Carlo Rovelli, The Order of Time (Literary Review)

The quest to unify quantum mechanics with Einstein's general relativity has challenged the world's finest theoretical physicists for decades. While no one has yet succeeded, one possible path is "loop quantum gravity". It is the option favoured by Carlo Rovelli, and the backdrop to the broader thoughts he offers here on the nature of time, in a book whose brevity and elegance 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 as 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", instead a leeway in the order of events.

This takes us to the next great insight that physics has provided: 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, though Rovelli highlights a flaw in that way of thinking. Order can mean different things depending on your point of view, as we all know when someone else decides to "tidy" our things. Rovelli maintains that entropy is relative, not according to personal taste, but 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 their looser kind of "order" by 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. A further analogy for his theory reflects his own cultural 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 Saint Augustine in his Confessions - says that the present alone exists. The second, advocated by Boethius in The Consolation of Philosophy, says 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 is often said to be 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. Einstein himself was to die only a few weeks 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 the chaotic microworld he envisages. "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 would 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 similar constructs; meaningful for molecules and elementary particles, but not at nature's deepest level.

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 formalisms? 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 swerves 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", admitting that perhaps this is "precisely what time is for us", but judging it beyond explanation.

Rovelli's rounded intellect makes pleasurable and rewarding company. He is alert to the existential insights of Heidegger, happy to quote Proust or the Mahabharata alongside Boltzmann or 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.

Anil Ananthaswamy, Through Two Doors At Once (Wall Street Journal)

Are you facing a difficult decision? Quantum physics may have the answer, says science journalist Anil Ananthaswamy. Type your dilemma into the Universe Splitter app, press a button, and a signal is sent to a laboratory in Switzerland. A message comes back telling you which choice to make, leaving you secure in the knowledge that there is now another universe where your double can opt for the alternative.

Mr Ananthaswamy was shown this high-tech coin toss by Sean Carroll, professor of theoretical physics at Caltech and an advocate of the "many worlds" interpretation of quantum mechanics. Through Two Doors At Once is a challenging and rewarding survey of how scientists like Professor Carroll are grappling with nature's deepest, strangest secrets. Though to understand where the story starts you don't need a particle collider or even an iPhone.

Hold your forefinger and thumb close to your eye and bring them gradually together. You'll see a black drop appear between them, crossed by lines. Diffraction effects like this show light consists of multiple waves whose peaks and troughs can interfere, combining and cancelling to create distinctive patterns. Most famous is the "double slit" experiment, where a light beam hits a pair of small, closely spaced holes. Instead of producing two bright dots on a screen placed beyond, the beam creates multiple images. Mr Ananthaswamy quotes Richard Feynman's famous remark that this is the "one experiment which has been designed to contain all of the mystery of quantum mechanics".

The mystery arises when we turn down the intensity of the light beam. There is a limit beyond which light cannot get fainter but instead breaks into individual pulses called photons. You can't do it with an ordinary bulb and a dimmer switch, but experiments show that when one photon is fired at a double slit it produces a lone speck beyond. The photon is therefore like a particle, so presumably must have gone through one or other slit. Yet when many photons are fired in succession they slowly build up the same pattern that a light beam would produce. So is light made of waves or particles?

Niels Bohr's answer was "both". Light can appear wave-like or particle-like in differing circumstances. This duality became part of quantum orthodoxy - the Copenhangen interpretation - where light is regarded as a probabilistic wavefunction. When a single photon makes a dot on a screen the wavefunction collapses to a point.

Could we somehow spot the photon as it passes through one or other slit? Attempts to do so have given rise to a succession of ever-more elaborate experiments that Mr Ananthaswamy describes in detail, culminating in the fiendishly intricate "delayed choice quantum eraser". The upshot is that any effort to spot a photon in flight destroys its waviness. Whether that really amounts to collapsing its wavefunction is a further question that Mr Ananthaswamy examines. One suggestion is that each photon goes through both slits, effectively in two places at once until its wave collapses. In the many-worlds scenario there is no collapse; the photon goes through each slit in two separate universes.

The wave-particle duality applies to matter as well as light; it's how an electron microscope works. It means the double-slit experiment can be done using atoms instead of photons. A Swiss team created a "bespoke molecule" of 810 atoms, with a high fluorine content "like a Teflon shell" to stop them melding. Austrian colleagues fired these non-stick bullets through microscopic slits and found them exhibiting wavelike behaviour. This prompts team-leader Markus Arndt to ask the author: "Why can I not be in two places at the same time?"

The Universe Splitter does not answer this question but illustrates it. The signal the app sends to Switzerland launches a single photon towards a half-silvered mirror which either reflects it to a first detector or lets it pass through to another. The fifty-fifty odds are exactly like those of a photon encountering a double slit; the decision sent back to the app user, determined by which way the photon goes, is a quantum event. This is quite unlike tossing a coin. Unless, that is, there is some wavefunction covering not only the tiniest particles but also coins, people, even entire galaxies. Erwin Schrödinger famously argued against such an idea with his paradoxical cat; the many-worlds scenario endorses it.

