A Choice of Catastrophes Page 4
In the long run, it would appear, nothing can withstand the rising level of entropy or keep it from reaching maximum, at which time the heat-death of the universe will arrive. And if human beings could escape all other catastrophes and somehow still exist trillions of years from now, then will they not finally bow to the inevitable and die with the heat-death?
From all I have said so far, it would seem so.
MOVEMENT AT RANDOM
Yet there is something disturbing in this picture of the steadily rising entropy-content of the universe, and it shows up as we look backward in time.
Since the entropy-content of the universe is rising steadily, the entropy of the universe must have been less a billion years ago than it is now, and still less two billion years ago, and so on. At some moment, if we go back far enough, the entropy of the universe must have been zero.
Astronomers currently believe that the universe began about 15 billion years ago. By the first law of thermodynamics the energy of the universe is eternal, so when we say that the universe began 15 billion years ago, we don’t mean that the energy (including matter) of the universe was then created. It always existed. All we can say is that it was 15 billion years ago that the entropy-clock started ticking and running down.
But what wound it up in the first place?
To answer that question, let’s go back to my two examples of spontaneous entropy-increase—the water flowing from a full container to a nearly empty one, and the heat flowing from a hot body to a cold body. I implied that the two are strictly analogous; that heat is a fluid as water is and behaves in the same way. Yet there are problems in that analogy. It is easy, after all, to see why the water in the two containers acts as it does. There is gravity pulling at it. The water, responding to the uneven gravitational pull on itself in the two containers, flows from the full container into the nearly empty one. When the containers each have water reaching the same level, the gravitational pull is equal on both and there is no further motion. But what is it that, analogously to gravity, pulls at heat and drags it from a hot body to a cold body? Before we can answer that, we must ask: what is heat?
In the eighteenth century, heat was actually thought to be a fluid, like water but much more ethereal, and therefore capable of pouring into and out of the interstices of apparently solid objects, much as water can pour into and out of a sponge.
In 1798, however, the American-born British physicist Benjamin Thompson, Count Rumford (1753–1814), studied the production of heat from friction when cannon were being bored, and suggested that heat was actually the motion of very small particles of matter. In 1803, the English chemist John Dalton (1766–1844) worked out the atomic theory of matter. All matter was made up of atoms, he said. From Rumford’s point of view it might be the motion of these atoms that represented heat.
About 1860, the Scottish mathematician James Clerk Maxwell (1831–79) worked out the ’kinetic theory of gases’, showing how to Interpret their behaviour in terms of the atoms or molecules7 that made them up. He showed that these tiny particles, moving in any direction at random, and colliding with each other and with the walls of any container housing them, again at random, could account for the rules governing gas behaviour that had been worked out over the previous two centuries.
In any sample of gas, the constituent atoms or molecules move in any of a wide range of velocities. The average velocity, however, is higher in hot than in cold gases. In fact, what we call temperature is equivalent to the average velocity of the constituent particles of a gas. (This holds, by extension, for liquids and solids, too, except that in liquids and solids, the constituent particles are vibrating rather than moving bodily.)
For the sake of simplifying the argument that follows, let’s suppose that in any sample of matter at a given temperature, all the particles making it up are moving (or vibrating) at the average velocity characteristic of that temperature.
Imagine a hot body (gas, liquid, or solid) brought into contact with a cold body. The particles at the edge of the hot body will collide with those at the edge of the cold body. A fast particle from the hot body will collide with a slow one from the cold body, and the two will then rebound. The total momentum of the two particles stays the same but there can be a transfer of momentum from one body to the other. In other words, the two particles can leave each other with different speeds than those with which they approached.
It is possible that the fast particle will give up some of its momentum to the slow particle, so that the fast particle will, after rebounding, move more slowly while the slow one will, after rebounding, move more quickly. It is also possible that the slow particle will give up some of its momentum to the fast one so that the slow particle will rebound more slowly still, and the fast particle will rebound still faster.
It is just chance that determines in which direction the transfer of momentum will take place, but the odds are that the momentum will transfer from the fast particle to the slow one, that the fast particle will rebound more slowly, and that the slow particle will rebound more quickly.
Why? Because the number of ways in which momentum can transfer from the fast particle to the slow one is greater than the number of ways in which momentum can transfer from the slow particle to the fast one. If all the different ways are equally likely, then there is a greater chance that one of the many possible transfers from fast to slow will be taken rather than one of the few possible transfers from slow to fast.
To see why this is so, imagine fifty poker chips in a jar all identical, labelled with numbers from 1 to 50. Pick one at random and imagine you have picked number 49. That’s a high number anti represents a fast-moving particle. Put chip 49 back in the jar (that represents a collision) and select another numbered chip at random (that represents the speed at rebound). You might pick 49 again and rebound at the same speed with which you had collided. Or you might pick 50 and rebound even more quickly than you had collided. Or you might pick any number from I to 48, forty-eight different choices, and in each case rebound more slowly than you had collided.
