The Infinity Puzzle

                                                                 
The Infinity Puzzle: How the quest to understand quantum field theory led to extraordinary science, high politics, and the world's most expensive experiment by Frank Close

Literary Review, December 2011


‘A desk or table, a chair, paper and pencils,’ was what Einstein asked for in 1933 when he arrived at the Institute for Advanced Study in Princeton. Then he remembered one last item: ‘Oh yes, and a large wastebasket, so I can throw away all my mistakes.’ In the next two decades before his death in 1955 there were plenty of them, but Einstein had earned the right to make those mistakes in search of his holy grail – a unified field theory.

In 1864 the Scottish physicist James Clerk Maxwell showed that electricity and

magnetism were different manifestations of the same underlying phenomenon – electromagnetism. His great achievement was to encapsulate the disparate behaviour of electricity and magnetism into a set of four elegant mathematical equations that were to be the crowning glory of nineteenth-century physics.

Einstein sought a single, all-encompassing theoretical structure that would unify electromagnetism with his theory of gravity, the general theory of relativity. Such a unification was the logical next step for Einstein, but few were convinced, for in the twentieth century two new forces were discovered and given names that alluded to their strengths relative to the electromagnetic: the so-called strong and weak forces.

The strong force is the binding force that holds atomic nuclei together; conversely the weak force destabilises nuclei, causing a form of radioactivity that plays an essential role in the way that the sun produces its energy. As the years passed the belief grew that these four forces – electromagnetism, gravity, and the strong and weak forces – would be reunited in a Theory of Everything.

With the exception of general relativity, physicists have been able to ‘quantize’ the other three forces, since quantum mechanics deals with the atomic and sub-atomic domain. In effect they managed to get three trains running on the same size track. The quantum gravity train is still stuck at the station. In The Infinity Puzzle Oxford particle physicist Frank Close tells the tale of quantum field theory – the attempts to understand and then unite electromagnetism and the strong and weak forces.

In the 1930s the union of Maxwell’s theory of electromagnetism, Einstein’s theory of special relativity, and quantum mechanics gave birth to a theory of the electromagnetic force known as quantum electrodynamics, or QED. However, in the bowels of the theory lurked a monster – infinity. The equations of QED kept predicting that the chance of some things occurring was ‘infinite’. When infinity pops up in physics it spells disaster since, as Close explains, it is ‘proof that you are trying to apply a theory beyond its realm of applicability’. In the case of QED, if you can’t calculate something as basic as a photon – a particle of light – interacting with an electron without getting infinity, you haven’t got a theory.

It was the late 1940s before a way was found to solve the infinity puzzle in QED by a process called renormalisation. The calculations of many properties of atoms and their constituent particles, including those for the mass and charge of an electron, gave infinity as the answer. However, these two quantities of the electron had already been measured to a high degree of precision using other methods and the results were sufficient to provide benchmarks for anything else physicists wished to compute in QED. Instead of infinity, many of the answers now turned out to be finite and correct. Some physical quantities that have been calculated using renormalisation agree with earlier experiments to an accuracy of one part in a trillion, which is an order of magnitude akin to the diameter of a hair when compared to the width of the Atlantic.

Renormalisation may have been inelegant but its ‘recipe for extracting sensible answers for QED worked’. Those who cooked it up independently of each other – Richard Feynman, Julian Schwinger and Sin-Itiro Tomonaga – won a share of the 1965 Nobel Prize in Physics.

Gerard 't Hooft

When it came to the weak force, infinity was not so easy to banish, even with the efforts of the world’s leading physicists over a quarter of a century. It was the brilliant Dutch postgraduate student Gerard ’t Hooft who finally found a solution. The nature of the problem, how it was solved, and the inevitable jostling for Nobel Prizes are major themes of Close’s gripping and extensively researched narrative history of particle physics over the last sixty years.

It may be a collective enterprise but, as Close’s book reveals, science is full of wrong turns, partial answers, missed opportunities and misunderstandings. How could it be otherwise, since the dispassionate, logic-driven stereotype of the scientist is a fiction? The physicists in The Infinity Puzzle ‘experience the same emotions, pressures and temptations as any other group of people, and respond in as many ways’.

