How to Make an Apple Pie from Scratch

by Harry Cliff

  Einstein had been catapulted to worldwide fame when his general theory of relativity had been spectacularly confirmed by measurements made during a total solar eclipse in 1919. With general relativity, Einstein had radically reimagined the concepts of space, time, and gravity, superseding the work of the man widely regarded as the greatest physicist in history, Isaac Newton. According to Einstein, space and time weren’t merely coordinates that tell you when or where an event takes place but a physical fabric that could be bent, stretched, compressed, and even set vibrating, like the elasticated surface of a trampoline. Newton had never been able to explain what gravity was, and when confronted with the question of how the Earth reaches out across empty space and pulls on the Moon, had famously written, “I feign no hypothesis.” Einstein resolved the conundrum, showing that the force of gravity is an illusion. Instead, the Earth bends spacetime around it, like a bowling ball resting on said trampoline, and the Moon merely follows the closest thing to a straight line (technically what is called a geodesic). It’s just that close to the Earth, straight lines are bent.

  General relativity was Einstein’s masterpiece, with consequences so profound that we are still grappling with them today: black holes, gravitational waves, and the whole discipline of cosmology to name just a few. But beyond its implications, the theory was exceptionally beautiful, concise in its assumptions, wide-ranging in its consequences. Einstein himself described the theory as being of “incomparable beauty.” Spurred by his success with general relativity, he now believed that an even greater, more beautiful so-called unified field theory was out there waiting to be discovered, one that would combine his own theory of gravity with the electromagnetic theory of his hero, James Clerk Maxwell.

  Working alone in his study Einstein pursued his vision with ever greater devotion. Over time, his quest led him further and further from the scientific mainstream, and he grew increasingly isolated, working alone on what many of his colleagues suspected was a fool’s errand. Einstein himself wrote that he had become “a lonely old fellow. A kind of patriarchal figure who is known chiefly because he does not wear socks*1 and is displayed on various occasions as an oddity. But in my work I am more fanatical than ever.”

  Einstein was chasing a dream that he would never see realized. He died in 1955, after having made perhaps the greatest contributions to our understanding of nature of any scientist who has ever lived, but having spent (some might say wasted) the last decades of his life on a quixotic quest for unity through beauty.

  Einstein was doomed to fail. Not only had he rejected quantum mechanics, a subject that he’d helped to found, he’d also ignored the rapid advances being made in nuclear and particle physics, including the discovery of the strong and weak forces. No unified theory that left them out had any chance of succeeding. What’s more, many of the great discoveries in both quantum field theory and general relativity still lay years in the future. The time simply was not ripe.

  Fast-forward two decades to the mid-1970s and things had changed dramatically. Charged by their success in unifying the electromagnetic and weak forces (although the actual experimental proof was still a decade away), theoretical physicists began to think big. The next logical step in the unification project was to combine the strong nuclear force with the newly unified electroweak force in what became known as a “grand unified theory.” A potential candidate was discovered by Sheldon Glashow and Howard Georgi in 1974, based on the symmetry group SU(5),*2 another one of those local symmetries that we discussed earlier. Amazingly, they found that this relatively simple symmetry not only generated the electromagnetic, weak, and strong forces, it also gave rise to the matter particles—the electron, the neutrino, and the up and down quarks—with exactly the right charges. Along with the fields of the standard model came a bunch of new force fields, but the trouble was the associated particles were predicted to have absolutely gigantic masses, around 1016 GeV, or ten thousand trillion times heavier than the proton, which with today’s technology would need a collider so big it would stretch from the Earth to Alpha Centauri.

  However, there was a way to test these grand unified theories. The new force fields that they predicted made it possible for protons to decay into antielectrons and a quark-antiquark pair known as a pion. Now the fact that there is still matter in the universe means that this must happen fantastically slowly, with an average lifetime of around a billion billion trillion years. But if you got enough protons together in one place it should be possible to catch a few of them decaying every so often. Happily, there was a fairly straightforward way to do this—dig a giant hole in the ground away from cosmic rays and sources of background radiation, fill it with a lot of water, surround it with light detectors, and wait for the occasional flicker in the dark produced by a decaying proton. In 1982–83, two such giant water tanks, one under the Kamioka Mountain (the current site of the larger Super-K experiment) in Japan and the other down an old salt mine on the shores of Lake Erie, began collecting data. However, as the years rolled by, neither of them spied a single proton decay, and before long the simplest grand unified theory discovered by Glashow and Georgi was all but ruled out.

  But just as grand unified theories were coming under pressure from proton decay experiments, a sudden fever tore through the theoretical physics world. In the autumn of 1984, a calculation by Michael Green and John Schwarz transformed what had been a relative backwater to the hot topic in theoretical physics. Forget grand unified theories; the phrase now on everyone’s lips was “string theory.”