Having picked 49 to begin with, your chance for rebound at a higher velocity is only 1 out of 50. The chance of rebounding more slowly is 48 out of 50.
The situation would be reversed if you had picked chip number 2 lo start with. That would represent a very slow speed. If you then threw it back and picked again, you would have only 1 chance out of 50 to pick a 1 and rebound even more slowly than you had collided, while you would have 48 chances out of 50 to pick any number from 1 to 50 and rebound more quickly than you had collided.
If you imagined ten people each picking poker chip 49 out of a separate jar, and each throwing it back to try their luck again, the chance that every one of them would pick 50 and that every one of them would rebound more quickly than he or she had collided would be 1 in about a hundred million billion. The chances are 2 out of 3, on the other hand, that every single one of the ten would come out with a rebound at a slower speed.
The same thing would happen in reverse if we imagined ten people each picking number 2 and then trying again.
Nor do all these people have to pick the same number. Let us say that a large number of people pick chips and get all sorts of different numbers, but that the average is quite high. If they try again, the average is much more likely to be lower than to be still higher. The more people there are, the more certain it is that the average will be lower.
The same is true of many people picking chips and finding themselves with a quite low average value. The second chance is very likely to raise the average. The more people there are, the more likely the average is to be raised.
In any body large enough to be experimented with in the laboratory, the number of atoms or molecules involved in each is not ten or fifty or even a million, but billions of trillions. If these billions of trillions of particles in a hot body have a high average speed, and if billions of trillions of particles in a cold body have a low average speed, then the odds are tremendous that random collisions among the lot of them are going to bring down the average of the particle Velocities in the hot body and bring up the average in the cold body.
Once the average particle-speed is the same in both bodies, then momentum is just as likely to transfer in one direction as in the other. Individual particles may go now faster now slower, but the overage speed (and therefore the temperature) will remain the dome.
This gives us our answer as to why heat flows from a hot body to a Void body and why both come to the same average temperature and remain there. It is simply a matter of the laws of probability, the natural working out of blind chance.
In fact, that is why entropy continually rises in the universe. There are so many, many more ways of undergoing changes that even out energy distribution than there are those that make it more uneven, that the odds are incredibly high that the changes will move in the direction of increasing entropy through nothing more than blind chance.
The second law of thermodynamics, in other words, does not describe what must happen, but only what is overwhelmingly likely to happen. There’s an important difference there. If entropy must increase then it can never decrease. If entropy is merely overwhelmingly likely to increase, then it is overwhelmingly unlikely to decrease, but eventually, if we wait long enough, even the overwhelmingly unlikely may come to pass. In fact, if we wait long enough, it must come to pass.
Imagine the universe in a state of heat-death. We might think of it as a vast three-dimensional sea of particles, perhaps without limit, engaged in a perpetual game of collision and rebound, with individual particles moving more quickly or more slowly, but the average remaining the same.
Every once in a while, a small patch of neighbouring particles develops a rather high average speed among themselves, while another patch, some way off, develops a rather low average speed. The overall average in the universe doesn’t change, but we now have a patch of low entropy and a small amount of work becomes possible until the patch evens out, which it will do after a while.
Every once in a longer while, there is a larger unevenness produced by these random collisions, and again in an even longer while, a still larger unevenness. We might imagine that every once in a trillion trillion trillion years so large an unevenness is produced that there is a patch the size of a universe with a very low entropy. It takes time for a universe-sized patch of low entropy to even out again; a very long time—a trillion years or more.
Perhaps that is what happened to us. In the endless sea of heat-death, a low-entropy universe found itself suddenly in existence through the workings of blind chance, and in the process of raising its entropy and evening itself out again, it differentiated into galaxies and stars and planets, brought forth life and intelligence, and here we are, wondering about it all.
Thus, the ultimate catastrophe of heat-death may be followed by regeneration after all, just as the violent catastrophes described in Revelation and Ragnarok were.
Since the first law of thermodynamics would seem to be absolute, and the second law of thermodynamics would seem to be only statistical, there is the chance of an infinite succession of universes, separated each from each by unimaginable eons of time, except that there will be no one and nothing to measure the time and no way, in the absence of rising entropy, to measure it even if instruments and inquiring minds existed. We might, therefore, say that the infinite succession of universes was separated by timeless intervals.
And how does that affect the tale of human history?
Suppose human beings have somehow survived all other possible catastrophes and that our species is still alive trillions of years from now when the heat-death is upon the universe. The rate of entropy increase drops steadily as the heat-death approaches and patches of comparatively low’ entropy (patches that are small in volume compared to the universe, but very large on the human scale) would linger here and there.
