A Different Kind of Theory of Everything
Physicists used to search for the smallest components of the universe. What if that’s not the point?
In 1964, during a lecture at Cornell University, the physicist Richard Feynman articulated a profound mystery about the physical world. He told his listeners to imagine two objects, each gravitationally attracted to the other. How, he asked, should we predict their movements? Feynman identified three approaches, each invoking a different belief about the world. The first approach used Newton’s law of gravity, according to which the objects exert a pull on each other. The second imagined a gravitational field extending through space, which the objects distort. The third applied the principle of least action, which holds that each object moves by following the path that takes the least energy in the least time. All three approaches produced the same, correct prediction. They were three equally useful descriptions of how gravity works.
“One of the amazing characteristics of nature is this variety of interpretational schemes,” Feynman said. What’s more, this multifariousness applies only to the true laws of nature—it doesn’t work if the laws are misstated. “If you modify the laws much, you find you can only write them in fewer ways,” Feynman said. “I always found that mysterious, and I do not know the reason why it is that the correct laws of physics are expressible in such a tremendous variety of ways. They seem to be able to get through several wickets at the same time.”
Even as physicists work to understand the material content of the universe—the properties of particles, the nature of the big bang, the origins of dark matter and dark energy—their work is shadowed by this Rashomon effect, which raises metaphysical questions about the meaning of physics and the nature of reality. Nima Arkani-Hamed, a physicist at the Institute for Advanced Study, is one of today’s leading theoreticians. “The miraculous shape-shifting property of the laws is the single most amazing thing I know about them,” he told me, this past fall. It “must be a huge clue to the nature of the ultimate truth.”
Traditionally, physicists have been reductionists. They’ve searched for a “theory of everything” that describes reality in terms of its most fundamental components. In this way of thinking, the known laws of physics are provisional, approximating an as-yet-unknown, more detailed description. A table is really a collection of atoms; atoms, upon closer inspection, reveal themselves to be clusters of protons and neutrons; each of these is, more microscopically, a trio of quarks; and quarks, in turn, are presumed to consist of something yet more fundamental. Reductionists think that they are playing a game of telephone: as the message of reality travels upward, from the microscopic to the macroscopic scale, it becomes garbled, and they must work their way downward to recover the truth. Physicists now know that gravity wrecks this naïve scheme, by shaping the universe on both large and small scales. And the Rashomon effect also suggests that reality isn’t structured in such a reductive, bottom-up way.
If anything, Feynman’s example understated the mystery of the Rashomon effect, which is actually twofold. It’s strange that, as Feynman says, there are multiple valid ways of describing so many physical phenomena. But an even stranger fact is that, when there are competing descriptions, one often turns out to be more true than the others, because it extends to a deeper or more general description of reality. Of the three ways of describing objects’ motion, for instance, the approach that turns out to be more true is the underdog: the principle of least action. In everyday reality, it’s strange to imagine that objects move by “choosing” the easiest path. (How does a falling rock know which trajectory to take before it gets going?) But, a century ago, when physicists began to make experimental observations about the strange behavior of elementary particles, only the least-action interpretation of motion proved conceptually compatible. A whole new mathematical language—quantum mechanics—had to be developed to describe particles’ probabilistic ability to play out all possibilities and take the easiest path most frequently. Of the various classical laws of motion—all workable, all useful—only the principle of least action also extends to the quantum world.
It happens again and again that, when there are many possible descriptions of a physical situation—all making equivalent predictions, yet all wildly different in premise—one will turn out to be preferable, because it extends to an underlying reality, seeming to account for more of the universe at once. And yet this new description might, in turn, have multiple formulations—and one of those alternatives may apply even more broadly. It’s as though physicists are playing a modified telephone game in which, with each whisper, the message is translated into a different language. The languages describe different scales or domains of the same reality but aren’t always related etymologically. In this modified game, the objective isn’t—or isn’t only—to seek a bedrock equation governing reality’s smallest bits. The existence of this branching, interconnected web of mathematical languages, each with its own associated picture of the world, is what needs to be understood.
