A Radical Reinterpretation of Einstein’s Theory

“It is not easy to walk alone in the country without musing upon something,” Charles Dickens once observed. For Julian Barbour, those musings most often involve the nature of space and time. Barbour, 78, is an independent physicist who contemplates the cosmos from College Farm, a rustic thatched-roof country house some twenty miles north of Oxford. He is perhaps best known for his 1999 book The End of Time: The Next Revolution in Physics, in which he argues that time is an illusion.

While country walks may be best enjoyed on one’s own, musings about theoretical physics can benefit from good, smart company—and Barbour has made a point of inviting a handful of bright young physicists to join him for periodic brainstorming sessions at College Farm—think Plato’s Academy in the English countryside.

Their latest offering is something called “shape dynamics.” (If you’ve never heard of shape dynamics, that’s OK—neither have most physicists.) It could, of course, be a dead end, as most bold new ideas in physics are. Or it could be the next great revolution in our conception of the cosmos. Its supporters describe it as a new way of looking at gravity, although it could end up being quite a bit more than that. It appears to give a radical new picture of space and time—and of black holes in particular. It could even alter our view of what’s “real” in the universe.

Geodesic Sphere Triangles
The shape of an object is a real, objective quality according to the theory of shape dynamics.

Last summer, Barbour and his colleagues gathered for a workshop at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, to hash out the ideas behind shape dynamics. During a break in the workshop, I sat down with a young physicist named Sean Gryb, one of Barbour’s protégés.

“We’re trying to re-evaluate the basic assumptions of Einstein’s theory of relativity—in particular, what it has to say about gravity,” Gryb says. “It’s a shift in what we view as the fundamental elements of reality.”

Gryb, 33, is a tall and athletic figure; he’s affable and good-humored. He’s now a postdoc at Radboud University in the Netherlands, but he grew up in London, Ontario, and did his PhD down the road from Perimeter, at the University of Waterloo. The fact that he travels so much—the Netherlands, England, Canada—may explain why Gryb’s accent is so hard to pin down. “If I’m in the UK, it turns more British,” he says.

His PhD supervisor was Lee Smolin, one of Perimeter’s superstar scientists. (Perimeter isn’t a degree-granting institution, so students who work with the institute’s scientists earn their degrees from Waterloo.) Smolin, like Barbour, is known for his outside-the-box ideas; he’s the author of The Trouble With Physics and several other provocative books and has been a vocal critic of string theory, the leading contender for a theory of quantum gravity, a framework that unites Einstein’s theory of gravity, known as general relativity, with quantum mechanics. Gryb, too, seems most comfortable outside the box. Sure, he could work on problems where the questions are well defined and the strategies clearly mapped, slowly adding to what we know about the universe. There’s no shame in that; it’s what most physicists do. Instead, like Barbour and Smolin, he focuses on the very foundations of physics—space, time, gravity.

Shape, Scale, and Gravity

Let’s stick with gravity for a moment. It’s surely the most basic of nature’s forces. You drop a hammer, it falls down. Of course, there’s a bit more to it than that: Three and a half centuries ago, Isaac Newton showed that the force that pulls the hammer to the ground is the same force that keeps the moon in its orbit around the earth—a pretty impressive leap of logic, but one that Newton was able to prove with hard data and mathematical rigor.

Then we come to Einstein, who tackled gravity in his masterpiece, general relativity—a theory that’s just celebrated its 100th anniversary. Back in 1915, Einstein showed how gravity and geometry were linked, that what we imagine as the “force” of gravity can be thought of as a curvature in space and time. Ten years earlier, Einstein had shaken things up by showing that space and time are relative: What we measure with our clocks and yardsticks depends on the relative motion of us and the object being measured.

But even though space and time are relative in Einstein’s theory, scale remains absolute. A mouse and elephant can roam the cosmos, but if the elephant is bigger somewhere, it’s bigger everywhere. The elephant is “really” bigger than the mouse. In shape dynamics, though, size is relative, but the shape of objects becomes a real, objective quality. From the shape dynamics perspective, we’d say that we can only be sure that the elephant is bigger than the mouse if they’re right next to each other, and we’re there too, with our yardstick. Should either beast stray from our location, we can no longer be certain of their true sizes. Whenever they reunite, we can once again measure their relative sizes; that ratio won’t change—but again, we can only perform the measurement if we’re all next to one another. Shape, unlike size, doesn’t suffer from such uncertainty.

“Absolute size is something that seems to be built into Einstein’s theory of relativity,” says Gryb. “But it’s something that actually we don’t see. If I want to measure the length of something, I’m always comparing it against a meter stick. It’s the comparison that’s important.”

Perhaps the best way to understand what Gryb is saying is to imagine that we double the size of everything in the universe. But wait: If we double the size of everything, then we’re also doubling the size of the yardsticks—which means the actual measurements we make don’t change.

This suggests that “size” isn’t real in any absolute sense; it’s not an objective quantity. With shape dynamics, says Gryb, “we’re taking this very simple idea and trying to push it as far as we can. And what we realized—which was a surprise to me, actually—is that you can have relativity of scale and reproduce a theory of gravity which is equivalent to Einstein’s theory—but you have to abandon the notion of relative time.”

Does this mean that Einstein was wrong about time being relative? Surely we’re not heading back to Isaac Newton’s notion of absolute space and time? Gryb assures me that we’re not. “We’re not going all the way back to Newton,” Gryb says.

