What is the point of a theory of everything?
(Image: Lorenzo Petrantoni)
History tells us that we will gain from the search for ultimate truth – just not what we expected
SUPERGRAVITY. Unified field theory. The ultimate theory.Theory of everything. Physicists give many names to their attempts to unify our understanding of nature under one banner. For some, it is the holy grail of their discipline, and there are few leaps of faith they will not make to reach it: that matter is made of tiny, vibrating strings; that extra dimensions of space exist beyond the three we know about; and that space and time observed closely enough are not smooth and continuous, but grainy and pixellated.
For others, the quest for a unified physics is like the hunt for the great white whale: an elusive, perhaps even non-existent, quarry. "Searching for a unification of everything today can be quite unproductive, in my opinion," says theoretical physicist Carlo Rovelli of the Centre for Theoretical Physics in Marseille, France. Helge Kragh, a historian of physics at Aarhus University in Denmark, identifies a more basic problem: even if we do find a promising candidate and our minds are equipped to fully understand it, who says it is the end of the road? "We cannot possibly know if it is the ultimate theory," he says. Meanwhile, our existing theories of nature, though far from perfect, are doing a great job in underpinning the technological innovations that improve our lives. Time to ask the question: what is the point of a theory of everything?
Unification has been a driving force in physics since at least the days of Newton. To the casual skywatcher of the 1660s, there was great mystery in the motion of celestial bodies. Why did some lights in the sky stay fixed, night after night, while others wandered across the darkness? Newton, studying at his home in a remote part of Lincolnshire during the Great Plague, had an idea. The force that causes planets and stars to move is the same one that causes objects on Earth to fall to the ground – a universal force between two bodies that depends only on their mass and the distance between them. Understand that, and it becomes clear how the planets near to Earth are pulled across the sky at different rates by the sun's gravity, while distant stars remain fixed relative to one another.
Newton's insight unified heavenly and Earthly realms previously considered irreconcilable. His neat set of universally valid equations carved a template for future generations of physicists, while allowing engineers to calculate the forces and torques that made possible the engines of the Industrial Revolution.
Wind forward 200 years, and James Clerk Maxwell performed a similarly revolutionary act of unification. In the 1860s, he showed that electricity and magnetism are two facets of the same force, electromagnetism. Maxwell's unifying set of equations also showed that light is a form of electromagnetic radiation, an insight that switched on the electric age in which we now live, enabling everything from radio broadcasts to smartphones.
Unity is strength
Today's theories of everything aim to continue on that path. We now think all physical phenomena can be explained by the action of four fundamental forces. There's gravity, the attractive force between objects with mass that Newton described, and Maxwell's electromagnetism, the interaction between bodies with electric charge. Electromagnetism is responsible for "contact" forces – for example, why despite gravity you don't fall through that chair you're sitting in. Two other forces regulate things on the subatomic scale: the strong nuclear force keeps protons and neutrons together in an atom's nucleus, while the weak nuclear force governs things like radioactive decay. A theory of everything would show that these four forces are really just the same thing in disguise.
In 1967, a century after Maxwell, theorists Steven Weinberg, Abdus Salam and Sheldon Glashow made a first step towards that goal. They showed that, under the highly energetic conditions last seen in the universe's first trillionth of a second, the electromagnetic and weak nuclear forces combine to form the electroweak force. Although no one has yet convincingly unified the strong nuclear force with the electroweak, the two play together nicely in the form of the standard model, which explains how fundamental particles from quarks to the Higgs boson interact.
Gravity, however, remains a problem child. Today, our best understanding of the force is given by Einstein's general theory of relativity. This replaced Newton's theory, and explains how mass warps space and time to produce gravity. But general relativity requires a smooth space-time at odds with the probabilistic roughness required by quantum forces such as the electroweak and strong nuclear forces. The result is one set of equations for very small phenomena, like particle interactions, and another for very large things, like stars and galaxies.
So what happens when big meets small? "There is only one nature, so presumably it forms a coherent whole," says Matt Strassler of Harvard University. "Surely there will be situations where you have to apply both sets of equations at the same time, and then you're going to run into contradictions."
Take black holes, which at their heart have the mass of a star compressed into a minuscule space. Or the conditions right at time's beginning, when all the universe's mass and energy was concentrated into the tiniest of pinpricks. Which theory, the large or the small one, governs their behaviour?
Then again, why should we care? Unlike Newton's unifying laws of motion, or Maxwell's electromagnetism, further bouts of unification seem unlikely to revolutionise our technology any time soon. Newton's and Maxwell's theories are valid in the conditions of our everyday world, but the four forces can only be unified at energies roughly a quadrillion times those generated in collisions at theLarge Hadron Collider near Geneva, Switzerland, says Michio Kaku, a physicist and futurist at the City College of New York. It will probably be 100,000 years before we are able to build particle accelerators large enough to reach the necessary energy, Kaku reckons – and we would need infrastructure on the scale of the entire solar system to do it.
If future humans were ever to generate and control energy on that scale, they would no doubt create a wealth of new technological possibilities. "They may begin to play with space and time," says Kaku. We might, for example, unlock wormholes that would allow us to pass between distant regions of space-time. These hypothetical objects are thought to start out as tiny quantum fluctuations in the fabric of space-time, and are prone to snap shut as unpredictably as they appear. Understanding how to prop them open to a useful size requires a theory that straddles the bubbly quantum physics of the very small to the smooth, large-scale realm of general relativity. "For that, you need a theory of everything," says Kaku.
