"A desk or table, a chair, paper and pencils”, was what Albert Einstein asked for in 1933 when he took up his new job 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 he knew he had earned the right to make them as he searched for his holy grail – a unified field theory.
In this fascinating and elegantly written book, science writer Graham Farmelo explains that Einstein was seeking an ambitious new schema that united electromagnetism and general relativity, his theory of gravity, using only his imagination and mathematics. It was a project that left him increasingly out of step with younger colleagues who were busy exploring the new vistas of particle and nuclear physics opened up by experiments that eventually led, in the 1970s, to the so-called Standard Model that describes quarks, gluons, neutrinos and all the other particles and forces that act between them. A riveting account of how physics has stimulated mathematical breakthroughs and mathematics led to advances in physics Einstein might have failed but there were precedents for his attempt to unite what appear to be disparate phenomena. One was Isaac Newton’s demonstration that the force that pulls an apple to the ground also keeps the planets in their orbits. Another was James Clerk Maxwell’s astonishing discovery, in 1864, that just as ice, water and steam are different states of the molecule H2O, so electricity, magnetism and light were different aspects of the same underlying phenomenon – electromagnetism. Since the 1980s, as Farmelo explains, Einstein’s mathematical approach has been embraced by many of the world’s leading theoretical physicists in the pursuit of a “theory of everything”. Superstrings is that theory and, as hard as it might be to envisage, particles previously thought of as tiny points are, in fact, not points at all but little oscillating bits of “string”, which move through space. The different levels of “vibration” of these strings require a mind-numbing 10 dimensions and correspond to the different particles. As theorists delved deeper it turned out there were actually five different string theories. Fortunately, one of the smartest physicists on the planet, Ed Witten, discovered that all five were just different descriptions of something more fundamental that he mischievously called “M-theory”. Some say M stands for magic, others mystery. Not everyone was happy. Sheldon Glashow, a Nobel prize-winning theorist, described superstring theory as a “new version of medieval theology” because it couldn’t be put to the test. Its proponents justified their creation, however, by pointing to its elegance, coherence and beauty. “It is more important to have beauty in one’s equations than to have them fit experiment,” argued the British physicist Paul Dirac. In 1928, he came up with an equation that predicted the existence of antimatter: it was the first time something never before seen in nature was “predicted”, postulated to exist based on theoretical argument rather than experimental evidence. In the past, experiments played a vital role in developing theory and vice versa. For some time now that back-and-forth has not existed in certain fields where experiments are barely managing to test theories developed over decades. Wherever experimental data can be coaxed out of nature, it suffices to corroborate or refute a theory and serves as the sole arbiter of validity. But where evidence is spare or absent – as it is for a growing number of questions in physics – other criteria, including aesthetic ones, have been allowed to come into play both in formulating a theory and evaluating it. Unsurprisingly from the author of The Strangest Man, an award-winning biography of Dirac, Farmelo has offered a thoughtful, well-informed reply to those who believe the quest for mathematical beauty has led theoretical physicists into adopting sterile, ultra-mathematical approaches divorced from reality. He makes a persuasive case as he argues that theorists have not spent the last 40 years wasting their time writing quasi-scientific fairytales and that many of the ideas and concepts that have emerged will endure. Most of this is not conventional science, Farmelo admits. Rather, it is speculative science. But it is science nonetheless because it’s rooted in the two great theories of the 20th century: quantum mechanics and relativity. At the heart of this book is an account of how physics has stimulated mathematical breakthroughs and maths has led to advances in physics. It was this interplay between the two that led to an understanding of how the extra dimensions of superstrings are “compactified”, curled up, into what’s called Calabi-Yau space. Many of the acclaimed advances in modern fundamental theoretical physics have yielded no predictions that can be tested in the near future. But that is no reason to despair. Galileo said: “Nature’s great book is written in mathematical symbols.” It would be foolhardy not to read it. • The Universe Speaks in Numbers: How Modern Maths Reveals Nature’s Deepest Secrets, by Graham Farmelo, is published by Faber (RRP £20) To order a copy go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.