by Marcus Chown
What is striking about the Standard Model is that so few ingredients interacting in so few ways generate so much of what we see all around us. As Gottfried Leibniz, the seventeenth-century German mathematician, so presciently observed: ‘God has chosen the most perfect world – that is, the one which is the most simple in hypotheses and the most rich in phenomena.’12
Remarkably, our physicist, locked in a windowless room with nothing more than a blackboard and chalk, is able to deduce the main features of the world. ‘Physics is shockingly constrained by quantum theory and relativity,’ says Arkani-Hamed. ‘They almost make the Universe inevitable.’
Almost. The twin constraints do not determine the masses of the fundamental particles nor the total number of quarks and leptons. All normal matter is assembled from just four particles – the up-quark, down-quark, electron and electron-neutrino. (A proton in an atomic nucleus, for instance, is made of two up-quarks and a down-quark, and a neutron two down-quarks and an up-quark.) But nature has not stopped here. It has created heavier versions of the basic four particles – the strange quark, charmed quark, muon and muon-neutrino – and heavier-still versions – the bottom quark and top quark, tau and tau-neutrino. Such particles play essentially no role in the Universe today since the energy to create them existed only in the first split-second of the big bang. To paraphrase the American physicist I. I. Raby: ‘Who ordered them?’13
The Standard Model does not reveal why nature has triplicated its basic building blocks – or why it has given the fundamental particles the masses they have. It is a strong indication that it is not the final word on nature but merely an approximation of a deeper theory, yet to be found. But these shortcomings should not detract from the fact that the principles of special relativity and quantum theory are so tight a constraint on the possible that they determine pretty much everything about the physical world. ‘What really interests me is whether God had any choice in the creation of the World,’ said Einstein. The lesson of special relativity and quantum theory appears to be that He did not.
As mentioned at the outset of this chapter, some people claim that theoretical physicists are fantasists who spend their time imagining all sorts of weird and wonderful things which are so impossibly beyond the reach of experimental test that they can never be proved wrong. But the fact that special relativity and quantum theory pretty much uniquely determine the Universe around us can mean only one thing: they are largely correct. This, in turn, means they are a severe straitjacket on any deeper theory invented by physicists. So little wriggle room is there that finding theories that fit inside is extremely difficult. ‘Almost everything you try fails,’ says Arkani-Hamed. ‘The overwhelming majority of theories that physicists can imagine are killed at birth.’
In fact, in 2017, there is only one candidate for a deeper theory that satisfies the constraints of both special relativity and quantum theory: ‘string theory’.14
A wonderful thing is a piece of string
String theory – also known as superstring theory – arose out of attempts to understand nature’s strong nuclear force. The force is not called strong for nothing. So much energy must be put into pulling apart a pair of quarks that, in the space between them, it spontaneously creates a quark-antiquark pair. Think of trying to reach a friend in a crowd as other people constantly and annoyingly insert themselves between you. This is the way it is for quarks. The strong nuclear force imprisons quarks within the protons and neutrons of atomic nuclei and makes it impossible to isolate a lone quark.15
The strong nuclear force is also weird in that its attraction gets stronger the further apart are two quarks. Contrast this with a familiar force such as gravity, which weakens the greater the separation of two masses; or magnetism, which weakens the greater the separation of two magnets. The reason that these forces become diluted is that they leak out in all directions.16 But if a force is instead confined to a narrow channel between two bodies, it can strengthen the further apart they are pulled. This is the case for the force in a stretched spring or an elastic band.17 And it is also the case for the strong nuclear force between two quarks. This behaviour was the first indication that the fundamental building blocks of the Universe, instead of being pointlike subatomic particles, may actually be tiny one-dimensional strings of energy.
