anyone hoping that the quest to measure the universe will culminate with the revelation of the dimensions of everything there is, such news will inevitably be disappointing. Big Bang theory has it that the observable universe amounts to 75 to 90 per cent of the total universe. In the inflationary version of Big Bang theory, the observable portion is only a minuscule fraction of the total, and no one knows what fraction. If there were an infinite number of ‘dots’ on the ‘balloon’, even talking about a ‘fraction’ is incorrect.

Andre Linde has proposed something even more extensive – that each microscopic region that inflates is made up in turn of microscopic sub-regions, which inflate and are in turn made up of microscopic sub-regions – and so on and so forth – an eternal inflationary universe scheme. As Linde describes it, instead of being a single expanding fireball created in the Big Bang ‘the universe is a huge, growing fractal. It consists of many inflating balls that produce new balls, which in turn produce more balls, ad infinitum.’

Is there any way to travel from one balloon or dot or ball to another? The idea of wormholes isn’t new, nor is the notion (much utilized in science fiction films and television series) that they might offer a way of travelling to distant regions and times in the universe or to other universes. They were ‘discovered’ as a solution to Einstein’s field equation in 1916 not long after he produced it. In the 1950s, American physicist John Archibald Wheeler led a research group that studied wormholes. Wheeler introduced the possibility of ‘quantum wormholes’. It was these
that
captured the attention of Sidney Coleman of Harvard and Stephen Hawking in the 1980s. Coleman and Hawking took a particular interest in the possibility that such wormholes are part of the process by which new universes come into existence.

These quantum wormholes would be extremely small, only about 10
^-33
centimetres across. Written out as a fraction, that is 1 as the numerator and 1 followed by thirty-three zeros for the denominator. These tiny holes flicker into existence and then vanish after an interval too short to imagine. Again, think of an enormous balloon, the cosmic balloon, our universe. Picture dots on the balloon’s surface. This time they represent not fledgling universes but stars and galaxies. Einstein predicted that massive objects curve spacetime, and the dots are doing that to the balloon’s surface, causing tiny dimples and puckers. In spite of these, the surface is relatively smooth, even when examined through a microscope. It will take a more powerful microscope than any existing in our present technology to reveal that it is not smooth after all. What we are picturing is something no human being has ever seen except in theory or imagination, what the universe looks like on a scale 1,000 million million million times smaller than the scale of an atomic nucleus. The surface at this magnification is vibrating furiously, creating a frothy foam. At this level, fluctuations in the curvature of spacetime are not big, smooth curves like swells on the ocean. They are continuously changing ripples, crinkles and swirls. The ‘surface’ is hardly a ‘surface’ at all. It is like a bubble bath.