The Collapse of the Universe
and the Reversal of Time
Hector C. Parr
This essay is a continuation of the paper entitled Infinity on this website. If you have not read this you are asked to do so before studying this essay. It is also hoped that you have read the chapter on Time in the book on Quantum Physics. You will find this at Quantum Physics: Chapter 2 .
Cosmologists today do not agree on whether the universe will expand forever, or will eventually recollapse. And among those who subscribe to the latter view, there is disagreement over the nature of the collapse. Some believe it will be a mirror image of the big bang, so that any intelligent creatures living during the second half of the universe's life will sense time moving in the reverse direction, and view today's events as lying in their future. This paper presents no answers to these questions, but attempts to analyse the possibilities rationally.
Writers on cosmology appear to speak with authority on the history of the universe. They describe its earliest moments in detail, and discuss its present structure and future large scale development. But many of their pronouncements have to take the form, "If such-and-such is true, then so-and-so. And if not, then ..." In fact our quantitative knowledge of the universe is very incomplete. True, we know the approximate distances of many celestial objects, both near and far, and we know the age of the universe fairly accurately. Although from time to time the different ways of calculating this age have produced results which appear inconsistent with the known ages of the earth and the stars, there is now general agreement that the big bang occurred between 10 and 15 billion years ago. But estimates of the present size of the universe, or the amount of matter and radiation it contains, differ widely, and any predictions we wish to make depend critically on these quantities. Indeed there is disagreement over whether these magnitudes are finite or infinite; surely this uncertainty is of considerable importance.
As explained in the Infinity essay referred to above, I believe that the quantity of matter in the universe must be finite, as must its dimensions in space and time provided these are measured in any reasonable manner. In the rest of this essay, therefore, we assume that the total amount of matter and radiation has some definite finite value, and that the universe has a finite volume. (This volume, of course, may not correspond with that of the visible universe; the expansion results in a "horizon" beyond which we cannot see because of the finite speed of light.) And because I believe the lifetime of the universe must also be finite, the following discussion assumes that the expansion we observe today will eventually be followed by a similar period of contraction, leading to a "big crunch", and the end of everything including space and time themselves.
In considering questions such as this it is essential to rid ourselves of the false impressions of time which our human limitations seem to impose upon us. This important matter is discussed in detail in the chapter referred to above. Briefly, I maintain that the idea of a "now" is a purely subjective phenomenon, existing only within the human mind, with nothing corresponding to it in the outside world. It follows that the impression of a moving time is false; there is nothing objective to move, and nothing with respect to which it could move. Above all we must rid ourselves of the belief that the future is in some way less determined than the past; if the borderline between past and future is illusory, then so must be the distinction between the two regions of time which it is supposed to separate. The only reason we believe the future to be still undecided while the past is immutable is that we can remember the one and not the other. To avoid these prejudices we must picture the history of the universe not as a three-dimensional stage on which things change, but as a static four-dimensional space-time structure of which we are a part. For reasons we cannot explore here (but which are presented in the chapter mentioned above), we all have the false impression of moving through this structure, taking with us a time value which we call "now", or "the present moment". We believe that events are not real until they "happen", whereas in reality past, present and future are all frozen in the four dimensions of space-time. Unfortunately, even if all this is accepted, we have to continue using the language of a "moving" time, for we have no other, but we must try to interpret this language always as a description of this unchanging space-time structure. We display again here the illustration from the preceding essay representing a spherical two-dimensional analogy of the four-dimensional life history we are envisaging.
Contemplating the history of the universe in this way, it is attractive to believe that the periods of expansion and contraction could be related to each other by symmetry, with the large scale features during the contraction phase presenting a mirror image of the expansion; Stephen Hawking admits accepting this view at one time, ("A Brief History of Time", p.150), and subsequently changing his mind. I hope to show below that both points of view merit serious consideration, and that we cannot say with any certainty whether or not the contracting universe will differ fundamentally from the expanding phase that we observe today.
