Borderlands of Science

by Charles Sheffield

  There is one big built-in assumption here: the observed red shift has to be associated with a velocity of recession, and therefore with distance. One mysterious class of objects with large red shifts has led some people to question that assumption. These are the quasars (a contraction of quasi-stellar radio source, or quasi-stellar object).

  Quasars are characterized by their large red shifts, which suggests they are very distant, and by their brightness, which means they have a very high intrinsic luminosity at least comparable with a galaxy. And they are small. We know this not because they fail to show a distinct disc, which is not surprising at their presumed distances, but because their variations in light patterns take place over such short periods that we know they cannot be more than a few light-hours across. That is no more than the size of our own solar system.

  The big question is, how can something so small be so bright?

  The only mechanism that anyone has been able to suggest is of a massive black hole (a hundred million times the mass of our sun, or more) into which other matter is falling. This proves an extraordinarily efficient way of creating lots of energy. Almost half the mass of the in-falling matter can be converted to pure radiation. If one or two stars a year were to fall into a monster black hole, that would be enough to power the quasar.

  There are, however, reputable scientists who do not believe this explanation at all. According to them, quasars are not at galactic distances. They are much closer, much smaller and less bright, and the red shift of their light is due to some other cause.

  What other cause? We will mention one possibility in Chapter 13. Meanwhile, we assume the validity of the Big Bang model.

  4.3 Early days. "Oh, call back yesterday," said Salisbury, in Shakespeare's Richard II. "Bid time return."

  What was the universe like, ten or twenty billion years ago, when it was compressed into a very small volume? Surprisingly, we can deduce a good deal about those early days. The picture is a coherent one, consistent with today's ideas of the laws of physics. It also, quite specifically, says something about the formation of elements during those earliest times.

  Like much of twentieth-century physics, the story begins with Albert Einstein. After he had developed the general theory of relativity and gravitation, he and others used it in the second decade of this century to study theoretical models of the universe. Einstein could construct a simple enough universe, with matter spread through the whole of space. What he could not do was make it sit still. The equations insisted that the model universe either had to expand, or it had to contract.

  To make his model universe stand still, Einstein introduced in 1917 a new, and logically unnecessary, "cosmological constant" into the general theory. With that, he could build a stable, static universe. He later described the introduction of the cosmological constant, and his refusal to accept the reality of an expanding or contracting universe, as the biggest blunder of his life. More on this in Section 4.11.

  When Hubble's work showed the universe to be expanding, Einstein at once recognized its implications. However, he himself did not undertake to move in the other direction, and ask about the time when the contracted universe was far more compact than it is today. That was done by a Belgian, Georges Lemaître. Early in the 1930s Lemaître went backwards in time, to the period when the whole universe was a "primeval atom." In this first and single atom, everything was squashed into a sphere only a few times as big as the Sun, with no space between atoms, or even between nuclei. Later scientific thought suggests that the primeval atom was far smaller yet. As Lemaître saw it, this unit must then have exploded, fragmenting into the atoms and stars and galaxies and everything else in the universe that we know today. He might justifiably have called it the Big Bang, but he didn't. That name was coined by Fred Hoyle (the same man who did the fundamental work on nucleosynthesis) in 1950. It is entirely appropriate that Hoyle, whose career has been marked by colorful and imaginative thinking, should have named the central event of modern cosmology. And it is ironic that Hoyle himself, as we will see in Chapter 13, denies the reality of the Big Bang.

  Lemaître did not ask about the composition of the primeval atom. It might be thought that the easiest assumption is that everything in the universe was already there, much as it is now. But that cannot be true, because as we go back in time, the universe had to be hotter as well as more dense. Before a certain point, atoms as we know them could not exist; they would be torn apart by the intense radiation that permeated the whole universe.

  The person who did worry about the composition of the primeval atom was George Gamow. In the 1940s, he conjectured that the original stuff of the universe was nothing more than densely packed neutrons. Certainly, it seemed reasonable to suppose that the universe at its outset had no net charge, since it seems to have no net charge today. Also, a neutron left to itself will decay radioactively, to form an electron and a proton. One electron and one proton form an atom of hydrogen; and even today, the universe is predominantly hydrogen atoms. So neutrons could account for most, if not all, of today's universe.

  If the early universe was very hot and very dense and all hydrogen, some of it ought to have fused and become helium, carbon, and other elements. The question, How much of each?, was one that Gamow and his student, Ralph Alpher, set out to answer. They calculated that about a quarter of the matter in the primeval universe should have turned to helium, a figure consistent with the present composition of the oldest stars.

  What Gamow and Alpher could not do, and what no one else could do after them, was make the elements heavier than helium. In fact, Gamow and colleagues proved that heavier element synthesis did not take place. It could not happen very early, because in the earliest moments, elements would be torn apart by energetic radiation. At later times, the universe expanded and cooled too quickly to provide the needed temperatures.

  Heavier element formation has to be done in stars, during the process known as stellar nucleosynthesis. The failure of the Big Bang to produce elements heavier than helium confirms something that we already know, namely, that the Sun is much younger than the universe. Sol, at maybe five billion years old, is a second, third, or even fourth generation star. Some of the materials that make up Sun and Earth derive from older stars that ran far enough through their evolution to produce the heavier elements by nuclear fusion and in supernovas.

