The most interesting problems in mathematics are those that any intelligent person, be they poet or physicist, can immediately understand. Examples abound, with the four-colour planar map problem and Fermat’s last theorem being perhaps the two most famous. Both are easy to state, and even those without any mathematical training beyond a little algebra can “play around” with them. They are seriously difficult on a technical level, however, with the first being supposedly “solved” by a computer programme, the details of which nobody but the programmers would claim to fully understand, and the second by an extraordinarily deep analysis that only a few mathematicians have actually gone through from start to finish.

The subject of Dan Falk’s In Search of Time is actually one step beyond these deeply perplexing mathematical questions. While we might think we understand time, unlike the “solidity” (and, dare I say it, the timelessness) of the above mathematical problems, there is absolutely nobody on Earth who knows what time is. Or, for that matter, if it even exists. Falk is frank about this right from the start, beginning with St Augustine’s famous lament in his Confessions: “What, then, is time? If no-one asks of me, I know. But if I wish to explain to him who asks, I know not.”

That has not stopped Falk from writing over 300 pages on the subject of time, and for the most part he has done an impressive job. Falk is a science journalist, not a scientist; however, it is clear that he has spent a lot of time reading about time, and understanding what he has read.

The book does get off to a slow start, with the first 100 pages devoted to a somewhat overly familiar historical tour of topics like the ancients’ fascination with the motion of celestial bodies and the development of the modern calendar. Although it is all well written, I suspect that most readers will flip through it quickly.

By chapter five, however, we are introduced to what modern physicists, psychologists and philosophers think about time, and Falk starts to hit his stride. This section begins with what Falk calls “mental time travel”, the ability of humans to think about both the past and the future, and the distinguishing of the past from the present and the future through the use of tenses in spoken and written languages. This is interesting stuff, but it is also fairly “squishy” when judged by the standards of argument that would appeal to a mathematical physicist. And so we have to wait a little longer, until the next chapter (“Isaac’s time”), before we really get to the nitty-gritty of time.

Here, we read of Newton’s conception of “mathematical time” as flowing uniformly, and of the statistical explanation for the apparent contradiction between the time reversibility of the laws of physics and the observed fact that the world inexorably moves only from past to future and never backwards (the so-called entropic or thermodynamic “arrow of time”). The trajectory of an object in space and time is called the world-line of that object, and we learn about the “block universe” in which all the world-lines are completely determined from beginning to end – which seems to toss the concept of free will under a bus. This last idea, which some have interpreted as having a sort of “seal of approval” from Einstein himself, brings philosophers and theologians into play with the physicists – an explosive mixture if there ever was one!

Einstein’s special theory of relativity introduced the idea of a 4D amalgamation of space and time – “space–time” – thus doing away with Newton’s uniform time and even providing a theoretical basis for time travel into the future. Einstein’s later general theory of relativity, with its “warped” space–time, goes even further, allowing the return trip through time along world-lines that bend back on themselves. In other words, the general theory provides support for the possibility of a time machine. Falk devotes an entire chapter to this topic, which fascinates just about everybody – even Stephen Hawking, who adamantly rejects the possibility of time travel to the past. Hawking, whose tongue-in-cheek “chronology protection conjecture” aims to “make the past safe for historians”, nevertheless studies time travel to the past because he wants to discover the (yet unknown) physics that he believes will forbid it.

The classical paradoxes of time travel to the past, such as the grandfather paradox (the attempt to go back in time and murder your grandfather before any of his children – one of your parents – is born) and causal loops, get some discussion, as does the consistency principle of the Russian physicist Igor Novikov. A world-line that bends backwards through space–time and connects with itself to form a closed world-line is called a “time loop”. If a time loop contains an event caused by a later event, which is itself caused by the first event, then we have a “causal loop”. For example, suppose a hitman-for-hire wishes to kill his victim in a “foolproof” way, and so takes a copy of tomorrow’s newspaper back to yesterday. It has the victim’s obituary in it which says he died while reading a newspaper, which so shocks the man when he reads it that he drops dead – thus explaining the obituary! Such a time loop, odd as it is, is not self-contradictory (unlike the classical grandfather paradox) and so satisfies the definition of Novikov’s principle. All such paradoxes are rendered moot if one accepts the controversial idea of parallel universes, where if you travel into the past and do something to change it, then that altered past becomes the past of a different universe. That is the belief of the Oxford University physicist David Deutsch, but it does ask a lot from nature simply to “solve” the paradox problem.

Throughout the book, Falk often presents his personal opinion on what he is discussing. However, he tries hard to give many alternative views as well, having interviewed numerous well-known scientists (including Roger Penrose and Lee Smolin) about their different takes on time and what it might actually be. And yet despite all this collective modern wisdom, when you finish In Search of Time, you may still feel like St Augustine did in the late 4th century AD. Indeed, Falk could have quoted the saint’s Confessions at even greater length, as the following passage demonstrates: “I confess to you, Lord, that I still do not know what time is. Yet I confess too that I do know that I am saying this in time, that I have been talking about time for a long time, and that this long time would not be a long time if it were not for the fact that time has been passing all the while. How can I know this, when I do not know what time is? Is it that I do know what time is, but do not know how to put what I know into words? I am in a sorry state, for I do not even know what I do not know!”

Amen to that.