A timeline of who did what when, together with a glossary, could be added to the paperback, to help readers as they grapple with gauge invariance, parity violation, spontaneous symmetry breaking, gluons, colour, the Higgs boson and SU(2)xU(1). Yet Close has succeeded in humanising a dramatic era of physics in what is my science book of the year. Some sections of his narrative are difficult because of the inherent nature of the ideas he’s trying to explain. But then, it took exceedingly clever people to devise them.

‘Hold Infinity in the palm of your hand,’ William Blake wrote in the ‘Auguries of Innocence’. Frank Close does a fabulous job of reconstructing how physicists like Feynman and ’t Hooft managed to do exactly that.

Solvay 1911

The Witches Sabbath 

Nature.com, 21 November 2011

The First Solvay Congress, Brussels, October 1911. Left-to right standing – Robert Goldschmidt, Max Planck, Heinrich Rubens, Arnold Sommerfeld, Frederick Lindemann, Maurice de Broglie, Martin Knudsen, Fritz Hasenöhrl, Georges Hostelet, Edouard Herzen, James Hopwood Jeans, Ernest Rutherford, Heike Kamerlingh Onnes, Albert Einstein, Paul Langevin. Seated – Walther Nernst, Marcel Brillouin, Ernest Solvay, Hendrik Lorentz, Emil Warburg, Jean-Baptiste Perrin (reading), Wilhelm Wien (upright), Marie Curie, Henri Poincaré.


In June 1911 Albert Einstein was a professor of physics in Prague when he received a letter and an invitation from a wealthy Belgium industrialist. Ernst Solvay, who had made a substantial fortune by revolutionizing the manufacture of sodium carbonate, offered to pay him one thousand francs if he agreed to attend a ‘Scientific Congress’ to be held in Brussels from 29 October to 4 November. He would be one of a select group of twenty-two physicists from Holland, France, England, Germany, Austria, and Denmark being convened to discuss ‘current questions concerning the molecular and kinetic theories’. Max Planck, Ernest Rutherford, Henri Poincare, Hendrik Lorentz and Marie Curie were among those invited. It was the first international meeting devoted to a specific agenda in contemporary physics: the quantum.

Planck and Einstein were among the eight asked to prepare reports on a particular topic. To be written in French, German, or English they were to be sent out to the participants before the meeting and serve as the starting point for discussion during the planned sessions. Planck would discuss his blackbody radiation theory, while Einstein had been assigned his quantum theory of specific heat. Accorded the honour of giving the final talk, there was no room on the proposed agenda for a discussion of his light-quanta – better known these days as photons.

‘I find the whole undertaking extremely attractive,’ Einstein wrote to Walter Nernst, ‘and there is little doubt in my mind that you are its heart and soul.’ Nernst with his love of motorcars was more flamboyant than the staid Planck, but was just as highly respected – in 1920 he was awarded the Nobel Prize for chemistry for what became known as the third law of thermodynamics. A decade earlier, in 1910 he was convinced that the time was ripe to launch a cooperative effort to try and get to grips with the quantum he saw as nothing more than a ‘rule with most curious, indeed grotesque properties’. Nernst put the idea to Planck who replied that such ‘a conference will be more successful if you wait until more factual material is available’. Planck argued that ‘a conscious need for reform, which would motivate’ scientists to attend the congress was shared by ‘hardly half of the participants’ envisaged by Nernst. Planck was sceptical that the ‘older’ generation would attend or would ‘ever be enthusiastic’. He advised: ‘Let one or even better two years pass by, and then it will be evident that the gap in theory which now starts to split open will widen more and more, and eventually those still remote will be sucked into it. I do not believe that one can hasten such processes significantly, the thing must and will take its course; and if you then initiate such a conference, a hundred times more eyes will be turned to it and, more importantly, it will take place, which I doubt for the present.’

Undeterred by Planck’s response, Nernst convinced Solvay to finance the conference. Interested in physics, and hoping to address the delegates about his own ideas on matter and energy, Solvay spared no expense as he booked the Hotel Metropole. In its luxurious surrounding, with all their needs catered for, Einstein and colleagues spent five days talking about the quantum and, as Lorentz said in his opening remarks, the reasons why the ‘old theories do not have the power to penetrate the darkness that surrounds us on all sides’. However, he continued, that the ‘beautiful hypothesis of the energy elements, which was first formulated by Planck and then extended to many domains by Einstein, Nernst, and others’ had opened unexpected perspectives, and ‘even those who regard it with a certain misgiving must recognize its importance and fruitfulness.’