In the rudimentary theory pioneered by Italian physicist Gabriele Veneziano in 1968, such entities vibrate much like violin strings, and each possible vibration corresponds to a different fundamental particle.18 ‘In essence, string theory describes space and time, matter and energy, gravity and light, indeed all of God’s creation . . . as music,’ says writer Roy H. Williams.19
In the way that a rapidly vibrating violin string is more energetic than a sluggishly vibrating violin string, a rapidly vibrating string corresponds to a subatomic particle with a lot of mass-energy, such as a top quark, while a sluggishly vibrating string corresponds to a particle with not much mass-energy, such as an electron. But, because of the complexity of the mathematics, physicists cannot yet be sure that all the possible vibrations of strings can account for all the known fundamental particles.
Strings can either be open-ended, or closed to form a loop. Whether a string is open or closed determines the way in which it interacts with other strings.
String theory automatically includes an integer spin (matter) partner for every half-integer (force-carrier), and vice versa. It is because the theory therefore incorporates supersymmetry that it is called ‘superstring’ theory and the strings are referred to as ‘superstrings’. As mentioned before, none of the superpartners of the known particles has been found, though string theorists maintain they are simply too massive to have been created at the LHC.
String theory resolves a potential conflict between two powerful ideas in physics. ‘Reductionism’ is the idea that the phenomena of the world are the result of the interaction of a handful of fundamental building blocks. In the Standard Model, those building blocks are quarks and leptons. ‘Unification’ is the belief that disparate phenomena of nature are in fact facets of a single, more fundamental phenomenon. Electric and magnetic fields, for instance, are merely aspects of the ‘unified’ electromagnetic field.
Reductionism, taken to its logical conclusion, is expected to reveal the world to be built out of a single type of building block. But, if such a building block is truly fundamental – that is, composed of no internal parts that can be rearranged — how can it have different faces? The answer is it cannot if it is a pointlike particle. It can, however, if instead it is a one-dimensional string, capable of a multitude of different vibrational modes. Thus strings neatly avoid the conflict between unification and reductionism.
Fundamental particles not only have distinct masses – which can be mimicked by the vibration rate of a string – they also interact via fundamental forces. In 1915, Einstein showed that the ‘force’ of gravity is nothing more than a manifestation of the warpage of four-dimensional space-time. In the 1920s, two physicists took Einstein’s idea a step further. Independently of each other, Theodor Kaluza and Oskar Klein showed that if there exists another space dimension, making space-time fivedimensional, the force of gravity and electromagnetism can both be consequences of the curvature of space-time. Such an extra space dimension is not obvious. But it might have gone unnoticed, claimed the two physicists, if instead of being a big dimension like north-south, east-west and up-down, it is curled up smaller than an atom.
In Kaluza and Klein’s scheme, a subatomic particle, even when at rest in normal space, is whirling ceaselessly round and round in the extra dimension like a demented hamster in a wheel. In fact, momentum in the extra dimension is electric charge. And the reason electric charge comes in multiples of a basic chunk, or is ‘quantised’, is that particles behave as waves, and the only waves permitted are those with a wavelength that fits around the circumference of the extra dimension once, twice, three times and so on. Such waves necessarily have a momentum (charge) that is a multiple of the momentum
(charge) of the longest permitted wave.
In the 1920s, when Kaluza and Klein proposed their idea, nature’s strong nuclear force and weak nuclear force, which hold sway only in the ultra-tiny domain of the atomic nucleus, had yet to be discovered. But it is perfectly possible to mimic the behaviour of these extra forces using yet more extra space dimensions, each rolled up so small they are unnoticeable. In fact, a total of six extra space dimensions are required. The hypothetical strings of modern string theory consequently quiver in ten-dimensional space-time – nine dimensions of space and one of time.
‘Einstein comes along and says, “Well space and time can warp and curve – that’s what gravity is,”’ says physicist and popular science writer Brian Greene of Columbia University in New York. ‘And now, string theory comes along and says, “Yes, gravity, quantum mechanics, electromagnetism all together in one package, but only if the Universe has more dimensions than the ones that we see.’”20
‘At first people didn’t like extra dimensions,’ says string theorist Edward Witten of the Institute for Advanced Study in Princeton, ‘but they’ve got a big benefit. The ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions.’