If you find it hard to think about half-silvered mirrors then be warned there are a great many of them in this book. Suitably arranged, they can be used to create a variety of photon mazes rich in theory-testing possibilities. Mr Ananthaswamy helpfully supplies schematic diagrams, though the actual mirrors are unlike the ordinary kind. An experiment proposed by Roger Penrose required the fabrication of ones "several orders of magnitude smaller than a grain of sand". Professor Penrose hoped to find if gravity might play a role in wave collapse. His collaborator confesses they are "still quite far away from it", though the apparatus cost "several millions".

Mr Ananthaswamy has interviewed many leading theoreticians and experimentalists in the course of writing this book, and he covers a large and complex field in an admirably accessible way. Historical or biographical details are mostly subordinated to scientific and philosophical issues, though we glimpse a few colourful characters. Alain Aspect, the first scientist to do the double-slit experiment using individual photons, reminds the author of Hercule Poirot, resplendent with his "luxurious, graying mustache". Theorist Chris Fuchs has shelves at his home filled entirely with books by materialist philosopher Daniel Dennett since, he says wryly, "You should know your enemy." Professor Fuchs thinks quantum waves are subjective, reflecting the differing perspectives of individual observers; a theory catchily named QBism. The Picasso link is echoed by philosopher David Albert in support of yet another idea, that photons ride on real yet hidden waves. Professor Albert sees the Copenhagen interpretation as an analogue of modern art. "Physics wanted to have its crisis of representation," he says.

It is a crisis that has now lasted the best part of a century. The mathematics of wavefunctions were worked out long ago by Schrödinger, Heisenberg, Dirac and others. The problem is trying to understand what the symbols actually mean; the dilemma being, as Mr Ananthaswamy puts it, "either that the wavefunction represents our knowledge of the quantum system... or that the wavefunction is part of reality itself." One way to answer that question might be to feed it into the Universe Splitter; though we wouldn't know which universe, if either, received the correct response. "Quantum mechanics is a provisional theory," Professor Penrose tells the author in Oxford. How long until someone can discover a more definitive one?

David N. Schwartz, The Last Man Who Knew Everything (Spectator)

Enrico Fermi's name may not be as familiar as Einstein, Feynman or Hawking, but he was one of the greatest figures of twentieth-century physics, with a reputation for infallibility. In Rome, pioneering atomic science under Mussolini, he was nicknamed "The Pope". Escaping to America where he created the world's first nuclear reactor, he was dubbed "the last man who knew everything". Yet he was no Renaissance man: he knew everything about physics, and didn't care much about anything else. It is testimony to Schwartz's excellence as a biographer that he can reveal the workaholic Fermi to have been such a fascinatingly complex figure.

He was, says Schwartz, a gifted teacher and natural leader. Fermi generously let younger colleagues publish joint work without his name, so he would not overshadow them. His insistence on personally carrying radioactive samples for his team may have led to the stomach cancer that killed him in 1954 at the age of only 53. Few physicists get memorialised as he was, in a double album of recorded reminiscences by colleagues, To Fermi with Love.

Yet beneath the charm there may have been a troubled inner life. As a child Fermi idolised his older and apparently more gifted brother, who died tragically in his teens, causing Fermi's mother to retreat into incurable depression. Schwartz's speculation that this random catastrophe helped inspire Fermi's later interest in statistics seems far-fetched, but the event does give an insight into a recurring pattern Schwartz highlights. As a student Fermi became part of a group who engaged in childish, sometimes nasty pranks. His next gang consisted of the fellow researchers who called him Pope, and who adopted similarly ecclesiastical nicknames of lower rank. The American Manhattan Project was Fermi's biggest and most powerful gang, though he seems to have harboured doubts and qualms about the enterprise, at times almost willing it to fail. After the attacks on Hiroshima and Nagasaki, Fermi's sister wrote from Italy saying how appalled she was by what he had done. "I recommend you to God," she wrote bitterly.

Fermi had kept his atomic work completely secret from his wife Laura, who had been puzzled by an atmosphere of celebration after what in fact had been the first test detonation. Witnessing the blast, Fermi famously dropped scraps of paper in the wind and quickly calculated the power of the bomb. As Schwartz convincingly argues, this betrayed another aspect of Fermi's character: his taste for showmanship. The apparently spontaneous paper experiment had been carefully considered beforehand, and the same probably applied to another legendary moment, when Fermi first directed his nuclear reactor to go critical, deciding at a crucial moment to halt proceedings for lunch. Everything, Schwartz suggests, was planned in advance, then performed for maximum effect.

This is not to detract from Fermi's genius or the greatness of his achievements, but it does hint at an insecurity we might trace back to his traumatic childhood. His fondness for juvenile party games and playful teasing amused friends, but Schwartz says that Laura grew weary of it. Their son Giulio, named after Fermi's dead brother, distanced himself from his famous father, preferring to be called Judd. Emotionally tormented as an adolescent, Judd attempted suicide.

