Supersymmetry, in the particular form known as superstring theory, offers one other possible source of hidden mass. This one is easily the most speculative. Back at the time, 10-43 seconds A.C., when gravity decoupled from everything else, a second class of matter may have been created that interacts with normal matter and radiation 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. The "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." Unfortunately, the invocation of shadow matter takes us back to such an early time that if we are sure of anything, it is that the universe then was unrecognizably different from the way that it is today.
I used shadow matter in a story ("The Hidden Matter of McAndrew," Sheffield, 1992). However, I took care to be suitably vague about its properties.
4.6 The end of the universe. "When I dipped into the Future far as human eye could see," said Tennyson in the poem "Locksley Hall." Writing in 1842 he did pretty well, foreseeing air warfare and universal world government. We can go a long way beyond that.
Let's start with the "near-term" future. We can model mathematically the evolution of our own sun. In the near-term (meaning in this case the next few billion years) the results are unspectacular. The sun is a remarkably stable object. It will simply go on shining, becoming slowly brighter. Five billion years from now it will be twice its present diameter, and twice as bright. Eventually, however, it will begin to deplete its stock of hydrogen. At that point it will not shrink as one might expect, but begin to balloon larger and larger. Eight billion years in the future, the sun will be two thousand times as bright, and it will have grown so big (diameter, a hundred million miles) that its sphere will fill half our sky. The oceans of Earth will long since have evaporated, and the land surface will be hot enough to melt lead.
That far future Sun, vast, stationary and dim-glowing in the sky of an ancient Earth, was described by H.G. Wells in one of the most memorable scenes in science fiction (The Time Machine, 1895). The details are wrong—his future Earth is cold, not hot—but the overall effect is incredibly powerful. If you have not read it recently, it well repays rereading.
In studying the long-term future of the sun, we have as an incidental dealt with the future of the Earth. It will be incinerated by the bloated sun, which by that time will be a red giant. The sun, as its energy resources steadily diminish even further, will eventually blow off its outer layers of gas and shrink to end its life, ten billion years from now, as a dense white dwarf star not much bigger than today's Earth.
None of this should be a problem for humanity. Either we will be extinct, or long before five billion years have passed we will have moved beyond the solar system. We can, if we choose, go to sit around a smaller star. It will be less prodigal with its nuclear fuel, and we can enjoy its warmth for maybe a hundred billion years. By that time the needs of our descendants will be quite unknowable.
However, before that time something qualitatively different may have happened to the universe. Just possibly, it will have ended. We know that the universe is open, closed, or flat, but no one knows which. We must examine all three alternatives.
4.7 The Big Crunch. We begin with the case of the closed universe, which is in many ways the least appealing. It has to it a dreadful feeling of finality—though it is not clear why a human being, with a lifetime of a century or so, should be upset by events maybe fifty to a hundred billion years in the future.
The Big Crunch could happen as "soon" as 50 billion years from now, depending on how much the average mass-energy of the universe exceeds the critical amount. We know from observation that the massenergy density is not more than twice the critical density. In that limiting case we will see about 17.5 billion more years of expansion, followed by 32.5 billion years of collapse. A smaller mass-energy density implies a longer future.
Not surprisingly, T-time is inappropriate to describe this future. The logarithm function has a singularity at t=0, but nowhere else. An appropriate time for the closed universe contains not one singularity (T=-infinity, the Big Bang), but two (T=-infinity, the Big Bang, and T=+infinity, the Big Crunch). As the universe approaches its end, the events that followed the Big Bang must appear in inverse order. There will come a time when atoms must disappear, when helium splits back to hydrogen, when electron/positron pairs appear, and so on.
A reasonable time transformation for the closed universe is Tc=log(t/(C-t)), where C is the time, measured from the Big Bang, of the Big Crunch.
TABLE 4.3 (p. 99) shows how this transformation handles significant times of the past and future. In this case, we have chosen Tc=0 as the midpoint in the evolution of the universe, equally far from its beginning and its end. For past times, the values are very similar to those obtained with T-time. For future times close to the Big Crunch, T-time and Tc-time are radically different. As the universe is collapsing to its final singularity Tc-time is rushing on to infinity, but the hands of the T-time clock would hardly be moving.
Tc is a plausible time to describe the evolution of a closed universe. When t tends to zero, Tc tends to minus infinity, and when t tends to C, Tc tends to plus infinity. Thus both end points of the universe are inaccessible in Tc-time. The transformation is symmetric about the "midpoint" of the universe, t=C/2. This does not mean, as is sometimes said, that time will "run backwards" as the Universe collapses. Time continues to run forward in either t-time or Tc-time, from the beginning of the Universe to its end. Note also that Tc has no real values, and hence no meaning, for times before the Big Bang or after the Big Crunch.