Time travel 100,000 years down the line seems a hard sell for an enterprise that costs money in the present. But it is wrong to judge the pursuit of a theory of everything purely in terms of obvious technological gain, says Peter Woit, a mathematical physicist at Columbia University in New York. If history is any guide, there's a good chance further unification will lead us to new places, and they won't necessarily be the ones we expected. "When we've found these things in the past that have worked, they've actually been intellectually very compelling. There's been some kind of unexpected insight or new idea that once you see it, all of a sudden explains a lot that you didn't understand before."
Despite his scepticism, Kragh agrees. "An ultimate theory of everything is an empty label," he says. "Nonetheless, the search for a theory of this kind can lead to new scientific insight."
To formalise his theories about gravity and motion, for example, Newton invented a mathematical technique for dealing with smoothly changing quantities such as speed. Calculus went on to revolutionise almost all fields of science, from biology to economics. Streaming that cute cat video to your phone would be unthinkable, for example, without the Fourier transform, which uses calculus to break apart any signal into simple sine waves, allowing audio and video files to be compressed to a transferable size.
Then there's what Einstein pulled out of Maxwell's equations. For mathematical consistency, these equations need a constant number for the speed of light that does not depend on the motion of whoever is measuring it. This led Einstein to a deeper truth: that the universe simply is so, and that space and time must bend to accommodate light's always-constant speed. "When Maxwell found that organising principle, Einstein saw a deeper understanding of how space and time themselves are linked," says Leo Stein, an astrophysicist at Cornell University in Ithaca, New York.
And so it went on. Near the end of the 1920s, Paul Dirac sought to reconcile Einstein's special theory of relativity with the still-young theory of quantum mechanics. His equations suggested that the electron should have a counterpart of the same mass but opposite electric charge – a positron. Dirac thought that was a mistake, but experiments soon revealed that such antimatter particles do exist. This surprising fundamental aspect of reality has practical applications today, such as the positron emission tomography (PET) scanners found in many hospitals. "You aim at one thing, and that causes other people to aim at another thing as a consequence, and then all kinds of serendipitous things happen instead," says Strassler.
So what of today's search for a theory of everything? Most hopes are pinned on one contender. "I regard string theory as the only serious candidate for being a framework for a theory of everything," says John Ellis, a theoretical physicist at King's College London.
String theory itself started out as something different. In the late 1960s, physicists trying to explain the strong nuclear force suggested that the particles involved could be better understood not as infinitesimally small points in space, but as strings that vibrate in different ways. Eventually, other approaches proved more fruitful in describing the strong force, but the mathematics seemed too elegant to discard. Throughout the 1970s and 1980s, the idea grew that string theory might work instead as a theory of quantum gravity, bridging the chasm between the physics of the very small and very large.
Except it hasn't. "We're certainly a long way away from having a definitive experimental signature that will give us a yes or no answer to whether string theory has anything to do with nature," says Ellis.
So what is its point? Perhaps what history tells us: not what we thought. In the late 1990s, theoristJuan Maldacena, then at Harvard University, was trying to find a quantum description of black holes by studying D-branes, massive multidimensional relatives of strings. He saw that the behaviour of D-branes could be described in two separate, but equivalent ways. One was through a variant of string theory that includes gravity and needs 10 dimensions to work. The other was a relatively mundane four-dimensional quantum theory without gravity, similar to the theories that underpin the standard model. The beauty was that, if something was too difficult to calculate using a quantum field theory, Maldacena's mathematical trick, called the AdS/CFT correspondence, allowed you to convert it into a different, relatively easier calculation in an alternative version of space.
In the past few years, Sean Hartnoll, a physicist at Stanford University, and his colleagues have shown that, bizarrely, our understanding of high-temperature superconductors might benefit from this approach. Superconductors conduct electricity without electrical resistance, but generally need extreme cold – the kind provided by liquid helium or liquid nitrogen – to operate, making them useful in only a narrow range of applications, such as the magnets in MRI scanners and maglev trains. A few "high-temperature" superconductors work at milder temperatures, but the details of how they function remain a mystery, impeding the development of better ones.
It turns out that certain aspects of the behaviour of these superconductors are much easier to capture using the mathematics of string theory. For example, under the right conditions, high-temperature superconductors conduct electricity in one direction while blocking it at right angles. Hartnoll and his colleagues have used Maldacena's correspondence to develop a "holographic strange metal" model that succeeds where other more conventional theories fail. "The holographic strange metal can capture this aspect of high-temperature superconductors that is difficult to capture otherwise," says Hartnoll (Nature Physics, DOI: 10.1038/nphys2701).
In the meantime, Maldacena's shortcut has been used to reveal that, essentially, every state of matter matches up with a gravitational scenario that can be described using the mathematics of string theory. Superconductors can be understood as stars made of charged particles and the recently discovered Higgs bosons. Classical liquids can be modelled using the mathematics of black holes that do not spin and have no electric charge. Such insights have "placed string theory research nearer to the centre of research in theoretical physics", says Shiraz Minwalla, a researcher at the Tata Institute of Fundamental Research in Mumbai, India.
There is a long list of outstanding questions in physics. Why is the mass of the Higgs boson so small? Why doneutrinos have mass at all? What is dark matter? What is dark energy? An ultimate theory might reveal all the answers, or none. But it is just as likely to deliver answers to questions we never asked of it in the first place.
Reason enough not to give up on that ultimate goal, says Nathan Seiberg of the Institute for Advanced Study in Princeton, New Jersey. "I think we are just continuing in the same direction, trying to understand better and maybe ultimately completely understanding the underlying principles of nature," he says. "We have made a lot of progress over the past few centuries and I see no reason to believe that progress will end now."
This article appeared in print under the headline "All or nothing?"
MacGregor Campbell is a New Scientist consultant based in Portland, Oregon