‘We all agree that the so-called quantum theory of today, although a useful device, is not a theory in the usual sense of the word, in any case not a theory that can be developed coherently at present,’ said Einstein. ‘On the other hand, it has been shown that classical mechanics…cannot be considered a generally useful scheme for the theoretical representation of all physical phenomena.’ Whatever slim hopes he abhorred for progress at what he called ‘the Witches’ Sabbath’, Einstein returned to Prague disappointed at having learnt nothing new. ‘The h-disease looks ever more hopeless,’ he wrote to Lorentz after the conference.

Nevertheless, Einstein had enjoyed getting to know some of the other ‘witches’. Marie Curie, whom he found to be ‘unpretentious’, appreciated ‘the clearness of his mind, the shrewdness with which he marshalled his facts and the depth of his knowledge’. During the congress it was announced that she had been awarded the Nobel Prize for chemistry. She had become the first scientist to win two, having already won the Physics prize in 1903. It was a tremendous achievement that was overshadowed by the scandal that broke around her during the congress. The French press had learned that she was having an affair with a married French physicist. Paul Langevin was another delegate at the congress and the papers were full of stories that the pair had eloped. Einstein, who had seen no signs of a special relationship between the two, dismissed the newspaper reports as rubbish. Despite her ‘sparkling intelligence’, he thought Curie was ‘not attractive enough to represent a danger to anyone’.

The Solvay Congress was the end of the beginning for the quantum. It dawned on physicists that it was here to stay and they were still struggling to learn how to live with it. When the proceedings of the conference were published it brought to the attention of others, not yet aware or engaged in the struggle, what an immense challenge it was to successfully do so. The quantum would be the focus of attention at the fifth Solvay conference in 1927. What happened in the intervening years is, as they say, history.

The Reason Why

The Reason Why: The Miracle of Life on Earth by John Gribbin

Literary Review, November 2011

In the summer of 1950 the New Yorker magazine published a cartoon suggesting that aliens were behind the mysterious disappearance of rubbish bins from the streets of New York. Not long after the cartoon appeared, a group of scientists at the Los Alamos Laboratory in New Mexico were joking about it with their distinguished visitor, the Italian physicist Enrico Fermi. During lunch Fermi suddenly asked, ‘Where is everybody?’ It took a moment for his colleagues to realise that he was referring to extraterrestrials.

With hundreds of billions of galaxies, the universe could easily be teeming with extraterrestrial life. However, the enormous intergalactic distances involved rules out the possibility of a visit. Yet Fermi was not thinking about the entire universe, only our tiny part of it – the Milky Way. After a quick calculation, then and there, he concluded that space-faring aliens, should they exist, would have colonised our galaxy long ago and therefore have visited Earth. As Fermi was regarded as one of the great physicists of the twentieth century, his back-of-the-envelope reasoning was taken seriously and led to what was called the Fermi Paradox: ‘If they are there, why aren’t they here?’ The reason why, argues science writer John Gribbin, is simple: ‘We are alone, and we had better get used to the idea.’

Gribbin begins his entertaining polemic by referring to an equation devised in 1961 by the American astronomer Frank Drake that attempted to quantify the chances of detecting intelligent life elsewhere in our galaxy. Starting with the total number of stars, Drake calculated how many of them were Sun-like, and then asked what fraction of these had planets, how many of them were capable of supporting life, and so forth. With one guesstimate piled upon another it’s a futile approach that, at best, succeeds only in demonstrating our ignorance, for the answers generated range from zero to the hundreds of billions.

Gribbin, though, is prepared to play the numbers game while treating Drake’s equation for what it is, ‘a kind of mnemonic to remind us of the sort of things we have to take into account when considering the possibility of finding intelligent life elsewhere’. For Gribbin, the reasonable thing to do is to look at the history and geography of our galaxy and try to understand why, and how, intelligent life emerged on Earth. For he seeks to understand not whether we are alone but why we are alone. It’s Fermi’s paradox repackaged as: ‘If they are not there, why are we here?’