The pros and cons of string theory
A theory which maintains that space-time is ten-dimensional is seriously in conflict with the fact we appear to live in a threedimensional reality (four-dimensional if you count time). But the theory has other problems as well. For a start, the strings are postulated to be mind-bogglingly tiny – equivalent to the Planck length, which is 10-35 metres, or a million billion times smaller than a hydrogen atom. Consequently, even the most violent particle collisions at the LHC have a million billion times too little energy to directly probe the world of strings. And because the strings exist at an energy scale and size scale so far removed from the everyday realm, they produce no noticeable imprint on the familiar world. So not only are strings inaccessible to terrestrial experiments, their existence leads to no testable predictions. ‘It is wonderful that both the Standard Model and general relativity come out of string theory,’ says David Tong. ‘But, really, what physicists would like to come out is something unpredictable.’
String theory also requires nature to use supersymmetry. As the LHC explores ever higher energy regimes, there are fewer and fewer places for supersymmetric particles to hide. If they do not come to light soon, the theory could be dead in the water. String theory is a beautiful mathematical structure, something which even its critics accept. But there are many equally beautiful ideas which nature, in its wisdom, has chosen not to implement.
Yet another problem with string theory is that there are a huge number of ways in which the extra dimensions can be intertwined. According to some estimates, this leads to at least 10500 distinct ‘string vacua’, in each of which the numbers and masses of fundamental particles are different, and even the number of fundamental forces and their respective strengths. Physicists had imagined that, because special relativity and quantum theory are so very hard to unite, any framework that united them would be unique, predicting the observed properties of the fundamental particles and fundamental forces. ‘This idea was wrong,’ says Arkani-Hamed.
Instead, physicists have found a mind-bogglingly large number of ‘solutions’ of string theory, all of which are compatible with special relativity and quantum theory. In fact, string theory has been called ‘a bunch of solutions in search of a theory’. This is by no means unprecedented in physics. For instance, there are an infinite number of possible electromagnetic waves, each with a distinctly different wavelength. All are solutions of Maxwell’s equations of electromagnetism. Then there are hydrogen atoms and tables and you, at this moment, reading these words. All are solutions of the Schrödinger equation.
The big question is: what is the underlying theory to which the 10500 string vacua are the solutions?
At one time, string theorists were exploring five distinctly different variations of string theory, which went by the name of Type I, Type II, Type IIb, Heterotic O (32) and Heterotic Eg × E8. But, in the mid-1990s, Paul Townsend of the University of Cambridge and Chris Hull of Queen Mary College, London, showed that all five are merely different ways in which supersymmetry is realised – different versions of a single eleven-dimensional theory. ‘M-Theory’ was named by Edward Witten but he has never stated what the ‘М’ stands for. ‘Eleven-dimensional M-theory is the umbrella theory,’ says David Berman of Queen Mary University in London.
The 10500 string solutions are solutions of M-Theory. Collectively, they look a lot like an ensemble of universes, or a ‘multi-verse’, except that they are probably all connected to each other. Science-fiction writer Arthur C. Clarke could have been writing about string vacua when he wrote: ‘Many and strange are the universes that drift like bubbles in the foam upon the River of Time.’21
Physicists would have preferred a theory that predicts the precise properties of the fundamental particles and fundamental forces. Instead, they must answer the question: why are we in the string vacuum we are in and not any of the 1-followed-by-500-zeroes others? ‘We don’t know yet,’ says Arkani-Hamed.
One way would be to count how many universes there are with each possible value of the electron mass, with each possible strength of the electromagnetic force, and so on. The most common universes should be ones whose subatomic particles have masses very close to ours and whose fundamental forces have strengths very close to ours. If we discover that we live in a very special and unusual Universe then that would be inexplicable and string theory would be dealt a serious blow. ‘The problem is no one can think how to count up universes,’ says Arkani-Hamed.