One of the most troubling aspects of Fermi's career is his apparent compliance with Mussolini's regime. He became a member of the Fascist party in 1929, and it was not until 1938 that he and Laura emigrated to the United States. Fermi was considered "ultra-conservative" by the FBI but it seems fair to say that he was as little interested in politics as he was in most things outside physics. Schwartz maintains that Fermi wanted to emigrate far earlier, lured by attractive job offers, but his wife resisted. Her father, an admiral in the Italian navy, was Jewish, and it was only when Mussolini introduced new racial laws that she finally gave way. There may, though, have been a further factor. Hitler had ordered German scientists to boycott the Nobel Prize, Mussolini was expected to follow suit, but Fermi's discoveries made him a clear candidate. He was discreetly asked if he would accept the prize, the only person ever to be pre-warned in this way. Emigration solved the issue: the Fermis stopped off in Stockholm where Enrico collected his award alongside literature laureate Pearl Buck.

The Last Man Who Knew Everything faces competition from another recent Fermi biography, The Pope of Physics, by Gino Segre and Bettina Hoerlin. The latter book is stronger on the scientific aspects, but more reticent about personalities. Schwartz gives an adequate if less detailed account of technical details, excelling instead in a portrayal that is balanced and nuanced, sympathetic but unflinching. Fermi's name endures in the massive Fermilab accelerator in Illinois, and the fermions that collide inside it. Like those eponymous particles, Fermi was energetic, elusive, and in the end perhaps unfathomable.

Clifford V. Johnson, The Dialogues; David Darling and Agnijo Banerjee, Weird Maths; Philip Ball, Beyond Weird (Spectator)

We all know that physics and maths can be pretty weird, but these three books tackle their mind-bending subjects in markedly contrasting ways. Clifford V. Johnson's The Dialogues is a graphic novel, seeking to visualise cosmic ideas in comic-book style. Darling and Banerjee's Weird Maths is a miscellany of fun oddities ranging from chess-playing computers to prime-counting insects. Philip Ball's Beyond Weird argues that we've got quantum mechanics all wrong: it's not so weird actually, but quite sensible. All three books do a fine job for their respective audiences. Just make sure you know which target group you're in.

The Dialogues is a sequence of illustrated conversations between pairs of youthful and attractive characters, appropriately diverse in race and gender, who happen to meet in a cafe, gallery or train carriage, and find themselves talking about physics. Perhaps "The Lectures" would be a better title, since one interlocutor is always the expert, while the other is an interested lay person whose role is to feed questions at appropriate intervals. The author shows himself to be a highly talented graphic artist as well as being a distinguished theoretician, and while the ping-pong chats may be somewhat lacking in narrative drive, they do provide a platform for some admirably lucid explanations of topics such as Maxwell's equations or Einstein's cosmological constant. Not the kind of comic book you roll up in your pocket, but a weighty hardback that would grace any coffee table.

Weird Maths is more traditional in concept, but remarkable for being co-authored by a seventeen-year old maths prodigy and the popular science writer who has helped nurture the lad's talent. The chapters cover a range of topics; and while higher dimensions, probability or code-breaking may be familiar to fans of the genre, others are delightfully abstruse. I especially enjoyed the section about "Ramsey theory", which produces numbers too big to write down in any conventional way, instead requiring entirely new notation and giving rise to contests to see who can come up with the largest non-infinite number. If you think that adding one to your opponent's offering would be sufficient, you ought to read this book.

Weird Maths is a step up from The Dialogues in technical detail, but still perfectly suitable for light dipping, and surely destined for many a geek's loo shelf (mine, for instance). With Philip Ball's Beyond Weird we get into something far meatier: the philosophical problems of quantum theory. Ball's book is aimed at readers already familiar with the idea that particles can be in two places at once, or that a cat in a box can be simultaneously alive and dead, or that our alter-egos exist in parallel worlds. His aim is to argue that all those statements are false, or at any rate are misrepresentations of what the equations really mean.

Rather than being in two places at once, a particle such as a photon may be found in whichever place you look for it, as experiments have shown. Schrödinger's Cat can be in quantum limbo only until its atoms interact with its environment, which happens long before anyone looks inside the box. As for the "many worlds" theory beloved of science fiction aficionados and cosmologists including Stephen Hawking, Ball considers it a worse headache than the one that its inventor, Hugh Everett, was trying to solve: the issue of "wave function collapse". Beyond Weird is structured as a succession of myths needing to be busted, but the book is not negative or even especially controversial, instead presenting an excellent account of modern quantum theory and the efforts being made to harness its effects. Among the most newsworthy of these has been the development of "quantum computers", which according to one interpretation would work by running simultaneous calculations in parallel worlds. Ball throws doubt on that view, saying instead that no one can quite decide exactly how they would work, or indeed whether they would be any better than a conventional computer, except for performing a few specific tasks. As for quantum teleportation, achieved so far only for single photons, Ball says, "when newspaper stories tell you that using it as a handy means of human travel is ‘still a long way off', what they mean is that the fantasy has become confused with the reality."

What all three books illustrate is the great variety that now exists in popularisations of physics and maths, both in technical level and mode of presentation. What they share is a sincerely didactic aim. Stupefied wonder is all well and good, but science isn't a magic show, and each of these authors is intent on showing exactly how the tricks are done. Which you might prefer is a matter of how much you'd like to know, and how much effort you'll feel willing to put in.