INSTABILITY OF THE UNIVERSE
There are two essential respects in which the universe today is unstable. The first of these is the wide range of temperatures existing today, and in particular the difference between the stars (with surface temperatures of several thousand degrees K) and the background radiation (about 3 degrees K). Bodies like the earth can maintain a temperature above the background because of the thermal inertia of their masses and their low conductivity. Radioactivity within a planet's core may also make a contribution. But in the case of the sun and stars the effect is greatly enhanced by nuclear reactions which provide a steady source of energy at their core. All these sources of heat will eventually be exhausted, and while thermal inertia might keep a body at a temperature substantially above the background for some millions of years, nuclear power can last for several billions. If for the moment we ignore complicating factors such as the expansion and contraction of the universe, all matter and radiation must eventually attain the same temperature, resulting in Sir James Jeans' "heat death".
The other instability present in the universe is gravitational. Given sufficient time, one might expect the galaxies to collapse through gravitational attraction, and eventually to fall together, to form one gigantic mass, or one great black hole, but at present they are distributed throughout space more or less uniformly. When matter does come together in this way, there are three effects which can resist the tendency to collapse. Bodies of planetary dimensions have sufficient structural rigidity to oppose successfully the gravitational pull on the solid material which comprises them. In the case of gaseous bodies like the stars the energy generated by their nuclear power house can prevent collapse until the fuel is exhausted; and galaxies themselves are able to maintain their integrity by their rotation. The first of these effects, the rigidity of solid bodies, can continue indefinitely, but both of the latter two, nuclear power and galactic rotation, will eventually be overcome. When a star's nuclear fuel is exhausted it collapses into a neutron star or a black hole, and eventually frictional and tidal forces within a galaxy will lead to its destruction also.
EXPANSION OF THE UNIVERSE
Both of the above types of instability, the progress towards a world in which everything is at the same temperature, and towards gravitational collapse, would apply even if the universe were not undergoing expansion or contraction, for each represents an irreversible process. The Second Law of Thermodymanics is wholly attributable to this asymmetry, and its source must be looked for in the initial state of the universe immediately after the big bang. In the absence of any information to the contrary, we would expect all the matter in the universe to be collected into one mass and to be at a uniform temperature, even at the moment of its creation. Then nothing could ever happen, and time would not have a direction. It is because the universe started off with its material distributed almost uniformly, a fact we are still far from explaining adequately, that we enjoy today the low entropy which makes the world interesting, and life possible.
But the expansion does have a significant influence on each of the above two effects, ensuring that each can endure for much longer than if the universe were static. The universal background radiation originated from matter at about 3000 degrees K, but because of the expansion which has occurred since it was emitted, it now appears to have come from matter at about 3 degrees. During the expansion phase this lowering of the ambient temperature plays an important part in maintaining temperature differences and delaying the "heat death". If the background were still at 3000 degrees, all matter would be at least as hot as this, and the range of temperatures at the present time would be narrower. Life would be impossible, and the heat death more imminent.
The expansion is also playing an important part in delaying gravitational collapse; a static universe comparable in size to ours would probably have collapsed within ten billion years, but because the remote regions are moving away at high speed many more billions must elapse before gravity can reverse the motion and the collapse can commence.
What will be the effect on these two processes as the universe approaches and enters its contracting phase? Clearly much will depend upon the different time scales. We have three processes approaching completion, (i) the move towards thermal equilibrium, with the stars burnt out, and all material at about the same temperature, (ii) gravitational collapse of all matter into black holes, and (iii) the collapse of space itself as it approaches the big crunch. To discuss the possibility of the contraction phase being a mirror image of the present expansion phase, we must consider carefully the different possible sequences in which these three influences could begin to dominate the universe as it progresses towards its eventual collapse.