If we assume that human technology has advanced more or less steadily over a trillion years, human beings should be able to take advantage of these patches of low entropy, discovering them and exploiting them as we now discover and exploit gold mines. These patches could continue running down, and supporting humanity in the process, for billions of years. Indeed, human beings might well discover new patches of low entropy as they form by chance in the sea of heat-death, and exploit those, too, in this way continuing to exist indefinitely, although under constricted conditions. Then, finally, chance will provide a patch of low entropy of universe size end human beings will be able to renew a relatively boundless expansion.
To take the absolute extreme, human beings may do as I once described them as doing in my science-fiction story ‘The Last Question’, first published in 1956, and seek to discover methods for bringing about a massive decrease in entropy, thus averting the heat-death, or deliberately renewing the universe if the heat-death is already upon us. In this way, humanity might become essentially Immortal.
The question is, however, whether human beings will still be in existence at a time when the he at-death becomes a problem, or whether Some earlier catastrophe of another kind is sure to wipe us out.
That is the question to which the rest of the book will seek an answer.
3
The Closing of
the Universe
THE GALAXIES
So far, we have been discussing the manner in which it. would seem the universe ought to behave in accordance with the laws of thermodynamics. It is time we took a look at the universe itself in order to see whether that would cause us to modify our conclusions. To do this, let us step back and try to look at the contents of the universe as a whole, generally; something we have only been able to do in the twentieth century.
Throughout earlier history, our views have been restricted to what we could see of the universe, which turned out to be very little. At first the universe was merely a small patch of Earth’s surface over which the sky and its contents were merely a canopy.
It was the Greeks who first recognized the Earth to be a sphere and who even gained a notion of its true size. They recognized that the sun, moon, and the planets moved across the sky independently of the other objects, and supplied each of them with a transparent sphere. The stars were all crowded into a single outermost sphere and were considered merely background. Even after Copernicus sent the Earth hurtling around the sun, and the coming of the telescope revealed interesting details concerning the planets, the consciousness of human beings did not really extend beyond the solar system. As late as the eighteenth century, the stars were still little more than background. It was only in 1838 that the German astronomer Friedrich Wilhelm Bessel (1784–1846) determined the distance of a star and the scale of interstellar distances was established.
Light travels at the speed of nearly 300,000 kilometres (186,000 miles) per second and in one year light will therefore travel 9.44 trillion kilometres (5.88 trillion miles). That distance is a light-year, and even the nearest star is 4.4 light-years away. The average distance between stars in our neighbourhood of the universe is 7.6 light-years.
The stars do not seem to be spread out through the universe in all directions alike. In a circular band around the sky there are so many stars that they fade off into a dimly luminous fog called the ‘Milky Way’. In other areas of the sky there are, by comparison, few stars.
It became clear in the nineteenth century, therefore, that the stars were arranged in the shape of a lens, much wider than it is thick, and thicker in the middle than towards the rim. We now know that the lens-shaped conglomeration of stars is 100,000 light-years across in its widest dimension and that it contains perhaps as many as 300 billion stars, with an average mass of perhaps half that of our sun. This conglomeration is called the ‘Galaxy’, from the Greek expression for ‘Milky Way’.
Throughout the nineteenth century, it was assumed that the Galaxy was just about all there was to the universe. There didn’t seem to be anything in the sky that was distinctly outside it except for the Magellanic clouds. These were objects in the southern sky (invisible from the North Temperate Zone) which looked like detached fragments of the Milky Way. They turned out to be small conglomerations of stars, only a few billion in each, that lay just Outside the Galaxy. They could be considered small satellite-galaxies of the Galaxy.
Another suspicious object was the Andromeda nebula just visible as a dim and fuzzy object to the naked eye. Some astronomers thought it was just a bright cloud of gas that was part of our own galaxy, but if so, why were there no stars visible inside it to serve as the source of the light? (Stars were visible in the case of other bright Clouds of gas in the Galaxy.) Then, too, the nature of its light deemed that of starlight and not that of luminous gas. Finally, novas (suddenly brightening stars) appeared in it with surprising frequency, novas that would not be visible at their ordinary brightness.
There was good reason to argue that the Andromeda nebula was a conglomeration of stars, as large as the Galaxy, that was so far distant that none of the individual stars could be made out—except (hat occasionally, one of its stars, brightening for some reason, would become bright enough to see. The most vigorous champion of this view was the American astronomer Heber Doust Curtis (1872–1942), who made a special study of the novas in the Andromeda nebula in 1917 and 1918.
Meanwhile, in 1917, a new telescope with a 100-inch mirror (the largest and best the world had seen up to that time) was installed on Mount Wilson, near Pasadena, Caliifornia. Using that telescope, the American astronomer Edwin Powell Hubble (1889–1953) finally managed to make out individual! stars on the outskirts of the Andromeda nebula. It was definitely a conglomeration of stars of the size of our galaxy and since then it has been called the Andromeda galaxy.