Berman is not unduly worried by this. ‘It is too early to be discouraged yet in our exploration of the mathematical structure of string theory,’ he says. ‘We are still a long way from real physics.’
Despite all the difficulties with string theory, however, it boasts a number of compelling features, which keep a large global community of physicists not only interested but positively enthusiastic about it. Most importantly, the theory contains a vibrating loop of string of spin 2. A particle of spin 2, as mentioned before, is the recipe for the graviton, the carrier of the gravitational force. Not only that but an unavoidable consequence of the existence of a spin 2 particle is the general theory of relativity. As already mentioned, the Holy Grail of physics is the uniting of quantum theory and Einstein’s theory of gravity. It is fantastically appealing that string theory is a quantum theory that automatically incorporates the general theory of relativity.
But, to Berman, it is its richness that makes string theory compelling, not just the fact it contains a quantum theory of gravity. He compares string theory with Newton’s theory of gravity. ‘It explained not just one thing but many things – the motion of planets, the ocean tides, the precession of the equinoxes, and so on – and it gave physicists things to work on effectively for ever,’ says Berman. ‘Similarly, we are far from finished exploring string theory. It can run and run.’
Until 1985, string theory languished in a backwater of physics, pursued by only a handful of aficionados who were convinced of its promise. Everything changed when John Schwarz of the California Institute of Technology in Pasadena and Mike Green of Queen Mary College in London made a breakthrough.
Physics contains many symmetries — aspects of a situation that remain the same when something else is changed, in much the same way that a square continues to look like a square if rotated by a quarter of a turn, half a turn, and so on. In 1918, the German mathematician Emmy Noether made the remarkable discovery that symmetries underpin many of the great laws of physics. Take the law of conservation of energy, which says that energy cannot be created or destroyed, merely morphed from one form into another. This is a consequence of ‘time-translational symmetry’, the fact that, if a particular experiment is done next week or next month or next year, the outcome, all thin
gs being equal, will be exactly the same.
Noether’s recognition that symmetry underlies the laws of physics is one of the most powerful ideas in modern physics and the reason why physicists at the LHC hunt for symmetries as indicators of new fundamental laws. Many theories, when quantised do not preserve classical symmetries such as the key ‘Lor-entz symmetry’ of Einstein’s special theory of relativity. Schwarz and Green discovered that string theory does. In the jargon, it is ‘anomaly free’. ‘All the symmetries of classical physics automatically apply,’ says Berman. ‘Miraculously, string theory is compatible with everything we already know to be true.’
Schwarz and Green’s discovery triggered the ‘first string revolution’, which saw string theory transformed from a niche research area into a mainstream field of enquiry. The ‘second string revolution’ was the realisation that string theories are versions of M-Theory, and that, ironically, the most important things in string theory are not strings.
Brane power
The three-dimensional everyday world contains not only one-dimensional objects such as lengths of cotton but twodimensional objects such as table-tops and three-dimensional objects such as trees and people. By analogy, the M-Theory Universe of ten space dimensions may contain not only onedimensional strings but objects with two dimensions, three dimensions, and so on . . . all the way up to ten dimensions. Collectively, physicists refer to these multi-dimensional entities as ‘branes’, more colourfully christened ‘p-branes’ by Townsend, where the p refers to the number of space dimensions. A string, in this terminology, is a 1-brane.
In M-Theory, it turns out that branes are not only possible, but required. And this proliferation of multi-dimensional objects means the theory is unlikely to be one in which strings play a fundamental role. It appears instead that a large ensemble of objects is needed to unite special relativity and quantum theory. ‘In some domains of the theory, particle phenomena will manifest themselves, in others string phenomena, in still others the phenomena of 2-branes, 3-branes, and so on,’ explains Arkani-Hamed.
