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In the Fullness of Time

by John G. Cramer

Alternate View Column AV-09
Keywords: proton, decay, cosmology, infinite time
Published in the October-1985 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 4/1/85 and is copyrighted © 1985, John G. Cramer. All rights reserved.
No part may be reproduced in any form without the explicit permission of the author.

    "Did anyone read on the front page of the Times that matter is decaying?  Am I the only one who saw that?  The universe is gradually breaking down.  There's not going to be anything left.  I'm not talking about my stupid little films here.  Eventually there's not going to be any Beethoven or Shakespeare or ..."

Woody Allen
Stardust Memories (1980)

    Consider the passage of time. In one year the Earth will have gone through a complete cycle of the seasons, there will be a few notable historical events, some important scientific discoveries will be made, 2% or so of the population will die and a new 2% will be born, there will be a few major events and minor wars. In one hundred years our civilization will have dramatically changed, our scientific knowledge and technological capabilities will be vastly different, nations and institutions will have disappeared and been replaced by others, and, in the absence of some life-extending medical breakthrough, none of us will then be around to watch the fun. In ten thousand years our descendants may be travelers among the stars or savages struggling in the grip of a new ice age. In a million years, humanity may have evolved into a completely new species, or may be long extinct. But modern cosmology leads us to believe that the Universe will continue not for 1 or 100 or 10,000 or 1,000,000 years, but forever. There is fairly good evidence (see my column "The Dark Side of the Force of Gravity" in the February, 1985 issue of Analog) that there is not enough matter in the Universe to reverse the cosmic expansion which started with the Big Bang some 16 billion (16,000,000,000) years ago. It would seem that the Universe is going to continue expanding into eternity.

    Eternity is a long time. Much can happen in an infinite amount of time. The consequences for the universe of infinite time, infinite expansion, and infinite aging have been carefully considered by Prof. Freeman Dyson of Princeton's Institute for Advanced Study, and I want to share some of his conclusions with you.

    The problem of discussing very long times is that we don't really have a frame of reference for time which allows us to comprehend such enormous durations. As a start, let's manufacture a very long unit of time which we can use. The present age of the universe, the elapsed time since the Big Bang, is about 16 billion years. So let's adopt that period as our time standard: 16 billion years is now one Big Bang second (BB-second) on our cosmic stopwatch, and the Universe has so far ticked off only one BB-second on this time scale. Then we can ask what will happen in a BB-hour, a BB-day, a BB-year, etc. How far into the infinite future might intelligent life survive?

    The significant events in the history of the universe so far, star and galaxy formation, synthesis of the elements, condensation of the sun, formation of the earth, continental drift, the evolution of life, all are "fast" processes on such a time scale. These events come and go so rapidly that we must ignore them. But on a slower scale other things are happening.

    Our sun is a thermonuclear "engine" which is slowly consuming its hydrogen fuel and producing heat, light, and helium "cinders". In a few dozen BB-minutes this fuel will all be consumed. Our sun will then become a moribund white dwarf star. In about 2 BB-hours even the longest lived of the stars in our galaxy will have similarly burned out, becoming white dwarfs, neutron stars, or black holes, depending on how much hydrogen fuel they had at the start and how fast it was burned. But of course even dead stars can have planets. Perhaps even after the stars go out intelligent life could survive by generating energy from fusion or by dumping matter into black holes. However, in a period of about 18 BB-hours the random near-collisions between the burned-out stars will detach all of the planets from their parent stars.

    Near-miss collisions between stars will also, after about 20 BB-years, have caused about 90% of the stars in our galaxy (and other galaxies) to become detached, so the galaxies will effectively evaporate. If by some chance the earth had not been detached from the sun through a near miss from a wandering star before the sun parted company with the galaxy, the earth will slowly spiral into the sun due to energy loss through the emission of "gravitational waves", (a small energy "leak" in the form of a moving gravitational disturbance, which is to gravity what light is to electromagnetism). This will take about 200 BB-years. The Universe by now has become a rather dreary place: the stars have all gone out leaving only a junkyard of cooling cinders: white dwarf stars, neutron stars, and black holes. There will be no planets. The galaxies will all have dissolved, leaving only isolated stellar debris. But more is yet to come.