This web of laws creates traps for physicists. Suppose you’re a researcher seeking to understand the universe more deeply. You may get stuck using a dead-end description—clinging to a principle that seems correct but is merely one of nature’s disguises. It’s for this reason that Paul Dirac, a British pioneer of quantum theory, stressed the importance of reformulating existing theories: it’s by finding new ways of describing known phenomena that you can escape the trap of provisional or limited belief. This was the trick that led Dirac to predict antimatter, in 1928. “It is not always so that theories which are equivalent are equally good,” he said, five decades later, “because one of them may be more suitable than the other for future developments.”
Today, various puzzles and paradoxes point to the need to reformulate the theories of modern physics in a new mathematical language. Many physicists feel trapped. They have a hunch that they need to transcend the notion that objects move and interact in space and time. Einstein’s general theory of relativity beautifully weaves space and time together into a four-dimensional fabric, known as space-time, and equates gravity with warps in that fabric. But Einstein’s theory and the space-time concept break down inside black holes and at the moment of the big bang. Space-time, in other words, may be a translation of some other description of reality that, though more abstract or unfamiliar, can have greater explanatory power.
Some researchers are attempting to wean physics off of space-time in order to pave the way toward this deeper theory. Currently, to predict how particles morph and scatter when they collide in space-time, physicists use a complicated diagrammatic scheme invented by Richard Feynman. The so-called Feynman diagrams indicate the probabilities, or “scattering amplitudes,” of different particle-collision outcomes. In 2013, Nima Arkani-Hamed and Jaroslav Trnka discovered a reformulation of scattering amplitudes that makes reference to neither space nor time. They found that the amplitudes of certain particle collisions are encoded in the volume of a jewel-like geometric object, which they dubbed the amplituhedron. Ever since, they and dozens of other researchers have been exploring this new geometric formulation of particle-scattering amplitudes, hoping that it will lead away from our everyday, space-time-bound conception to some grander explanatory structure.
Whether these researchers are on the right track or not, the web of explanations of reality exists. Perhaps the most striking thing about those explanations is that, even as each draws only a partial picture of reality, they are mathematically perfect. Take general relativity. Physicists know that Einstein’s theory is incomplete. Yet it is a spectacular artifice, with a spare, taut mathematical structure. Fiddle with the equations even a little and you lose all of its beauty and simplicity. It turns out that, if you want to discover a deeper way of explaining the universe, you can’t take the equations of the existing description and subtly deform them. Instead, you must make a jump to a totally different, equally perfect mathematical structure. What’s the point, theorists wonder, of the perfection found at every level, if it’s bound to be superseded?
It seems inconceivable that this intricate web of perfect mathematical descriptions is random or happenstance. This mystery must have an explanation. But what might such an explanation look like? One common conception of physics is that its laws are like a machine that humans are building in order to predict what will happen in the future. The “theory of everything” is like the ultimate prediction machine—a single equation from which everything follows. But this outlook ignores the existence of the many different machines, built in all manner of ingenious ways, that give us equivalent predictions.
To Arkani-Hamed, the multifariousness of the laws suggests a different conception of what physics is all about. We’re not building a machine that calculates answers, he says; instead, we’re discovering questions. Nature’s shape-shifting laws seem to be the answer to an unknown mathematical question. This is why Arkani-Hamed and his colleagues find their studies of the amplituhedron so promising. Calculating the volume of the amplituhedron is a question in geometry—one that mathematicians might have pondered, had they discovered the object first. Somehow, the answer to the question of the amplituhedron’s volume describes the behavior of particles—and that answer, in turn, can be rewritten in terms of space and time.
Arkani-Hamed now sees the ultimate goal of physics as figuring out the mathematical question from which all the answers flow. “The ascension to the tenth level of intellectual heaven,” he told me, “would be if we find the question to which the universe is the answer, and the nature of that question in and of itself explains why it was possible to describe it in so many different ways.” It’s as though physics has been turned inside out. It now appears that the answers already surround us. It’s the question we don’t know.