  String theory had first been studied at the start of the 1970s as an attempt to understand the strong force that binds quarks together. It ultimately failed in that task, but as time passed it slowly morphed into something far more ambitious, a quantum theory of gravity. During the 1970s, theorists had discovered that string theory contained an object with the precise properties of the graviton, a hypothetical particle that is for gravity what the photon is for electromagnetism. However, string theory’s previous failure in describing the strong force led most theorists to treat it with skepticism, that is until the autumn of 1984. Green and Schwarz had managed to show that string theory was free of the mathematical nasties known as anomalies.*3 A theory with anomalies is a nonstarter, like a sailing ship with a dirty great hole below the waterline, so showing that string theory was anomaly-free suddenly opened up the possibility that it really could be the answer to the long-sought quantum theory of gravity.

  The autumn of 1984 was the beginning of what became known in theory folklore as the “first superstring revolution.” Theoretical physicists piled into the subject, smelling the whiff of the grand synthesis that Einstein had dreamed of. The great promise of string theory was not only as a quantum theory of gravity but as a theory of everything, a single framework that would explain all the features of the subatomic world. What’s more, there were hints that string theory might be unique, the kind of perfect final theory that Weinberg would write about in 1992 inspired by string theory’s successes over the previous ten years.

  Endless books have been written about string theory by people far more expert than I am, so if you want the full lowdown in all its mind-melting complexity then I encourage you to go read one of them*4. However, for the purposes of our story I’ll just outline the key points. At the heart of string theory is the captivating idea that if you zoomed in on a particle like an electron, you would eventually see that it wasn’t a particle but a tiny vibrating string. The string is the fundamental building block of everything, with all the different particles in nature corresponding to different ways the string can vibrate. You can think of these like notes on a guitar string: one note gives you an electron, another a quark, another a graviton. String theory turns the subatomic world into a quantum mechanical symphony.

  But this beguiling picture comes at a price. First of all, string theory only makes sense if the universe is supersymmetric, which is why i
t’s often described as “superstring theory.” However, unlike the version of supersymmetry that was introduced to stabilize the Higgs, in string theory the superparticles can have any mass you like, going all the way up to the Planck energy, and so not finding sparticles at the LHC doesn’t rule out string theory.

  The more serious price for string theory is that it only works if there are at least nine dimensions of space. This might seem like a pretty fatal flaw given that we live in a decidedly 3D world, but again this can be gotten around by hiding the six extra dimensions way, way down at the Planck length, far beyond the reach of any experiment. You might be starting to notice a theme here. Nevertheless, in its glory days of the late 1980s and early 90s, there were hopes that at some point in the future string theory would start to make predictions that could be tested in the fire of experiment.

  Over the subsequent decades those hopes have gradually waned. The problem lies in those extra dimensions. To get a string theory that makes statements about the world you first have to hide these extra dimensions through a process known as “compactification,” which more or less corresponds to screwing them up into a tiny, complicated shape, a bit like screwing up a bit of paper into a ball, except this is a piece of hyperpaper with six instead of two dimensions. Anyway, how you screw up the extra dimensions completely changes the kind of universe the theory describes, as their shape determines the different ways that the strings are allowed to vibrate, effectively changing the possible notes you can play on the strings. This in turn gives rise to universes with completely different forces and different particles.

  Physicists had hoped that there might be only one unique way of compactifying the extra dimensions, giving rise to one unique theory of the universe. Unfortunately, the number turned out to be much bigger than one. Much, much bigger. Prepare to meet the largest number you are ever likely to encounter except infinity: 10500. That’s a one with five hundred zeroes after it. I’m not going to write that out in full because my editor will kill me. It is a number so vast that if you wanted to write it down with tally marks—that is, if you wanted to scribble down 10500 lines on paper—you couldn’t do it. There aren’t enough atoms in the universe. Not by a long shot.

  This is something of a problem. Imagine you’re a string theorist and you want to see if your favorite version of string theory predicts the particles that exist in our universe. You screw up the extra dimensions in your preferred way and calculate the consequences. Oh dear, this universe had eight quarks instead of six. Never mind, though, there are still 10500–1 other string theories left to choose from. Unfortunately, even if you converted every atom in the universe into string theorists you would never be able to come close to checking all the possible different versions. To date, no one has managed to find a version of string theory that succeeds in describing the particle content of our universe, leading some to rather unkindly refer to it as “the theory of everything else.”

  Weinberg’s dream of a final theory seems to have turned into a nightmare; far from being a unique description of our universe, string theory appears to be so flexible that it’s impossible to prove wrong. Some still hold out hope that eventually a new principle will be found that shows that there are really only a small number of ways, perhaps even just one way, of screwing up the extra dimensions. However, a more common response is to accept a more limited brief for string theory.

  Someone in this camp would argue that it is unreasonable to expect string theory to predict precisely the particles that we happen to find in our universe, just as it would be unreasonable to expect Newton’s law of gravity to predict the number of planets in the solar system. Newton could beautifully describe how the planets orbit the Sun, calculate the shape of their orbits and the length of their years, but the exact structure of the solar system—two ice giants, two gas giants, and four rocky inner planets*5—is just a historical accident. We know there are hundreds of billions of stars in our galaxy, almost all of them with their own planetary systems, most of which are very different from ours.

