Time is a commodity: ours to buy, spend, save, keep, mark or waste. Time has volition: it flies, drags, stands still. The verbs alone suggest that we have always understood time as subjective, something experienced according to individual circumstance.

But they also suggest we may be a little confused about the journey from then to now. We are right to be confused, according to Carlo Rovelli’s elegant and wonderfully brief summary of what we do and don’t know about time. “One after another,” he says “the characteristic features of time have proved to be approximations, mistakes determined by our perspective, just like the flatness of the Earth or the revolving of the sun.”

Forget about universal time, a simultaneous now across the cosmos. In 1972, physicists sent a quartet of caesium clocks jetting around the planet in different directions to confirm Einstein’s special relativity. People who live at altitude really do have more time, as do people who stay still. The difference as measured on an atomic clock is counted only in billionths of a second, and we on Earth can conveniently ignore this temporal untidiness. But everything in the universe is in motion; everything feels gravity’s grasp. Time shifts with both mass and velocity, to be different at every point in the universe: we live, Rovelli says, in a “spiderweb of time”.

People who live at altitude really do have more time​, as do people who stay still

There is a more profound puzzle underlying this spacetime confusion. At the deepest level of mathematical physics, time does not exist at all. There is, according to Rovelli, just one basic equation that points to an arrow of time: the second principle of thermodynamics, which says that entropy is always increasing, that the journey from order to disorder is down a one-way street. We observe this journey because heat flows towards the cold things and one day all the heat will have dissipated, and we will experience neither past nor future. “What makes the world go round are not sources of energy, but sources of low entropy.” That suggests we can be sure of a before and an after, but that is only because we see the world as an approximation, and not as a buzz of its ultimate constituents, a ferment of atoms, and beyond the atoms, a fizzing of subatomic particles that in turn may be thought of as quivering fields embedded in yet more gravitational and electromagnetic fields.

Reality is not what it seems – the British title of Rovelli’s popular book from 2016 – and at this level there is no evidence of time, let alone direction. “The difference between past and future, between cause and effect, between memory and hope, between regret and intention … in the elementary laws that describe the mechanism of the world, there is no such difference.” In a quantum world, with neither what we understand as substance or order, there are only events, which crowd around chaotically. A freshly emitted electron is just a cloud of possibilities until it slams into a screen. A kiss is an event – where is it now? – but then so, ultimately, is a stone, or a planet. Nothing is for ever, not even diamonds.

None of this is new. Aristotle and St Augustine both wrestled with the protean question of time, and Rovelli takes his title from the only words written by Anaximander known to have survived the last 26 centuries. There is a paradox of course: even fundamental physicists count the days and contemplate the years. Time, Rovelli suggests, is not to be considered a fundamental entity of creation, but rather a property that emerges from a set of variables, and a special perspective, in the way a football team emerges from a group of kids who have decided to play football. We can consider our local circumstances as a special subset of the universe where entropy “is low in the past, the second law of thermodynamics obtains; memories exist, traces are left – and there can be evolution, life and thought”. Time, as evidenced by our language for it, becomes more easily appreciated as a set of layers, a complex collection of structures, and our use of the word “when” becomes a matter of social and personal convenience. In a sense, we make time.

Rovelli is a professor of physics at Aix-Marseille University, with a close interest in an intellectual monster called quantum loop gravity, and this book is a re-examination of, and a reframing of, one of the enduring questions of the philosophy of nature. It is a joy to read. That does not mean that his reasoning is always easy to follow, and when you close the book you still won’t know whether time really exists, or not. But you will have a sharper sense of why you don’t know.

He writes easily, vividly and brilliantly: – he is as at ease with Beethoven’s Missa Solemnis as he is with Boltzmann’s constant – closes the work with a contemplation of time’s milestone: mortality. Verses by Horace launch each chapter, one of which ends with a couplet from the Grateful Dead. As he says in one of those throwaway observations that make The Order of Time a delight: “Perhaps poetry is another of science’s deepest roots: the capacity to see beyond the visible.”