This may already sound like pure science fiction. It is not. It is today’s science — though it certainly may be wrong. But at last we have reached the time when McAndrew’s “hidden matter” was created. And today’s Universe seems to require that something very like it exist.
The argument for hidden matter goes as follows: The Universe is expanding. 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 to end in a Big Crunch? Or is the Universe poised on the infinitely narrow dividing line between expansion and ultimate contraction, so that it will increase more and more slowly, and finally (but after infinite time) stop its growth?
The thing that decides which of these three possibilities will occur is the total amount of mass in the Universe, or rather, since we do not care what form 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. And 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 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 say that the critical mass-energy density has to be equal to unity just to slow the expansion, we observe in visible matter only a value of about 0.01.
There is evidence, though, from the rotation of galaxies, that there is a lot more “dark matter” present there than we see as stars. 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 possible 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. Recent (1999) observations seem to confirm that result.
Unfortunately, that is not the answer that most cosmologists 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 really 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. One suggestion is that the Universe is filled with energetic (“hot”) neutrinos, each with a small but non-zero mass. However, there are problems with the Hot Neutrino theory. 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 in the history of the Universe.
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 mass. 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. At least neutrinos are known to exist!
Supersymmetry, in a particular form known as superstring theory, offers another possible source of hidden mass. This one is easily the most speculative. Back at a time, 10-43 seconds A.C., when gravity decoupled from everything else, a second class of matter may have been created that is able to interact with normal matter and radiation, today, only through the gravitational force. We can never observe such matter, in the usual sense, because our observational methods, from ordinary telescopes to radio telescopes to gamma ray detectors, all rely on electromagnetic interaction with matter.
This “shadow matter” produced at the time of gravitational decoupling lacks any such interaction with the matter of the familiar Universe. We can determine its existence only by the gravitational effects it produces, which, of course, is exactly what we need to “close the Universe,” and also exactly what we needed for the fifth chronicle.
One can thus argue that the fifth chronicle is all straight science; or, if you are more skeptical, that it and the theories on which it is based are both science fiction. I think that I prefer not to give an opinion.
Invariance and science.
In mathematics and physics, an invariant is something that does not change when certain changes of condition are made. For example, the “connectedness” or “connectivity” of an object remains the same, no matter how we deform its surface shape, provided only that no cutting or merging of surface parts is permitted. A grapefruit and a banana have the same connectedness — one of them can, with a little effort, be squashed to look like the other (at least in principle, though it does sound messy). A coffee cup with one handle and a donut have the same connectedness; but both have a different connectedness from that of a two-handled mug, or from a mug with no handle. You and I have the same connectedness — unless you happen to have had one or both of your ears pierced, or wear a ring through your nose.
The “knottedness” of a piece of rope is similarly unchanging, provided that we keep hold of the ends and don’t break the string, There is an elaborate vocabulary of knots. A “knot of degree zero” is one that is equivalent to no knot at all, so that pulling the ends of the rope in such a case will give a straight piece of string — a knot trick known to every magician. But when Alexander the Great “solved” the problem of the Gordian Knot by cutting it in two with his sword, he was cheating.