Probability, Time and the Heat of Black Holes | Part A’

Probability, Time and the Heat of Black Holes | Part A’

‘What is heat?’


Until the mid-nineteenth century, physicists attempted to understand heat by thinking of it as a kind of fluid, called ‘caloric’; or two fluids, one hot and one cold. The idea turned out to be wrong. Eventually James Maxwell and the Austrian physicist Ludwig Boltzmann understood. And what they understood is very beautiful, strange and profound – and takes us into regions which are still largely unexplored.



What they came to understand is that a hot substance is not one which contains caloric fluid. A hot substance is a substance in which atoms move more quickly. Atoms and molecules, small clusters of atoms bound together, are always moving. They run, vibrate, bounce and so on. Cold air is air in which atoms, or rather molecules, move more slowly. Hot air is air in which molecules move more rapidly. Beautifully simple. But it doesn’t end there.



Heat, as we know, always moves from hot things to cold. A cold teaspoon placed in a cup of hot tea also becomes hot. If we don’t dress appropriately on a freezing cold day we quickly lose body heat and become cold. Why does heat go from hot things to cold things, and not vice versa?



It is a crucial question, because it relates to the nature of time. In every case in which heat exchange does not occur, or when the heat exchanged is negligible, we see that the future behaves exactly like the past. For example, for the motion of the planets of the solar system heat is almost irrelevant, and in fact this same motion could equally take place in reverse without any law of physics being infringed. As soon as there is heat, however, the future is different from the past. While there is no friction, for instance, a pendulum can swing forever. If we filmed it and ran the film in reverse we would see movement that is completely possible. But if there is friction then the pendulum heats its supports slightly, loses energy and slows down. Friction produces heat. And immediately we are able to distinguish the future (towards which the pendulum slows) from the past.


The difference between past and future only exists when there is heat. The fundamental phenomenon that distinguishes the future from the past is the fact that heat passes from things that are hotter to things that are colder. So, again, why, as time goes by, does heat pass from hot things to cold and not the other way round?



The reason was discovered by Boltzmann, and is surprisingly simple: it is sheer chance. Boltzmann’s idea is subtle, and brings into play the idea of probability. Heat does not move from hot things to cold things due to an absolute law: it only does so with a large degree of probability. The reason for this is that it is statistically more probable that a quickly moving atom of the hot substance collides with a cold one and leaves it a little of its energy, rather than vice versa. Energy is conserved in the collisions, but tends to get distributed in more or less equal parts when there are many collisions. In this way the temperature of objects in contact with each other tends to equalize. It is not impossible for a hot body to become hotter through contact with a colder one: it is just extremely improbable.

I may not know something with certainty, but I can still assign a lesser or greater degree of probability to something. For instance, I don’t know whether it will rain tomorrow here in Marseilles, or whether it will be sunny or will snow, but the probability that it will snow here tomorrow – in Marseilles, in August – is low. Similarly with regard to most physical objects: we know something but not everything about their state, and we can only make predictions based on probability. Some behaviour is more probable, other behaviour more improbable. In this same sense, the probability that when molecules collide heat passes from the hotter bodies to those which are colder can be calculated, and turns out to be much greater than the probability of heat moving toward the hotter body.





Carlo Rovelli

Translated by Simon Carnell and Erica Segre



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