    We have now arrived at another time scale problem. Beyond this stage in the future history of the universe the time required for changes becomes so enormous that the (one BB-second = the present age of the Universe) time scale is no longer useful. We will have to revert to a normal time measure and use power-of-ten notation.

    The Woody Allen quote at the beginning of the column was prompted by a New York Times article announcing the instability of the proton, the fact that recent progress in particle physics indicates that protons may, with a low probability and long half-life, decay into lighter particles accompanied by a large release of energy. ( See my Alternate View column in the July, 1984 Analog for a discussion of this). So in 1034 years or so, all of the free protons in the universe should have decayed away.

    In 1975, Stephen Hawking pointed out that black holes are not stable, as had been previously supposed. Instead, because of the strong change in the gravitational force near the curved outer surface of a black hole, there is an effective surface temperature. All black holes are "hot" and will slowly "evaporate" by emitting light. If the temperature becomes high enough, they will also emit electrons, positrons (antimatter electrons), and even some heavier particles. The smaller the black hole, the more curved its surface, the hotter it becomes and the more rapidly this happens. Large black holes evaporates away so slowly that the effect is undetectable. But a small black hole reaches a vicious cycle in which the more it evaporates, the hotter it becomes, so it evaporates even more, becomes even hotter, ... The result is that small black holes literally explode, making a grand exit from the universe with a brilliant flash of light and particles. A black hole with a mass about equal to that of our sun is quite "cold" in these terms, so this process takes a long time, about 1064 (normal) years. (This time is so large that our previous time scaling trick is useless.) In the words of Dyson, "the cold expanding universe will be illuminated by fireworks for a very long time".

    What about the degenerate white dwarf and neutron star remnants formed by stars having too little mass to collapse to black holes? The proton decay process should take care of these from within, one nucleon at a time, destroying them in about 1034 years. But even if proton decay, for some unsuspected reason does not occur, there is still a process called quantum leakage which in the fullness of time will destroy them. In 101600 years all of the degenerate white dwarfs will collapse into neutron stars. The collapse of neutron stars into black holes takes a bit longer, about 10 to the power 1076 years. (This is a truly enormous number which would have to be written in ordinary notation as a one followed by 1076 zeroes!) The resulting black holes will evaporate in a time very short by comparison, leaving behind in the universe only photons (light), neutrinos, electrons, and positrons. These convert back and forth among themselves, reaching an equilibrium of gradually thinning residue as the universe continues to expand.

    Those of you who have followed A Hitch Hiker's Guide to the Galaxy on radio or television will be interested to learn that the Ultimate Answer to Life, the Universe, and Everything is not 42 after all!! Astrophysicists at Pennsylvania State University have shown that the Answer is one-twelfth of the square-root of 105 minus 3 or about 0.6039. This is the Ultimate Ratio of the density of electrons and positrons divided by the density of light photons in the universe after all the dust has settled, the stars have gone out, and the black holes and dead stars themselves have decayed away. And that is what the end of time will really be like.

    So Woody Allen's pessimism seems justified. There will inevitably come a time when art and music, history and philosophy, science and culture have all vanished from the universe, leaving behind only a thin unstructured scum of photons and leptons. This, of course, assumes that there will not be life sufficiently intelligent and powerful that it can intervene to change the odds and hold things together.

    Dyson is more optimistic. He gives arguments that intelligent life can adapt to the lowering temperatures of the aging universe and survive indefinitely, preserving and improving science, art, and culture indefinitely in the fullness of time. You can draw your own moral from all this, but mine is that we should try to enjoy the universe while it is still in good condition.


Freeman J. Dyson, Reviews of Modern Physics 51, 447 (1979).

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