  4.4 All the way back. We are now going to run time backward toward the Big Bang. (Note: this section draws heavily from the book The First Three Minutes [Weinberg, 1977]. I strongly recommend the original.)

  Where should we start the clock? Well, when the universe was smaller in size, it was also hotter. In a hot enough environment, atoms as we know them cannot hold together because high-energy radiation rips them apart as fast as they form. A good time to begin our backward running of the clock is the time when atoms could form and persist as stable units. Although stars and galaxies would not yet exist, at least the universe would be made up of familiar components: hydrogen and helium atoms.

  Atoms formed, and held together, somewhere between half a million and a million years after the Big Bang. Before that time, matter and radiation interacted continuously. Afterward, radiation could not tear matter apart as fast as it was formed. The two "de-coupled," or nearly so, became quasi-independent, and went their separate ways. Matter and radiation still interacted (and do so to this day), but more weakly. The temperature of the universe when this happened was about 3,000 degrees. Ever since then, the expansion of the universe has lengthened the wavelength of the background radiation, and thus lowered its temperature. The cosmic background radiation discovered by Penzias and Wilson, at 2.7 degrees above absolute zero, is nothing more than the radiation at the time when it decoupled from matter, now grown old.

  Continuing backwards: before atoms could form, helium and hydrogen nuclei and free electrons could exist; but they could not combine to make atoms, because radiation broke them apart. The form of the universe was, in effect, controlled by
radiation energetic enough to prevent atom formation. This situation held from about three minutes to one million years A.C. (After Creation).

  If we go back before three minutes A.C., radiation was even more dominant. It prevented the build-up even of helium nuclei. As noted earlier, the fusion of hydrogen to helium requires hot temperatures, such as we find in the center of stars. But fusion cannot take place if it is too hot. For helium nuclei to form, three minutes after the Big Bang, the universe had to "cool" to about a billion degrees. All that existed before this time were electrons (and their positively charged forms, positrons), neutrons, protons, neutrinos, and radiation.

  Until three minutes A.C., you might think that radiation controlled events. Not so. As we proceed backwards and the temperature of the primordial fireball continues to increase, we reach a point where the temperature is so high (above ten billion degrees) that large numbers of electron-positron pairs are created from pure radiation. That happened from one second to 14 seconds A.C. After that, the number of electron-positron pairs decreased rapidly, because less were being generated than were annihilating themselves and returning to pure radiation. When the universe "cooled" to ten billion degrees, neutrinos also decoupled from other forms of matter.

  We have a long way to go, physically speaking, to the moment of creation. As we continue backwards, temperatures rise and rise. At a tenth of a second A.C., the temperature of the universe is 30 billion degrees. The universe is a soup of electrons, protons, neutrons, neutrinos, and radiation. However, as the kinetic energy of particle motion becomes greater and greater, effects caused by differences of particle mass are less important. At 30 billion degrees, an electron easily carries enough kinetic energy to convert a proton into the slightly heavier neutron. In this period free neutrons are constantly decaying to form protons and electrons, but energetic proton-electron collisions undo their work by remaking neutrons.

  The clock keeps running backward. The important time intervals become shorter and shorter. At one ten-thousandth of a second A.C., the temperature is one thousand billion degrees. The universe is so small that the density of matter, everywhere, is as great as that in the nucleus of an atom (about 100 million tons per cubic centimeter; a fair-sized asteroid, at this density, fits in a thimble). The universe is a sea of quarks, electrons, neutrinos, and energetic radiation.

  We can go farther, at least in theory, to the time, 10-35 seconds A.C., when the universe went through a super-rapid "inflationary phase," growing from the size of a proton to the size of a basketball in about 5x10-32 seconds. We can even go back to a time 10-43 seconds A.C. (termed the Planck time), when according to a class of theories known as supersymmetry theories, the force of gravity decoupled from everything else, and remains decoupled to this day.

  The times mentioned so far are summarized in TABLE 4.1 (p. 98). Note that all these times are measured from the moment of the Big Bang, so t=0 is the instant that the universe came into being.

  TABLE 4.1 displays one inconvenient feature. Everything seems to be crowded together near the beginning, and major events become farther and farther apart in time as we come closer to the present. This is even more apparent when we note that the origin of the solar system, while important to us, has no cosmic significance.

  Let us seek a change of time scale that will make important events more evenly spaced on the time line. We make a change of the time coordinate, defining a new time, T, by T=log(t/tN), where tN is chosen as 15 billion years, the assumed current age of the universe.

  That produces TABLE 4.2 (p. 98). All the entries in it are negative, since we have been dealing so far only with past times. However, the entries for important events, in cosmological terms, are much more evenly spaced in T-time.

  We will return to TABLE 4.2 later. Note, however, that we cannot get all the way to the Big Bang in T-time, since that would correspond to a T value of minus infinity. However, a failure to reach infinite pressure and temperature is no bad thing. In T-time, the Big Bang happened infinitely long ago.

