Probability, Time and the Heat of Black Holes

One of the biggest mysteries in modern physics is something that we experience literally every moment of our lives. Physics describes the world by means of formulas that tell us how things vary as a function of time, but it does not explain what time is. We can write formulas that tell us how things vary in relation to their position, or how the taste of a risotto varies as a function of the ‘variable quantity of butter’. Something about time is different, though. Time seems to flow, whereas the quantity of butter or its location in space does not flow. Where does the difference come from?

Another way of posing the problem is to ask: what is the present? We say that only the things of the present exist; the past no longer exists and the future doesn’t exist yet. But in physics there is nothing that corresponds to the notion of the ‘now’. Compare ‘now’ with ‘here’. ‘Here’ designates the place where a speaker is. For two different people, ‘here’ points to two different places. Consequently ‘here’ is a word whose meaning depends on where it is spoken. The technical term for this kind of utterance is ‘indexical’. ‘Now’ also points to the instant in which the word is uttered and is also classed as indexical.

No one would dream of saying that things ‘here’ exist, whereas things that are not ‘here’ do not exist. So then why do we say that things that are ‘now’ exist and that everything else doesn’t? Is the present something that is objective in the world, that flows, and that makes things exist one after the other, or is it only subjective, like ‘here’?

This may seem like an abstruse mental problem, but modern physics has made it into a burning issue, since Einstein’s theory of special relativity has shown that the notion of the present is also subjective. Physicists have come to the conclusion that the idea of a present that is common to the whole universe is a generalisation that doesn’t work. When his great friend Michele Besso died, Einstein wrote a moving letter to Michele’s sister: ‘Michele has left this strange world a little before me. This means nothing. People like us, who believe in physics, know that the distinction made between past, present and future is nothing more than a persistent, stubborn illusion.’

Illusion or not, what explains the fact that for us time flows? The passage of time is obvious to us all. Our thoughts and our speech exist in time. The very structure of our language requires time – a thing ‘is’ or ‘was’ or ‘will be’. The German philosopher Martin Heidegger emphasised our ‘dwelling in time’. Is it possible that the flow of time that Heidegger treats as primal is absent from descriptions of the world?

Some philosophers, the most devoted followers of Heidegger among them, conclude that physics is incapable of describing the most fundamental aspects of reality, and they dismiss it as a misleading form of knowledge. But many times in the past we have realised that it is our immediate intuitions that are imprecise. If we had kept to these, we would still believe that Earth was flat and that it was orbited by the sun. Our intuitions have developed on the basis of our limited experience. When we look a little further ahead, we discover that the world is not as it appears to us: Earth is round, and in Cape Town their feet are up and their heads are down.

As vivid as it may appear to us, our experience of the passage of time does not necessarily reflect a fundamental aspect of reality. But if it is not fundamental, where does it come from?