Since the collapse applies to the whole universe, there is no escape—unless one can find a way to leave this universe completely, or modify its structure. I dealt with both those possibilities in the novel Tomorrow and Tomorrow (Sheffield, 1997).
4.8 At the eschaton. I want to mention another aspect of the end of the universe, something that appears only in the case where it is closed. Consider the following statement:
The existence of God depends on the amount of matter in the universe.
That is proposed, as a serious physical theory, by Frank Tipler. It was the subject of a paper (Tipler, 1989) and a later book (Tipler, 1994). Both concern the "eschaton." That is the final state of all things, and it therefore includes the final state of the universe.
Tipler argues that certain types of possible universes allow a physicist to deduce (his own term is prove) the ultimate existence of a being with omnipresence, omniscience, and omnipotence. This being will have access to all the information that has ever existed, and will have the power to resurrect and re-create any person or thing that has ever lived. Such a being can reasonably be called God.
The universe that permits this must satisfy certain conditions:
1) The universe must be such that life can continue for infinite subjective time.
2) Space-time, continued into the future, must have as a boundary a particular type of termination, known as a c-boundary.
3) The necessary c-boundary must consist of a single point of space-time.
Then, and only then, according to Tipler, God with omnipresence, omniscience, and omnipotence can be shown to exist.
Conditions 2) and 3) are satisfied only if the universe is closed. It cannot be expanding forever, or even asymptotically flat, otherwise the theory does not work. The choice, open or closed, depends as we already noted on the mass-energy density of the universe.
The definition of "omnipotent" now becomes extremely interesting. Would omnipotence include the power to avoid the final singularity, by changing the universe itself to an open form?
I like to think so, and in Tomorrow and Tomorrow I took that libe
rty.
When the question of missing matter and the closed or open universe was introduced, it seemed interesting but quite unrelated to the subject of religion. Tipler argues that the existence of God, including the concepts of resurrection, eternal grace, and eternal life, depends crucially on the current mass-energy density of the universe.
We already noted the surprising way in which the observation of those remote patches of haze, the galaxies, showed that the universe began a finite time ago. That was a striking conclusion: Simple observations today defined the far past of the universe.
Now we have a still stranger notion to contemplate. The search for exotic particles such as "hot" neutrinos and "cold" photinos and axions will tell us about the far future of the universe; and those same measurements will have application not only to physics, but to theology.
4.9 Expansion forever. Suppose that the universe is open rather than closed. Then it will expand forever.
Freeman Dyson was the first to analyze this situation (Dyson, 1979). First, all ordinary stellar activity, even of the latest-formed and smallest suns, will end. That will be somewhat less than a million billion (say, 1014) years in the future. After that it is quiet for a while, because everything will be tied up in stellar leftovers, neutron stars and black holes and cold dwarf stars.
Then the protons in the universe begin to decay and vanish.
That requires a word of explanation. A generation ago, the proton was thought to be an eternally stable particle, quite unlike its cousin, the unstable free neutron. Then a class of theories came along that said that protons too may be unstable, but with a vastly long lifetime. If these theories are correct, the proton has a finite lifetime of at least 1032 years. In this case, as the protons decay all the stars will finally become black holes.
The effect of proton decay is slow. It takes somewhere between 1030 and 1036 years before the stellar remnants are all black holes. Note that on this time scale, everything that has happened in the universe so far is totally negligible, a tick at the very beginning. The ratio of the present age of the universe to 1036 years is like a few nanoseconds compared with the present age of the universe.
In terms of T-time, the stellar remnants collapse to form black holes between T=19.8 and T=25.8. The T-transformation still does pretty well in describing the open universe.
Long after the protons are all gone, the black holes go, too. Black holes evaporate, as we saw in Chapter 3. Today, the universe is far too hot for a black hole of stellar mass to be able to lose mass by radiation and particle production. In another 1064 years or so that will not be true. The ambient temperature of the expanding universe will have dropped and dropped, and the black holes will evaporate. Those smaller than the Sun in mass will go first, ones larger than the Sun will go later; but eventually all, stars, planets, moons, clouds of dust, everything, will turn to radiation.
In this scenario, the universe, some 1080 years from now, will be an expanding ocean of radiation, with scattered within it a possible sprinkling of widely-separated electron-positron pairs.
The idea of proton decay is controversial, so we must consider the alternative. Suppose that the proton is not an unstable particle. Then we have a rather different (and far longer) future for the universe of material objects.
All the stars will continue, very slowly, to change their composition to the element with the most nuclear binding energy: iron. They will be doing this after some 101600 years.
Finally (though it is not the end, because there is no end) after somewhere between 10 to the 1026 and 10 to the 1076 years, a time so long that I can find no analogy to offer a feel for it, our solid iron neutron stars will become black holes. Now our T-time scale also fails us. A t-time of 10 to the 1026 years corresponds to T=1026, itself a number huge beyond visualization.
