Mathematics & Science

The best books on Time

recommended by Carlo Rovelli

Our experience of time is only weakly related to the fundamental realities of physics, says the physicist and best-selling author Carlo Rovelli. Here he selects five works for understanding the nature of time in its truer sense.

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  • 1

    The Odes
    by Horace

  • 2

    In Search of Lost Time
    by Marcel Proust

  • 3

    The Direction of Time
    by Hans Reichenbach

  • 4

    Time's Arrow and Archimedes' Point
    by Huw Price

  • 5

    The Mūlamadhyamakakārikā, or Fundamental Wisdom of the Middle Way
    by Nagarjuna

Our experience of time is only weakly related to the fundamental realities of physics, says the physicist and best-selling author Carlo Rovelli. Here he selects five works for understanding the nature of time in its truer sense.

Carlo Rovelli

Carlo Rovelli is a theoretical physicist. He is director of the quantum gravity research group of the Centre de Physique Théorique in Marseille, and his books Seven Brief Lessons on Physics and Reality is Not What It Seems were international bestsellers translated into forty-one languages

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Where is a good place to begin when thinking about the nature of time? In the Confessions, Augustine suggested that time — at least as we experience it — is nothing other than the tension of consciousness itself.

The richness of the problem of time is precisely that we can start addressing it from all sorts of places. ‘Time’ is the single most used noun in the English language. It has a multiplicity of meanings.

My interest in time didn’t start with Augustine. It grew from the surprise learning that physics shows that our common ideas about time do not work well for the real world, as soon as we study it with more precision. The precise time of the clocks is something different from the time of our experience.

After a long detour, however, I have indeed ended up thinking that Augustine is basically right: what we call ‘time’ in our everyday life, the time of our experience, has something to do with clocks, but much more to do with what happens in our brain and in our emotions.

Your new book, The Order of Time, describes that detour. It takes us through the insights of Aristotle, Newton and Einstein and others. What are some of crucial junctions and turning points?

The first are the big surprises from the physics of the last two centuries. I describe three of them: first, time passes at different speed depending where you are: you age faster up in the mountains than down by the sea; second, the notion of the ‘present’ only makes sense in a bubble around us, there is no ‘present’ objectively defined all over the universe; third, the distinction between past and future is only statistical and due to our incomplete knowledge of the world. These are facts that have been discovered and confirmed. Each of them demolishes one aspect of our common understanding of time. That common understanding, where time is unique, the same all over the universe and the future is fundamentally different from the past, is adequate for our daily life, but is inadequate for understanding the nature at large.

“Our common understanding, where the future is fundamentally different from the past is inadequate for understanding the nature at large”

The concept of time that Newton used in building mechanics is equally inadequate. It works well at our scale but fails when velocities are very high or when the gravitational field is strong. Einstein understood this a century ago, and over the last hundred years it has become increasingly clear that the world is precisely as he deduced. Aristotle gave a much more general definition of time, which is that it is simply a way of counting the changing of things. Time defined in this manner does not have all the features that we intuitively and conventionally attribute to time (and that are physically wrong in the vast universe!). For instance, time defined in this way does not need to be the same all over the universe. So, in a sense, we are going back to the Aristotelian definition of time.

Each chapter of The Order of Time opens with verses from your first book choice, the Odes of Horace. What do you value in this poet of ancient Rome?

I have a passion for Horace. A dear friend of my youth, who is not with us anymore, gave me as a gift, long ago, a small book with a choice of Horace’s Odes [note: Rovelli is referring to In questo breve cerchio, which contains Italian translations by Giulio Galetto]. I have been carrying this with me since ever, and re-reading it often. Horace is probably the greatest poet in Latin, and has many sides. There is an aulic, or courtly, aspect of his poetry, which I dislike, and is related to his official role of poet of the empire. But then there is an intimate and lyrical side of him which is marvellous, because it merges the clarity and concreteness of his visual, colourful, classical style, with a subtle modulation of universal sentiments which are deeply human — above all the soft melancholy of the running away of time. Horace is the great cantor of time, of the effect of the flight of time upon our deepest emotions. There is nothing screaming in him, no romantic exaggeration, and yet there is an intensity of emotion that reaches deep inside us and seems to capture the essence of what is to be human, and mortal. Consider this:

Perhaps God has many more seasons
in store for us
or perhaps the last is to be
this winter
that guides back the waves
of the Tyrrhenian Sea
to break against
the rough pumice cliffs.
You must be wise. Pour the wine
and enclose in this brief circle
your long-cherished hope.

Your second choice is In Search of Lost Time. What does Marcel Proust bring to our understanding of time?