  This sort of argument works for Newton’s law of gravity because we know there are a gigantic number of stars in the universe. However, string theory is making statements about the basic ingredients of the entire universe. For this sort of argument to hold, you need there to be multiple universes, potentially around 10500 of them, to give ours a decent chance of forming. Accept this, and the fact that we have the fundamental particles that we do is just an accident of history. Some unknown mechanism, presumably at the moment of the big bang, randomly screwed up the extra dimensions in just the right way to give rise to the world we find ourselves in. In most of the other universes the particle content and the laws of nature are completely different, and we find ourselves living in the universe we do because the conditions randomly turned out right for our form of life to evolve.

  The multiverse is a get-out-of-jail-free card. Not only does it relieve string theory of the duty to explain the universe we live in, it’s an all-purpose solution to pretty much any problem you can think of. Why is the Higgs field miraculously tuned such that atoms can exist? The multiverse. How did matter win out over antimatter in the big bang? The multiverse. Why did my mum accept the offer of a vodka and orange from my dad at a British Telecom training course in 1974? You guessed it, the multiverse.

  I’m not saying that the multiverse isn’t logically possible; if anything, the history of science suggests it could well be true. We used to think that the Earth was the center of the universe, then we realized, after a bit of arguing, that we were just one planet of several orbiting the Sun. Then our Sun got demoted to just one of a vast number of stars in the Milky Way, and finally the Milky Way turned out to be just one of billions upon billions of galaxies. Philosophically, the idea that our universe isn’t unique makes a lot of sense. It’s just that we have no way of knowing.

  We can’t disprove the existence of the multiverse, in much the same way we can’t disprove the existence of God. It’s true that the effects of other universes could show up in the sky if one happened to bump into ours, just as God could unzip the sky one day and give us a cheery wave and/or rain hellfire, depending on your religious preferences (I was brought up Church of England, so in my case he’d offer us tea and a custard cream). But just because we don’t see that happening doesn’t mean that either God or the multiverse doesn’t exist. And God as a hypothesis does an equally good job of explaining why we live in the universe we do.

  The multiverse amounts to giving up, throwing our hands in the air, and saying, “Oh, it’s all too hard.” It makes us stop looking for answers, and so, as far as I’m concerned, it isn’t worth spending more than a moment thinking about. The multiverse is boring!

  Given this rather unpalatable situation, what then is string theory good for? Well, there are many answers to that question. For one, it is a quantum theory of gravity, and probably the only one that’s been found so far. When you zoom out and look at string theory at long distances it turns into Einstein’s general theory of relativity, and when you zoom in, it looks like quantum mechanics, which is an achievement that none of its rivals can yet match. It is more than possible that string theory is the quantum theory of gravity needed to describe the moment of the big bang, and that the standard model has to be bolted on to explain particle physics. While this wouldn’t be the idealized theory of everything that many dreamed of, between them these two theories could describe more or less any situation you could care to imagine in the entire history of the universe.*6

  What is more, it is an immensely rich mathematical structure and a powerful tool. Most people working in string theory today aren’t looking for a fundamental theory of everything, or even studying quantum gravity, but are using it to make discoveries in pure mathematics, to better understand quantum field theory, and even to study the physics of solids and quark-gluon plasmas. It is this richness that makes string theory so interesting t
o the thousands of theoretical physicists and mathematicians who work in the string community. All power to them I say, and indeed to everyone pursuing other potential approaches to quantum gravity. Compared to experiments, theorists are cheap; they only really need somewhere to sit, an inexhaustible supply of paper and coffee, and a garbage can.

  However, a not altogether unjustified critique of string theory as an approach to a fundamental theory of the universe is that many of its adherents don’t worry much about the fact that it has yet to make any experimentally testable predictions. To be fair, this isn’t just a problem for string theory—it’s a problem for all quantum theories of gravity. The essence of the issue is this: quantum gravity theories, by definition, describe nature when both quantum and gravitational effects are strong, and this only happens at indescribably extreme energies and densities, those that we believe existed at the moment of the big bang.

  The Large Hadron Collider can reach energies of 14,000 GeV. However, to reach the Planck energy, where we would expect to see the effects of quantum gravity, we’d need a collider that could smash particles together with energies close to 1019 GeV, a thousand trillion times higher. How big would such a collider need to be if it worked along similar lines as the LHC? About the size of the Milky Way galaxy. Given the current funding climate, I can’t see that getting approved anytime soon.

  Trying to predict the future is a mug’s game, and who’s to say that there won’t be some incredible breakthrough in accelerator technology that might make reaching the Planck energy possible someday. But I would be happy to bet that it won’t happen this century, or even in the next. In fact, I suspect it might never be possible. If that’s right, then even if string theory does describe the physics of the moment of the big bang, we will probably never be able to test it in the lab.