Is this the end of the road? No. The black holes themselves will disappear, quickly on these time scales. The whole universe, as in the previous scenario, becomes little more than pure radiation. This all-encompassing bath, feeble and far-diluted, is much too weak to permit the formation of new particles. A few electron-positron pairs, far apart in space, persist, but otherwise radiation is all.
TABLES 4.4, 4.5 and 4.6 (pp. 99-100) show the calendar for the future in "normal" t-time, for the closed and open universes with the unstable and stable proton. Time is measured from today, rather than the beginning of the universe.
4.10 Life in the far future. There is something a little unsatisfactory about the discussion so far. A universe, closed or open, without anyone to observe it, feels dull and pointless.
What are the prospects for observers and conscious participants, human or otherwise? We will certainly not equate "intelligence" with "humanity," since over the time scales that we have encountered, the idea that anything like us will exist is remotely improbable.
Let us note that, on the cosmological scale, life as we know it on Earth has a respectable ancestry. Life emerged quite early in this planet's lifetime, about three and a half billion years ago, so life is now about a fourth as old as the universe itself.
Land life appeared much later, 430 million years ago for simple plants. The first land animals came along a few tens of millions of years later. Mammals have existed for maybe 225 million years, and flowering plants about a hundred million. Recognizable humans, with human intelligence, appeared a mere three or four million years ago. We are upstarts, in a universe where ordinary turtles have been around, essentially unchanged in form and function, for a couple of hundred million years. Perhaps that is why we lack the calm certainty of the tortoise.
Humans have a short past, but we could have a long future. We have already taken care of the "near-term" future. The Earth should remain habitable (unless we ourselves do something awful to it) for a few billion years. After that we can head for a dwarf star, and be comfortable there for another thirty to a hundred billion years. Dwarf stars shine dimly, but a planet or free-space colony in orbit a few million miles away from one will find more than enough energy to support a thriving civilization; and of all the stars in the universe, the inconspicuous, long-lived dwarf stars appear to form the vast majority.
Earth, of course, will be gone—unless perhaps our descendants, displaying a technology as far beyond ours as we are beyond the Stone Age, decide to take the home planet along on their travels for sentimental reasons.
If we are to consider longer time scales, beyond thirty billion years, we must distinguish between the cases of an open and a closed universe.
In the universe of the Big Crunch it seems obvious that life and intelligence cannot go on forever. The future contains a definite time at which everything in existence will be compressed to a single point of infinite pressure and temperature. If we continue to measure time in the usual way, life can exist for a finite time only. However, we have already noted that in Tc-time, even the Big Crunch is infinitely far away. Although the transformation that we introduced seemed like a mere mathematical artifice, it can be shown that there is enough time (and available energy) between now and the Big Crunch to think an infinite number of thoughts. From that point of view, if we work with subjective time, in which life survives long enough to enjoy infinite numbers of thoughts, that will be like living "forever" according to one reasonable definition. It is all a question of redefining our time coordinates.
The open universe case has no problem with available time, but it does have a problem with available energy. In the far future our energy sources will become increasingly diluted and distant.
Dyson has also analyzed this situation (personal communication, Dyson, 1992). He has examined the possibility of continued life and intelligence for the case of an asymptotically flat spacetime, where the universe sits exactly on the boundary of the open and closed cases. I have not seen the details of his analysis, and to my knowledge they have not been published. Here, however, are his conclusions.
First, hibernation will be increasingly necessary. The fraction of time during whic
h a thinking entity can remain "conscious" must become less, like t-1/3. Also, the thinking rate must decrease, so that "subjective time" will proceed more slowly, like t-1/3. To give an example of what this implies, one million billion years from now you will be able to remain awake for only ten years out of each million. And during those ten years, you will only be able to do as much thinking as you can do now in one hour. There will be no more "lightning flashes of wit." Instead it will all be Andrew Marvell's "vaster than empires and more slow." All thought must be "cool calculation."
The good news is that you have an indefinitely long time available, so that you can eventually think an infinitely large number of thoughts.
Curiously enough, in an ultimately flat universe an infinite number of thoughts can be thought with the use of only a finite amount of energy. That's just as well, because in such a universe free energy becomes less and less easy to come by as time goes on.
4.11 Complications from the cosmological constant. Recent observations (1999) suggest that the universe is not only open, but is expanding faster over time. If these observations hold up, they will eliminate the Big Crunch possibility. They also force me, in a late addition to the text, to say a little more about something that I had hoped to avoid: the "cosmological constant."
Since the presence of matter can only slow the expansion of the universe, what could possibly speed up expansion?
Let's go back again to the early days of the theory of general relativity, when Einstein noted that his equations permitted the introduction of a single extra variable, which he called the cosmological constant, generally denoted by ?. It was not that the equations required the added term, they merely permitted it; and certainly the equations appeared more elegant without ?. However, by including the cosmological constant, Einstein was able to produce a universe that neither expanded nor contracted.
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