Proust’s reflection on the nature of time is deep and spread over his writing. Reflect for a moment: the three thousand pages of his magnificent novel, packed with people, emotions, parfums, reflections, are not presented as happening in reality, but as emerging from the memory of the protagonist. A vast universe hidden among the folds of his brain, in the few inches between his ears. Proust’s art thus brings to life a key intuition that we can find in thinkers ranging from St Augustine to Husserl, and which I think is crucial for understanding our experience: the fact that the time of our experience is only weakly related to the time of physics. Mostly, it is a space, a clearing, opened up by our memories and anticipations. What we call time in our daily life is these memories and anticipations.

In The Order of Time you write that “perhaps the emotion of time is precisely what time is for us.”

The main message of my book is that time is a multilayered notion. What we mean when commonly say ‘time’ is a rather stratified concept, most layers of which refer to aspects of reality that have more to do with the specific functioning of our brain than to the simple structure of physical reality. We often make the mistake of forgetting this, and attribute to the external world what is really the emotional coloring that the external world generates in us. So, yes, to some extent the emotion of time is precisely what time is for us.

Your third choice, The Direction of Time, is the final work of a philosopher of science of the mid-20th century. What is its enduring importance?

Hans Reichenbach analysed the implications of discoveries about time made by physicists with the clarity that characterises analytical philosophy at its best, and remains a master for most of the philosophy of space and time. But his book is not widely known today, and this is a pity because it contains fundamental ideas, which are correct and are often disregarded.

“ the growth of entropy is the only law of physics that distinguishes the past from the future”

For instance, he was the first, as far as I know, to fully grasp the implications of the fact that the growth of entropy is the only law of physics that distinguishes the past from the future. This means that the existence of traces, memories and causation are just byproducts of entropy growth. This is a shocking realisation, which I believe has not been fully digested yet. He writes lucidly, and the book remains a model of clarity about the nature of time.

Broadly speaking, entropy is a measure of the disorder in the system. Entropy growth is, therefore, increasing disorder. A cup of coffee left on a table cools down: the heat, instead of remaining concentrated in one place, and in that sense ordered, dissipates. Is that about right?

Yes! Entropy is a fancy name to indicate the amount of disorder. Things naturally tend to get out of order for the simple reason that there are many ways of being in disorder and only few of being in order. Therefore random motion disorders: if you shake a box full of numbered balls you do not expect then to find them in the right order given by their numbers. The big surprise of the physics of time direction is that this disordering appears to be the single and only source of the difference between past and future.

What makes your fourth choice Time’s Arrow and Archimedes’ Point by Huw Price worth our attention?

I consider Huw Price one of the best living philosophers and I have learned a lot from several of his books. His book about time teaches us an important lesson: we are so used to think time as naturally oriented that we instinctively think that the future is determined by the past even if we try not to. The Archimedes’ Point of the title is Huw’s metaphor for a correct external a-temporal perspective in thinking about time. Archimedes famously said that if had a point outside the world to place his lever, he could move the world. Huw asks us to do so conceptually about time.

Tell us about your final choice The Mūlamadhyamakakārikā, or The Fundamental Wisdom of the Middle Way, a text by Nagarjuna with a commentary by Jay L. Garfield

This is a book from a very different cultural universe. I include it here because I stumbled upon it, without previously knowing anything about it, while writing my book, and it had a very strong impact on me. Nagarjuna was a Buddhist monk of the second century and this book is a major philosophical text in the Buddhist tradition. Garfield is a contemporary analytical philosopher and his commentary has been essential for me to open up the ideas in the book. Nagarjuna’s philosophy is centred on the idea of the interdependence of all things and the absence of autonomous essence of anything. This implies that, in a precise sense, there is no ultimate reality. Ultimate reality is neither matter, nor energy, nor mind, nor platonic ideas, nor language, nor phenomena, nor Kantian noumen… It is just not there. I have found this a tremendously attractive and useful perspective.

Do you regard the riddle of time as essentially solved, at least in terms of the underlying physics?

No, I don’t. I do think that we are beginning to understand the complexity of time and that we have an overall picture that makes sense; but there are several aspects of this picture that are still unclear, including for the physics. Why, for instance, was entropy low in the past? Is this just a feature of the universe we happen to inhabit, or is it our peculiar perspective on the universe that gives us this impression, like the apparent rotation of the heavens? This is one of the questions I am working on now, and where I hope better understanding will come.

Interview by Caspar Henderson

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Carlo Rovelli

Carlo Rovelli is a theoretical physicist. He is director of the quantum gravity research group of the Centre de Physique Théorique in Marseille, and his books Seven Brief Lessons on Physics and Reality is Not What It Seems were international bestsellers translated into forty-one languages