This is the last in a series of posts prompted by Stephen Wolfram’s lengthy paper “How Did We Get Here? The Tangled History of the Second Law of Thermodynamics” (click here for it on ArXiv). The Second Law of Thermodynamics says, in brief, that the universe is Doomed, which leads to questions of how we can be so lucky as to not have reached Doom yet.
In post #3 (click here for all posts in this series), we saw lots of apocalyptic language about the Doom part of all this. We got to the question of how to rescue the universe from the Doom implied by science and its Second Law of Thermodynamics, and to explain why we are here.
The answer is… bring in a random multiverse! And a jar of beads. That solves everything. Or maybe not.
Remember the jar of beads from post #1 in this series? Even after the beads are randomly mixed, there will be regions within the jar where there are more red beads clustered together, just by chance, and regions where there are more yellow beads clustered together. After all, flip a coin 100 times, and there will be occasions when, by chance, you get a string of heads or tails in a row.
Remember those moving molecules and that molecular speed distribution from the second post in this series? Well, if molecular motions are random, then at any given instant, in a chunk of matter there will be some places where we find, purely by chance, some faster-moving molecules together in one place; likewise we will we find, purely by chance, some slower-moving molecules together in one place.
The point is, small zones of greater order will exist here and there, just by chance. So Ludwig Boltzmann, another great pioneer in thermodynamics, proposed in an 1895 paper that random chance could form pockets of order that we see as habitable realms within a far larger universe of disorder. Here are his words, in italics, with my comments interspersed:
We assume that the whole universe is, and rests for ever, in thermal equilibrium. The probability that one (only one) part of the universe is in a certain state, is the smaller the further this state is from thermal equilibrium.
In other words, it is more likely to find smaller pockets of chance order than larger ones. The chances of finding twelve red beads together in the mixed-up jar of beads are less than the chances of finding three red beads together.
If we assume the universe great enough we can make the probability of one relatively small part being in any given state (however far from the state of thermal equilibrium), as great as we please.
In other words, the bigger the jar, the more likely we will find even twelve red beads together — and if we make the jar big enough, the chances of finding even large clusters of red beads become very good.
We can also make the probability great that, though the whole universe is in thermal equilibrium, our world is in its present state. It may be sayd that the world is so far from thermal equilibrium that we cannot imagine the improbability of such a state. But can we imagine, on the other side, how small a part of the whole universe this world is? Assuming the universe great enough, the probability that such a small part of it as our world should be in its present state, is no longer small.
In other words, if we imagine that the universe is big enough, then it can all be in thermal equilibrium like the Second Law says, with the habitable region we see — that is, “our world” — existing within it by the fluctuations of random chance; just like, in a sufficiently large jar of mixed beads, we can expect to find 1000 red beads together, just by chance.
If this assumption were correct, our world would return more and more to thermal equilibrium; but because the whole universe is so great, it might be probable that at some future time some other world might deviate as far from thermal equilibrium as our world does at present…. worlds where visible motion and life exist.
In other words, our world will proceed toward heat death, just like those 1000 red beads will disperse as the jar is mixed further. However, other habitable zones, other collections of red beads, will pop up by random chance, or have done so already, elsewhere in the unobservable vastness of the universe. Ta-da! We now have a cycle, one that can continue eternally, of random formation and destruction of universes within a broader universe (a multiverse).
There you go — randomness and a multiverse explain our existence. As Wolfram puts it, Boltzmann’s discussion is,
an argument that we’ll see in various forms repeated over the century and a half that follows. In essence what it’s saying is that, yes, the Second Law implies that the universe will end up in thermal equilibrium. But there’ll always be fluctuations. And in a big enough universe there’ll be fluctuations somewhere that are large enough to correspond to the world as we experience it, where “visible motion and life exist”…. the rather anthropic–style argument that “we live in a fluctuation” comes up over and over again as an ultimate way to explain the fact that the universe as we perceive it isn’t just a featureless maximum–entropy [i.e. maximally disordered] place.
But this argument was originally put forward well over a hundred years ago. Today we see multiverses and randomness being proposed in other ways, with no connection to that whole nineteenth-century Second Law business, as an explanation for how we can be here in a habitable universe. Just search around a bit for books published within the last decade that have the word “multiverse” in the title.
It would seem, however, that there is nothing new about the idea of multiverses. They have a long history as the “go-to” argument for explaining away the difficulties that arise from science’s discovery that the universe is not unchanging!
Wolfram finds that in 1951 the Soviet physicists Lev Landau and Evgeny Lifshitz attacked this “go-to” argument in a book they wrote on thermodynamics. They noted that it seems that the universe ought to be in a state of complete equilibrium. However,
Everyday experience shows us… that the properties of Nature bear no resemblance to those of an equilibrium system; and astronomical results show that the same is true throughout the vast region of the Universe accessible to our observation.
We might try to overcome this contradiction by supposing that the part of the Universe which we observe is just some huge fluctuation in a system which is in equilibrium as a whole. The fact that we have been able to observe this huge fluctuation might be explained by supposing that the existence of such a fluctuation is a necessary condition for the existence of an observer (a condition for the occurrence of biological evolution).
But then, they say,
This argument, however, is easily disproved, since a fluctuation within, say, the volume of the solar system only would be very much more probable, and would be sufficient to allow the existence of an observer.
Now there you have an interesting attack on the idea that randomness and multiverses can explain it all! If we exist because of a random fluctuation, then why do we not see that only our immediate vicinity is the random fluctuation? Why is our universe not small? After all, a small fluctuation — a small universe — would be much more likely than a big one; ten red beads together are more likely than 1000. This would seem to apply to modern multiverse arguments. If we exist through randomness, wouldn’t we expect to find ourselves in a very small universe?
How about that? Stephen Wolfram has reason to be interested in the Second Law of Thermodynamics. There is a lot to be found in that Law. If we think about this bit of nineteenth-century science that told us the universe is Doomed, we find out something about multiverses, a hot idea of today!
Gee, the history of science sure is cool. (And, according to the Second Law, getting cooler!)
CLICK HERE for all posts in this series.