Considering first the gravitational problems, it is clear that processes (ii) and (iii), as described above, are related. If the big crunch approaches before most of the matter in space has fallen into black holes, then the rapidly decreasing volume of space will accelerate the process; the last few moments of the universe's existence will certainly see everything in one black hole. On the other hand, if the formation of black holes proceeds more quickly, it may be possible for the collapse of matter to precede the collapse of space itself; then the whole material universe will occupy only a small part of the total volume, with empty space occupying the remainder. Whatever happens, however, it seems that the processes are irreversible. There appears to be no way in which these gravitational influences could result in a symmetrical history, with the final stages of the universe's life mirroring its beginning, and the material contents of the universe becoming more uniformly distributed as the big crunch is approached.
Turning now to the thermal effects, there are many uncertainties. At the present time the thermal behaviour of systems is dominated by the Second Law of Thermodynamics. Heat always passes from a hotter to a cooler body, and never the reverse, resulting in a continual reduction of temperature differences, and the approach of the "heat death". This uni-directional process presents an enigma, for all the fundamental processes of physics, on which these thermal phenomena depend, are themselves time-symmetric, but as shown above, and discussed in Chapter 2 of "Quantum Physics", the irreversibility is explained by the special conditions existing in the very first moments of the universe's existence.
In trying to picture this asymmetrical process, we must be careful not to allow our false impressions of time to influence our reasoning. It may be true that the whole history of the universe is determined by the nature of the big bang, but we should not think of this as an example of cause and effect, a conception which depends essentially on the false idea of time moving. As explained in the chapter referred to, we should think of the state of affairs immediately after the big bang providing a set of boundary conditions, on which the rest of history depends. This shows how any later state of a system can be influenced by an earlier state, in virtue of their different temporal distances from the big bang. This picture has no need of the false notion of a flowing time.
Now what predominant thermal influences will be at work during the contracting phase? As the size of the universe begins to decrease, the gradual lowering of the background radiation temperature will be reversed, and it will start to increase again, just as the temperature of a gas increases when it is compressed. If we assume that, by then, the stars are all burnt out and the material universe is approaching a uniform temperature, the background radiation will eventually overtake this temperature, and matter will once again begin to heat up. We cannot, of course, apply the Second Law to the universe as a whole, for its expansion and contraction effectively provide an influence from outside. But it seems certain that during the contracting phase the Second Law will continue to apply to sub-systems in the same direction as at present. Heat transfer between neighbouring bodies will still be from the hotter to the cooler. This asymmetry is not dependent upon the universal expansion or contraction, but will still be determined by the boundary conditions established at the beginning of time, even at a distance of so many billions of years.
So it seems likely that the thermal behaviour of the universe during the second half of its life, like its gravitational behaviour, will differ greatly from those we find in its first half. There appears to be no possibility of it providing a "mirror image" era.
But perhaps there is a glimmer of hope for those who want to believe in a symmetrical universe. Hawking maintains that black holes eventually evaporate, all the mass that has fallen into them becoming radiation. The time scale required for this process in the case of massive black holes is enormous, but if we can imagine that all matter has collapsed long before the universe reaches maximum volume, is it possible that by then all the black holes could have radiated away? The universe would then contain only radiation. This would be a condition of the highest possible entropy, and might be a half-way stage, separating two symmetrical histories. We could then suppose that the second half of history would be constrained by another set of boundary conditions at the big crunch, just as those in the present phase are determined by the conditions at the big bang. One half could be a time-reversal of the other, and we would have symmetry, with the second half dominated by a decreasing entropy. In such a world, records and memories would necessarily be of the future, and any intelligent living creatures suffering from the illusion of a moving time, as we do, would believe it to move in the opposite direction to that we experience.
Our present knowledge is far from resolving these questions. From time to time cosmologists decide that the universe is, or is not, finite in size, or finite in lifespan, and they appear satisfied that their current theory settles the argument. But outsiders can see that they are still groping, with insufficient evidence to decide the matter. Meanwhile those of us who find it aesthetically pleasing to think of a finite universe, with its two temporal halves related by symmetry, may do so with a clear conscience.