Gribbin sets out the arguments that the Earth occupies a special location in both space and time that has allowed the development of the only technological civilisation in the Milky Way. The Sun, for example, is fortuitously situated in what is called the Galactic Habitable Zone, a kind of Goldilocks region that’s just right for life. Critically, five billion years ago when the solar system was being formed, the zone had an abundance of metallic elements that allowed the formation of a planet like Earth. Any closer to the galactic centre would have been hazardous for life because of radiation from supernovae explosions, while the outer regions were poor in metals.

Gribbin only entertains the possibility of ‘life as we know it’ and therefore the presence of water is essential. Fortunately for us, Jupiter is of the right size and in the right place to have sent water-rich asteroids and icy comets crashing to Earth early in its history. In yet another piece of luck, the Earth acquired a relatively large moon. Others have covered before much of what Gribbin describes about the Moon’s essential role in the development of life on Earth, but he does so in an easily accessible style befitting the author of more than 100 books. He explains how the fledgling Earth was formed close to Theia, another proto-planet the size of Mars, and that when the two collided the surface of the Earth turned into magma as it swallowed up Theia’s core.

The vast quantities of debris ejected into space as the result of these worlds colliding eventually formed the Moon. The collision tilted the Earth on its axis and set it spinning much faster than it does today. The Moon has acted as a stabilising influence ever since and continues to shield the Earth from the full effect of Jupiter’s gravity. And our neighbour has certainly prevented cosmic debris from striking the planet, says Gribbin. He argues convincingly that the Moon is the single most important factor in making life on Earth possible.

The collision that led to the creation of the Moon resulted in the Earth having a thin crust and, through plate tectonics, the dynamic surface required to sustain the temperature range required for liquid water – and therefore, eventually, us. Otherwise it would probably have become a hot desert like Venus or a frozen world as cold as the Moon.

Life on Earth, argues Gribbin, is the product of such an improbable sequence of chance events that the possibility of finding any other technological civilisation in the galaxy is effectively nil. Yet the fact remains that we are here to ponder the reason for our existence because things are the way they are, because they were the way they were. Elsewhere they could have been different, leading to life, but not as we know it.

Art of Science

The Art of Science: A Natural History of Science by Richard Hamblyn

Independent, 4 November 2011                     

is a thing of beauty. It's the inscription carved on the memorial stone in Westminster Abbey commemorating the life and work of the greatest British physicist of the 20th century, Paul Dirac. By accounting for the spin of the electron, Dirac's equation managed to reconcile Einstein's special theory of relativity with one of the few genuine revolutions in human thought, quantum mechanics. Does it matter, asks Richard Hamblyn, that Dirac's equation remains a closed book to all but a handful of initiates able to translate its compact hieroglyphics into a statement about the nature of the universe?

For Hamblyn, it does. Few of us can read ancient Aramaic or have ever finished Finnegan's Wake; nevertheless we manage to struggle along just fine. So why is Dirac's equation, and other such mathematical statements, different? Hamblyn worries that while an inability to read an ancient language or an experimental novel rarely leads to a wholesale rejection of all other languages or literature, there is a tendency among non scientists to characterise the whole of science as being as reductive, difficult and as alien as   Dirac's equation.

Introducing this anthology, Hamblyn overstates the case to reinforce his point, especially when the likes of Brian Cox and Alice Roberts make science on TV accessible to all. Intellectual engagement and entertainment are the key ingredients as scientists try to connect with audiences beyond the lab and lecture theatre. Hamblyn achieves that in this collection as he showcases not only readable translations of key scientific ideas but situates those ideas in their cultural and historical context.

The hundred-odd pieces selected either reflect the situation in which a moment of scientific understanding took place or reveal the personalities of the scientists involved. The extract from James Watson's account of the events leading up to the discovery of the structure of DNA, for example, highlights the egotism and insensitivity to be found on virtually every page of The Double Helix – yet these character traits were important factors in Watson's scientific success.

