The End of Time: The Next Revolution in Physics

(2) (p. 27) It is worth quoting here two passages from Boltzmann himself. In 1895 he published (in perfect English—I wonder if he had assistance) a paper in Nature with the title ‘On certain questions of the theory of gases’. It ends with a truly remarkable and concise statement of what much later became known as the anthropic principle. This expression was coined in 1970 by the English relativist Brandon Carter (who had earlier made important discoveries about the physics of black holes in the period leading up to Hawking’s discovery that they can evaporate). The anthropic principle, which gained widespread attention initially through the book The Anthropic Cosmological Principle by John Barrow and Frank Tipler, expresses the idea that any universe in which intelligent life exists must have special and unexpected (from a purely statistical viewpoint) properties, since otherwise the intelligent life that observes these properties could not exist. Therefore we should not be surprised to find ourselves in a universe that does have special and remarkable properties.

In the following passage, the summits of the H curve to which Boltzmann refers correspond to states with very low entropy and high order. Note that Boltzmann credits his assistant with the idea.

1 will conclude this paper with an idea of my old assistant, Dr. Schuetz.

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; but this probability is greater, the greater the universe itself. 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. 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 [sic] 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.

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. Then the aforementioned H curve would form a representation of what takes place in the universe. The summits of the curve would represent the worlds where visible motion and life exist.

Boltzmann returned to this theme a year later, this time writing in German. The following is my translation:

One has a choice between two pictures. One can suppose that the complete universe is currently in a most unlikely state. However, one can also suppose that the eons during which improbable states occur are relatively short compared with all time, and the distance to Sirius is small compared with the scale of the universe. Then in the universe, which otherwise is everywhere in thermal equilibrium, i.e. is dead, one can find, here and there, relatively small regions on the scale of our stellar region (let us call them isolated worlds) that during the relatively short eons are far from equilibrium. What is more, there will be as many of these in which the probability of the state is increasing as decreasing. Thus, for the universe the two directions of time are indistinguishable, just as in space there is no up or down. But just as we, at a certain point on the surface of the Earth, regard the direction to the centre of the Earth as down, a living creature that at a certain time is present in one of these isolated worlds will regard the direction of time towards the more improbable state as different from the opposite direction (calling the former the past, or beginning, and the latter the future, or end). Therefore, in these small regions that become isolated from the universe the ‘beginning’ will always be in an improbable state.

Time Without Time (p. 29) In connection with my suggestion that the brain may be deceiving us when we see motion, it is interesting to note that, as Steven Pinker points out in his How the Mind Works, people with specific types of brain damage see no motion when normal people do see motion. In his words, they ‘can see objects change their positions but cannot see them move—a syndrome that a philosopher once tried to convince me was logically impossible! The stream from a teapot does not flow but looks like an icicle; the cup does not gradually fill with tea but is empty and then suddenly full’.