  The time transformation that we made to T-time has no physical motivation. It gives us a convenient time scale for spacing past events, in terms of a familiar function, but there is no reason to think it will be equally convenient in describing the future.

  A value of T=+60.7, which is as far ahead of the present on the T-time scale as the Planck time is behind us, corresponds to a time of 7.5x1070 years from now.

  Does the future of the universe admit such a time? We shall see.

  At this point, however, I want to pause and ask, does it make any sense to go back so far? If we try to press "all the way back" to zero time, we find ourselves faced with a singularity, a time when matter density and temperature tend to infinity. The appearance of infinity in a physical theory is one good way of knowing that there is something wrong—not with the universe, but with the theory. The most likely problem is that physical laws derived under one set of conditions cannot be applied to grossly different conditions. However, it is also possible that the theory itself is too naive.

  In either case, we are already far away from the scientific mainland, well into science fiction waters. We are certainly beyond the realm of the physical laws that we can test today. We are at this stage no more plausible than Archbishop Ussher, convinced that he had pinned down the time of creation.

  More to the point, does the early history of the universe make any difference to anything today?

  Oddly enough, it does. The early history was crucial in deciding the whole structure of today's universe. Let us see why.

  4.5 The missing matter. The universe is expanding. Almost every cosmologist today agrees on that. Will it go on expanding forever, or will it one day slow to a halt, reverse direction, and fall back in on itself in a "Big Crunch"? Or is the universe perhaps poised on the infinitely narrow dividing line between expansion and ultimate contraction, so that it will increase more and more slowly in size and finally (but after infinite time) stop its growth?

  We also ought to mention still another possibility, that the universe oscillates, going through endless phases of expansion followed by contraction. This idea, known as kinematic relativity, was developed by E.A. Milne (not, please, to be confused with A.A. Milne), but it has now fallen from favor.

  The thing that chooses among the three main possibilities is the total amount of mass in the universe; or rather, since we do not care what form the mass takes, and mass and energy are totally equivalent, the future of the universe is decided by the total mass-energy content per unit volume.

  If the mass-energy is too big, the universe will end in the Big Crunch. If it is too small, the universe will fly apart forever. Only in the Goldilocks situation, where the mass-energy is "just right," will the universe ultimately reach a "flat" condition.

  The amount of matter needed to stop the expansion of the universe is not large, by terrestrial standards. It calls for only three hydrogen atoms per cubic meter.

  Is there that much available?

  If we estimate the mass and energy from visible material in stars and galaxies, we find a value nowhere near the "critical density" needed to make the universe finally flat. If we arbitrarily say that the critical mass-energy density has to be unity to end the expansion after infinite time, we observe a value of only 0.01.

  There is evidence, though, from the rotation of galaxies, of more "dark matter" than visible matter. It is not clear what this dark matter is—black holes, very dim stars, clouds of neutrinos—but when we are examining the future of the universe, we don't care. All we worry about is the amount. And that amount, from galactic dynamics, could be at least ten times as much as the visible matter. Enough to bring the density to 0.1, or possibly even 0.2. But no more than that.

  One might say, all right, that's it. There is not enough matter in the universe to stop the expansion, by a factor of about ten, so we have confirmed that we live in a forever-expanding universe.

  Unfortunately, that is not the answer that most cosmolo
gists would really like to hear. The problem comes because the most acceptable cosmological models tell us that if the density is as much as 0.1 today, then in the past it must have been much closer to unity. For example, at one second A.C., the density would have had to be within one part in a million billion of unity, in order for it to be 0.1 today. It would be an amazing coincidence if, by accident, the actual density were so close to the critical density.

  Most cosmologists therefore say that, today's observations notwithstanding, the density of the universe is exactly equal to the critical value. In this case, the universe will expand forever, but more and more slowly.

  The problem, of course, is then to account for the matter that we don't observe. Where could the "missing matter" be that makes up the other nine-tenths of the universe?

  There are several candidates. And now, I should point out, we are very much into science fiction territory.

  One suggestion is that the universe is filled with energetic ("hot") neutrinos, each with a small but nonzero mass (as mentioned earlier, the neutrino is usually assumed to be massless). Those neutrinos would be left over from the very early days of the universe, so we are forced back to studying the period soon after the Big Bang. However, there are other problems with the Hot Neutrino theory, because if they are the source of the mass that stops the expansion of the universe, the galaxies, according to today's models, should not have developed as early as they did.

  What about other candidates? Well, the class of theories already alluded to and known as supersymmetry theories require that as-yet undiscovered particles ought to exist.

  There are axions, which are particles that help to preserve certain symmetries (charge, parity, and time-reversal) in elementary particle physics; and there are photinos, gravitinos, and others, based on theoretical supersymmetries between particles and radiation. These candidates are slow-moving (and so considered "cold") but some of them have substantial masses. They too would have been around soon after the Big Bang. These slow-moving particles clump more easily together, so the formation of galaxies could take place earlier than with the hot neutrinos. We seem to have a better candidate for the missing matter—except that no one has yet observed the necessary particles. Neutrinos are at least known to exist!