Among the classics Hamblyn has chosen is Tycho Brahe on the supernova, William Harvey on the circulation of blood, Galileo on the moons of Jupiter, Einstein on the quantum theory of light, Fahrenheit on his temperature scale and Darwin on the Origin of Species. However, the strength of the collection lies in the surprises from among the contributions made by amateurs: Seneca on whirlwinds; the schoolteacher and champion of atomism John Dalton on colour blindness; the classification of clouds into cirrus, cumulus, and stratus that remains in use today by the pharmacist Luke Howard; the account by the country doctor Gideon Mantell of how he reconstructed the Iguanodon from its fossilised teeth, and - my favourite – a piece on snowflakes by Vermont farmer Wilson Bentley.

With the ingenious aid of a bellows camera rigged up to a microscope, in 1885 Bentley became the first person successfully to photograph snowflakes. Over the next 40 years, having built up thousands of images, Bentley concluded that no two snowflakes are the same. His life's work was "one of the little romances of science". Although there are other such romances, Hamblyn has largely chosen pieces that have documentary value.

James Lind's account of his clinical trials on board HMS Salisbury affords us a surgeon's-eye view of everyday life on an 18th-century warship complete with barrels of baked biscuits and a scurvy-ridden crew. We get a glimpse of the reaction to Copernicus's new ordering of the cosmos through contemporary accounts that also shed light on the means by which his ideas began to spread.

"Art is the Tree of Life," wrote William Blake. "Science is the Tree of Death." This collection proves such accusations to be groundless as it offers ample evidence, to be dipped into at leisure, for what Hamblyn describes as the greatest invention of the human imagination, "the art of scientific thinking".

Dawkins' new book impresses the kids

The Magic of Reality: How we know what's really true by Richard Dawkins

New Humanist, Nov-Dec 2011

Richard Dawkins has a new book out, his first for “a family audience”, called The Magic of Reality: How We Know What’s Really True. But is it any good? I turned it over to the experts to find out – my sons Ravinder, 12, and Jaz, nine. Before I tell you what they said, a brief summary: evolution, dinosaurs, natural selection, time, continental drift, rainbows, earthquakes, DNA and the FoxP2 gene, supernova, the Goldilocks zone, the law of averages are among the array of ideas and concepts explained by Dawkins.

Each chapter is headed by a question, such as “what is reality?”, “what are things made of?”, “how did everything begin?”, “who was the first person?”,  and Dawkins begins with mythical answers to them from around the world – because “they are colourful and interesting and real people believed them and some still do” – before explaning the science. Dawkins cleverly uses the fact that we all love a good story to hook the reader before revealing what science has discovered, since “the truth is more magical …than any myth or made-up mystery or miracle”.

My boys, raised on Harry Potter and the Percy Jackson series of books by Rick Riordan about the adventures of a young demi-god, needed no persuading that myths and magic can be fun. Equally, as the children of a science writer, they have no trouble distingishing myth from science, and recognise that facts can have their own magic: “I didn’t know my 185,000,000 great grandfather was a fish, 417 million years ago!’ said Ravinder, complaining that they had never taught him this astonishing fact when he did evolution at school.

They also seemed to grasp that some questions are not amenable to a precise scientific answer. They both readily accepted that the question of who was the first person, and when did they live, can’t have a precise answer because it’s like asking, “When does someone stop being a baby and become a toddler?” Dawkins does narrow it down to somewhere between a million and a hundred thousand years ago “when our ancestors were sufficiently different from us that a modern person wouldn’t have been able to breed with them if they had met”, which is all well and good although it did leave me having to explain to the nine-year-old what “breed” means.

The boys wanted to make sure that Dawkins’s collaborator, illustrator Dave McKean, got a special mention for his “fantastic” and “brilliant” illustrations, “which make the book come alive” (their words), because “just seeing them makes you want to look more closely and read the words”. But they warned me not to look at pages 94 and 95 before going to bed “because reality is a bit too real in that picture”. Like a typical adult I ignored them and regretted it: the close-up of dust mites had me scratching all night long.

For Jaz, Dawkins is fun to read “because he writes like he’s talking to you”. Ravinder’s verdict? “This is the best non-fiction book I’ve ever read.” Coming from someone who reads more than I do, that’s some endorsement. Having written a book on quantum physics, I hope that when the boys get round to reading it one day they will see it for what it clearly is, and revise their all-time list. But it seems I’ll just have to accept that with the help of McKean, Dawkins has conjured up a book that deserves the top slot, at least for the time being.

