Stephen Hawking (12 page)

But an atom is largely empty space. The nucleus is tiny but very dense, and the cloud of electrons is (by comparison) huge and insubstantial. In proportion to the size of a whole atom, the nucleus is like a grain of sand in the middle of a concert hall. In white dwarf stars, some of the electrons are knocked off their atoms by the high prevailing pressure, and the nuclei are embedded in a sea of electrons that belong to the whole star, not to any particular nucleus. But there is still a lot of space between the nuclei, even though that space contains electrons. Each nucleus has a positive charge, and like charges repel, so the nuclei keep their distance from each other.

But quantum theory said that there is a way to make a star denser than a white dwarf. If the star were squeezed even more by gravity, the electrons could be forced to combine with protons to make more neutrons. The result would be a star made entirely of neutrons, and these could be packed together as closely as the protons and neutrons in an atomic nucleus. This would be a neutron star.

Calculations suggested that this ought to happen for any dead star with a mass more than 20 percent larger than that of our Sun (that is, more than 1.2 solar masses). A neutron star would have that much mass packed within a radius of about 10 kilometers, no bigger than many mountains on Earth. The density of the matter in a neutron star, in grams per cubic centimeter, would be 10
¹⁴
—that is, 1 followed by 14 zeros, or one hundred thousand billion.

Even an object this dense would not be a black hole, though, for light could still escape from its surface into the Universe at large.

Making a black hole from a dead star would require, as the theorists of the early 1960s were well aware, crushing even neutrons out of existence. The quantum equations said, in fact, that there was no way that even neutrons could hold up the weight of a dead star of three solar masses or more and that, if any such object were left over from the explosive death throes of a massive star, it would collapse inward completely, shrinking to a mathematical point called a singularity. Long before the collapsing star could reach this state of zero volume and infinite density, it would have wrapped spacetime around itself, cutting off the collapsar from the outside Universe.

Indeed, the equations said that if you squeezed any collection of matter hard enough, it would collapse in this way. The special feature of objects of more than three solar masses is that they will collapse anyway, under their own weight. But if it were possible to squeeze our own Sun down into a sphere with a radius of about 3 kilometers, it would become a black hole. So would the Earth, if it were squeezed down to about a centimeter. In each case, once the object had been squeezed down to the critical size, gravity would take over, closing spacetime around the object while it continued to shrink away into the infinite density singularity inside the black hole. But notice that it is much easier to make a black hole if you have a lot of mass. The critical size is not simply proportional to the amount of mass you have; the density at which a black hole forms is larger if you have less mass to squeeze.

For any mass there is a critical radius, called the Schwarzschild radius, at which this will occur. As these examples indicate, the Schwarzschild radius is smaller for less massive objects—you have to squeeze the Earth harder than the Sun,
and the Sun harder than a more massive star, in order to make a black hole. Once it had formed, there would be a surface around the hole (a bit like the surface of the sea) marking the boundary between the Universe at large and the region of highly distorted spacetime from which nothing could escape. It would be a one-way horizon (unlike the surface of the sea!) across which both radiation and material particles could happily travel inward, tugged by gravity to join the accumulating mass of the singularity, but across which nothing at all, not even light, could travel outward.

Some mathematicians worried, fifty years ago, about the prediction that black holes must contain singularities. The notion of a point of infinite density made them uneasy. But most astronomers were more pragmatic. First of all, they doubted whether black holes could really exist at all. Probably, they thought, some law of physics would prevent any dead star from having enough leftover mass to collapse in this way. And even if black holes did exist, by their very nature they would keep the singularities at their hearts locked away from sight or investigation. Did it really matter, after all, if theory said that points of infinite density could exist, if the same theory said that such singularities were safely locked away behind uncrossable horizons?

One thing, however, should have worried those astronomers, even in the early 1960s. Just as you need to squeeze a small mass hard to make a black hole, a larger mass needs less of a squeeze to do the same trick. Indeed, a mass of about 4.5 billion solar masses would form a black hole if it were all contained within a sphere only twice the diameter of our Solar System. That mass sounds ludicrous at first. But remember
that there are a hundred billion stars in our Milky Way Galaxy. If just 5 percent of the total mass were involved, such a supermassive black hole could indeed form. And the density of such an object would be nothing like the density of the nucleus of an atom or a neutron star. It would be just 1 gram per cubic centimeter—the same density as water. You could actually make a black hole out of water, if you had enough of it!

One way to understand how this can happen is by analogy with running tracks. The important thing about a black hole is that it bends spacetime completely around itself, so that light rays at the horizon would circle endlessly around the central singularity. But the photon “orbits” can be either very tight or follow a gentle curve. Indoor running tracks are usually tightly curved, to make them fit into the space available. Outdoor running tracks are more gently curved and take up more space. But in both cases, if you run round the track, you get back to where you started from—you follow a closed loop. Similarly, a black hole can be very small, with spacetime tightly folded around itself, or very large, with light rays following gradual curves around the horizon (or, indeed, they can be any size in between).

Very slowly, during the 1960s, the implications of this began to dawn on cosmologists. The whole Universe, they realized, might behave in some ways like the biggest black hole of them all, with everything in the Universe held together by gravity, and all of spacetime forming a self-contained, closed entity that folded around on itself with the ultimate in gradual curvature. But there is one big difference—black holes pull matter inward, toward the singularity; the Universe expands,
outward from the Big Bang. The Universe is like a black hole inside out.

