The quest to reconcile quantum mechanics with Einstein’s theory of general relativity has challenged the world’s finest theoretical physicists for decades. While no one has yet succeeded, a possible path is via the theory of ‘loop quantum gravity’. It is the option favoured by Carlo Rovelli, and it provides the backdrop to the broader thoughts he offers here on the nature of time in this book, the brevity and elegance of which belie its depth.

Rovelli is mindful that when we speak of time we mean many things. What a clock measures is not the same as what we feel when we wait for a bus or run from a tiger. But as a physicist, he has to start from clock time and hope it might eventually lead to an understanding of time as we experience it. So we begin with Newton’s idea of absolute time, ticking steadily across the entire universe. This is how most of us still imagine time, though Einstein showed there is no single ‘now’ but instead some leeway in the order of events.

This takes us to the next great insight that physics has provided, which relates to the ‘arrow’ pointing from the past towards the future, indicating the direction of time. Why don’t we see broken shards turning into chandeliers, or ashes unburning themselves to become trees? The answer is entropy, loosely defined as the tendency for things to become disordered. Rovelli highlights a flaw in that way of thinking, though, since order can mean different things depending on your point of view, as we all know when someone else decides to ‘tidy’ our stuff. Rovelli points out that entropy is relative, dependent on physical conditions. Time’s arrow becomes manifest only in systems complex enough to show order: ‘At the fundamental level, the world is a collection of events not ordered in time.’

Rovelli’s research focuses on this fundamental level, where the hope is that ‘spin networks’ will provide a mathematical basis for understanding a world without time. He spares us technical details, but illustrates the looser kind of ‘order’ he has in mind through the analogy of family trees, which show paths of descent, but need not indicate whether a person on one branch is older or younger than someone on another.

All of this is presented in a way that is accessible and engaging. He offers a further analogy for his theory that draws on his own background: ‘The events of the world do not form an orderly queue, like the English. They crowd around chaotically like Italians.’

Two major ideas in the philosophy of time are ‘presentism’ and ‘eternalism’. The first, expounded by St Augustine in his Confessions, proposes that the present alone exists. The second, put forward by Boethius in The Consolation of Philosophy, states that all of time exists at once, but we only see it moment by moment. The modern version of the latter view is the ‘block universe’, and it is often said to have been the one favoured by Einstein, thanks to his remark that ‘the distinction between past, present and future is only a stubbornly persistent illusion.’

As Rovelli points out, Einstein’s comment was made in a letter of condolence after the death of one of his oldest friends, Michele Besso. Einstein himself was to die a little over a month later. With such a heightened sense of mortality, he can surely be forgiven for having favoured solace over reasoned argument.

Rovelli rejects both eternalism and presentism in favour of a chaotic microworld: ‘It does not even form a four-dimensional geometry. It is a boundless and disorderly network of quantum events. The world is more like Naples than Singapore.’

Another comparison might be with a glass of water. A thermometer shows the liquid to have a certain temperature, and we know this to be a measure of the average kinetic energy of trillions of water molecules. Time – and space as well – could be similarly conceived as constructs meaningful for molecules and elementary particles, but not at nature’s deepest level: ‘it is not the evolution of time that determines the state, it is the state … that determines a time.’

Here, though, we reach the greatest puzzle. If time and space are to be truly explained, then it has to be in terms of things that are neither time nor space. Should we consider spin networks – or their rivals, superstrings – to be real entities or mere mathematical formulations? Rovelli does not tackle this question head on; I suspect he would say, as he does here in a different context, ‘we should be careful with questions that it is not possible to formulate properly … When we cannot formulate a problem with precision, it is often not because the problem is profound: it’s because the problem is false.’

The ‘false problem’ Rovelli seeks to navigate is the gulf between the timeless Neapolitan microworld of his networks and the mysterious thing whose flow we feel with the passage of minutes, days, years. We can imagine consciousness without space but not without time; we feel time speeding or dragging yet can’t express its rate, except perhaps redundantly as ‘one second per second’. Rovelli calls this feeling ‘the emotion of time’. He admits that this is perhaps ‘precisely what time is for us’, but considers it beyond explanation.

Rovelli’s rounded intellect makes him pleasurable and rewarding company. He is alert to the existential insights of Heidegger, and is happy to quote Proust or the Mahabharata alongside Boltzmann and Einstein. That he is unable to solve the riddle of time should come as no surprise or disappointment. Whether an answer can even exist is itself an open question.