The Quantum Universe

The Quantum Universe: Everything that can happen does happen by Brian Cox and Jeff Forshaw

Daily Telegraph, 22 October 2011

More than 10,000,000,000, 000,000,000 transistors are manufactured each year. For an idea of the magnitude of this number, it is roughly 100 times greater than all the grains of rice consumed annually by the people of planet Earth. This astonishing fact about the fundamental building block of all electronic devices is buried deep within The Quantum Universe, the latest book from Brian Cox and Jeff Forshaw.The very first transistor computer built in 1953 had just 92 transistors, but today more than 100,000 can be bought for the cost of a single grain of rice and there are around a billion of them in a mobile phone. It is easy to see why Cox and Forshaw believe the invention of this device was “the most important application of quantum theory”, while the theory itself is “the prime example of the infinitely esoteric becoming the profoundly useful”.

It is esoteric because the theory describes a reality in which a particle can be in several places at once and moves from one place to another by exploring the entire universe simultaneously. The American physicist Richard Feynman unveiled a piece on the quantum universe, but nevertheless cautioned: “I think I can safely say that nobody understands quantum mechanics. Do not keep asking yourself, if you can possibly avoid it, ‘But how can it be like that?’ Nobody knows how it can be like that.”

Heeding this advice and sticking to the maxim that “following the rules is far simpler than trying to visualise what they actually mean”, Cox and Forshaw set out to “demystify quantum theory”. If they do not entirely succeed, it says more about the size of the task they have set themselves than its execution. The word “quantum”, they warn at the outset, is at “once evocative, bewildering and fascinating”. Having written a narrative history myself with that one word as a title, I know exactly what they mean.

Peppered with diagrams and equations, The Quantum Universe is not an easy read. We encounter Planck's constant (nature’s own axe for chopping up energy and much else besides); the principle of least action; the wave function; the uncertainty principle; electron standing waves; the exclusion principle; semiconductors; Feynman diagrams; quantum electrodynamics; the Higgs boson and the standard model of particle physics. The reader is made to work along the way and for those prepared to do so there is much to learn. Why, for example, empty space isn’t empty but is a seething maelstrom of subatomic particles.

While they sidestep the question of its interpretation and the decades-long debate between Albert Einstein, Niels Bohr and others, for Cox and Forshaw there is no better demonstration of the power of the scientific method than quantum mechanics. Nobody could have come up with the theory without the aid of detailed experiments, and the physicists who came up with it were forced to suspend and then discard their previously held beliefs to explain the evidence that confronted them. In an attempt to convince any sceptical readers about the power of quantum mechanics, the authors turn to the death of stars and the Chandrasekhar limit as they champion curiosity-driven research.

The sun is a gaseous mix of protons, neutrons, electrons and photons with the volume of a million earths that is slowly collapsing under its own gravity. This compression heats the core to such temperatures that protons fuse together to form helium nuclei. The fusion process releases energy that increases the pressure on the outer layers of the star, thus balancing the inward pull of gravity. And so it will go on for the next five billion years until the sun runs out of material to fuse and ends up as a super dense ball of nuclear matter in a sea of electrons known as a white dwarf. It’s a fate that will befall more than 95 per cent of the stars in our galaxy. Though the highlight of the book is confined to the epilogue, Cox and Forshaw show how it’s possible to approximately calculate the largest possible mass of these stars.

The detailed and more complex calculation was originally published in 1931 by the Indian astrophysicist, and future Nobel laureate, Subrahmanyan Chandrasekhar. It led to two remarkable predictions: white dwarf stars exist and they cannot have a mass greater than 1.4 times that of the sun. Astronomers have catalogued some 10,000 white dwarves and the largest recorded mass is just under 1.4 solar masses. Depending on four of nature’s fundamental numbers – Planck’s constant, the speed of light, Newton’s gravitational constant and the mass of the proton – Chandrasekhar’s limit is a stunning triumph of the scientific method. “The eternal mystery of the world is its comprehensibility,” Einstein wrote. “The fact that it is comprehensible is a miracle.”