Einstein's equations—the general theory of relativity—said that the Universe could not be static, but must be either expanding or contracting. Observations showed that the Universe is, indeed, expanding. So what did Einstein's equations say about conditions long ago, when galaxies were packed tightly together, and before? Taken at face value, the equations said that the Universe must have emerged from a point of infinite density, a singularity, about 13.8 billion years ago. “Obviously” (to astronomers of the 1940s and 1950s, that is), that was ridiculous. The fact that the equations predicted a singularity must mean that they were flawed in some way; no doubt in due course somebody would come up with a better theory, one that didn't make such extreme predictions. But meanwhile it seemed fairly reasonable to take the equations at face value as far as they applied to conditions that bore some resemblance to those we observe today.

The densest form of matter familiar to us today is nuclear matter: protons and neutrons packed together in the hearts of atoms. So a few brave souls were prepared to contemplate the possibility that the general theory might provide a good guide to how the Universe had evolved from a state in which the overall density was as great as that of the nucleus of an atom, a “primeval atom,” if you like, containing all the mass of the Universe in a kind of neutron superstar.

What came “before” that? How did this primeval super-density—sometimes referred to as the “cosmic egg”—come into being? Nobody knew; they could only make guesses. Perhaps the cosmic egg had existed for all eternity, until
something triggered it into expansion. Or perhaps there had been a previous phase of the Universe in which spacetime was collapsing, in line with Einstein's equations. Such a contracting universe might compress itself to nuclear densities and then “bounce” outward again, into a phase of expansion, without encountering the troublesome singularity.

The notion of the primeval atom, or cosmic egg, emerged in the early 1930s and was refined over the next couple of decades. Even at the beginning of the 1960s, however, this was all still just a mathematical game played by a few experts, as much as anything for their own amusement. The notion of a super-dense cosmic egg, only about thirty times bigger than our Sun but containing everything that had burst asunder to create the expanding Universe, fitted Einstein's equations and the observations. But nobody seems to have felt, deep down in their hearts, that their equations described the Universe. Nobody would have been too worried if it had turned out that the whole idea of the cosmic egg was wrong.

You can get a feel for the way people regarded the idea in the 1950s from their own shorthand terms for describing their work. The equations of the general theory of relativity actually allow for more than one possible description of the overall behavior of spacetime. As we have mentioned, either expansion or contraction (but not stasis) is allowed by the equations. Obviously, the Universe we live in cannot be expanding and contracting at the same time; the two solutions to the equations cannot both apply to the Universe today. So the solutions are called models. A cosmological model is a set of equations that describes how a universe (with a small “u”) might behave. The equations have to obey the known laws of physics, but
they do not necessarily purport to describe the actual behavior of the real Universe (with a capital “U”). Both the expanding and the contracting solutions to Einstein's equations describe model universes, intriguing mathematical toys; the expanding solution might describe the real Universe. At the beginning of the 1960s, however, most cosmologists would have preferred to call even the expanding solution simply a model universe.

But during the 1960s the whole notion of the Big Bang, as the theory was known, firmed up. Cosmologists began to believe, as more evidence came in confirming the accuracy of the predictions implicit in the general theory of relativity, that their equations really did describe what was going on out there in the real Universe. This encouraged more theoretical calculations, leading to new predictions, and more observations, in a self-stimulating upward spiral that led to a dramatic revolution in our understanding of the birth of the Universe. By 1976 the Big Bang theory was so well established that American physicist Steven Weinberg was able to write a best-selling popular book,
The First Three Minutes
, describing the early stages of the Big Bang, how the Universe had emerged from the super-dense state of the cosmic egg. Although written in the 1970s, the book encapsulated what was essentially the 1960s understanding of the Big Bang; we will not be getting too far ahead of our story if we give a brief résumé of that understanding now.

One of the strangest things to grasp about all these descriptions of the Universe—the relativistic cosmological models—is that the Big Bang does not consist of a huge primeval atom sitting in empty space and then exploding outward. Many people still have this image, in which the galaxies are like
fragments of an exploding bomb, hurtling outward through space. But it is wrong.

What Einstein's equations tell us is that it is space itself that expands, taking galaxies along for the ride. Galaxies were closer together long ago, when the Universe was younger, because the distances between them were more compressed than they are today. You can see this by imagining two spots of paint on a strip of elastic or on a rubber band. When you pull on the ends of the strip, it stretches, and the two paint spots move apart, but they do not move through the material the strip is made of.

So in the very early Universe, at the time of the explosion of the primeval atom, there was no “outside” for the fragments of the explosion to move into. Space was tightly wrapped around itself, so that the cosmic egg was a completely self-contained ball of matter, energy, space, and time. It was, indeed, a super-dense black hole. It still is a black hole—the only difference is that, by expanding, it has become a very low-density black hole in which light now follows very gently curving orbits at the horizon.

We live inside a black hole, but one so huge that the bending of spacetime within it is too small to be measured by any astronomical instruments on Earth. The “explosion” of the Big Bang stretched space, literally creating more room in which the material components of the cosmic egg could move. Starting out very hot and dense, the fireball thinned and cooled as the space available expanded. The process is exactly the same as the way the fluid in the pipes of your refrigerator keeps the fridge cool. In the fridge, fluid expands into a large chamber and cools; at the back of the fridge, it is
squeezed into a smaller space and gets hot, but the heat escapes from the piping on the outside before the fluid goes back into the fridge to repeat the cycle. Like that fluid being squeezed, or like air being compressed in a bicycle pump when we use it to inflate a tire, the Universe must have been much hotter when it was more compressed.

How much hotter? If you run your cosmological model all the way back to the singularity predicted by Einstein's equations, you would be dealing with infinite temperatures, as well as infinite density. But nobody in the 1960s went to that extreme. The infinities were still taken as indicating a breakdown in the general theory of relativity, but even so the moment at which the infinities occurred in the models could be used as a marker for the beginning of time (at least until someone came up with a better theory).