Foundations

Even though Newton’s conception of space and time turned out to be flawed, his ideas have continued to serve as an inspiration—or at least a jumping-off point—for countless scientists following in his footsteps. In fact, Julian Barbour tells me that his own thinking on shape dynamics began with an analysis of exactly how and why the Newtonian picture fails. Some 50 years ago, Barbour picked up a book called The Science of Mechanics by Ernst Mach, the 19th-century Austrian physicist and philosopher. In the book, Barbour found Mach’s nuanced critique of Newton’s conception of space and time. (I interviewed Barbour at length for a 2008 radio documentary called “Living on Oxford Time,” which aired on the CBC.)

Newton had imagined that space was laced with invisible grid-lines—something like the lines of latitude and longitude on a globe—that specify exactly where every object is located in the universe. Similarly, he imagined a “universal clock” that ticks away the hours, minutes, and seconds for all observers at a single, uniform rate. But Mach saw that this was wishful thinking. In real life, there are no grid lines and no universal clock.

“What happens in the real universe is that everything is moving relative to everything else,” Barbour says. It is the set of relative positions that matters. Only that, Mach concluded, can serve as a foundation for physics. Einstein, as a youngster, was deeply influenced by Mach’s thinking. Now Barbour, too, was hooked—and he’s devoted his life to expanding on Mach’s ideas.

Barbour isn’t alone. “Julian’s interpretation of Mach’s ideas are at the bedrock of what we’re doing,” Gryb says.

About 16 years ago, Barbour started collaborating with an Irish physicist, Niall Ó Murchadha. Together they struggled to work out a theory in which only angles and ratios count. Size would have no absolute meaning. (To see why angles are important, think of a triangle: As it moves through space, we can misjudge its size, but can’t misjudge the angles of its three vertices; those angles, which determine the triangle’s shape, will not change.) Ideas like these—together with a good deal of advanced mathematics—would eventually evolve into shape dynamics.

Intriguingly, shape dynamics reproduces all of the peculiar effects found in general relativity: Massive objects still warp the space around them, clocks still run more slowly in a strong gravitational field, just like in Einstein’s theory. Physicists call this a “duality”—a different mathematical description, but the same end results.

“In many ways, it’s just Einstein’s theory in a radically different description,” says Barbour. “It’s a radical reinterpretation.”

Identical, Almost

In most situations, shape dynamics predicts what Einstein’s theory predicts. “For the vast majority of physical situations, the theories are equivalent,” Gryb says. In other words, the two frameworks are almost identical—but not quite.

Imagine dividing space-time up into billions upon billions of little patches. Within each patch, shape dynamics and general relativity tell the same story, Gryb says. But glue them all together, and a new kind of structure can emerge. For a concrete example of how this can happen, think of pulling together the two ends of a long, narrow strip of paper: Do it the usual way, and you get a loop; do it with a twist and you get a Möbius strip. “If you glue all the regions together to form a kind of global picture of space and time, then that global picture might actually be different.” So while shape dynamics may recreate Einstein’s theory on a small scale, the big-picture view of space and time may be novel.

There is one kind of object where the shape dynamics picture differs starkly from the traditional view—the black hole. In the standard picture, a black hole forms when a massive star exhausts its nuclear fuel supply and collapses. If the star is large enough, nothing can stop that collapse, and the star shrinks until it’s smaller than its own event horizon—the point of no return for matter falling toward it. A black hole’s gravitation field is so intense that nothing—not even light—can escape from within the event horizon. At the black hole’s core, a singularity forms—a point where the gravitational field is infinitely strong, where space and time are infinitely curved. The unlucky astronaut who reaches this point will be spaghettified, as Stephen Hawking has put it, or burned to a crisp. Singularities don’t sit well with physicists. They’re usually seen as a sign that something is not quite right with the underlying theory.

But according to shape dynamics’ proponents, the theory does away with singularities—a definite selling point. But the picture of black holes in shape dynamics is more radical than that. “It looks like black holes—in shape dynamics—are qualitatively different from what happens in general relativity,” Gryb says.

At first, the astronaut approaching the black hole sees nothing that’s different from the Einsteinian description; outside of the event horizon, general relativity and shape dynamics give the same picture. But beyond the horizon, the story changes dramatically.

Not only is there no singularity in a shape dynamics universe, there’s no head-long rush toward the place where you’d expect it to be. In fact, an astronaut who sails past the event horizon finds herself not in a shrinking world but an expanding one. The astronaut “comes into this new region of space—which was formed effectively by the collapse of a star—and is now free to wander around in that space.” You can think of the black hole as a wormhole into that new space, Gryb says.

True, the astronaut can never exit back to the region outside the event horizon—but in this new space “he or she is free to wander around wherever they would like. And that’s a very different picture,” Gryb says. “But it’s still very early, and we’re trying to understand better what that means.”

Is it a parallel world? “I wouldn’t necessarily call it that—it’s just a pocket of space that was created by the collapse of the star,” he says. It’s “basically the region between the horizon and the surface of the collapsed star. And that region gets larger and larger as the star starts to collapse more and more.”

In other words, space—dare we say it—has been turned inside out. The region inside the event horizon, which had seemed tiny, now appears huge. What had been the surface of the collapsing star is now the “sky,” and rather than shrinking, it’s getting larger. The space inside the event horizon “is the mirror image” of the space that our traveller left behind, outside the horizon, Gryb says.

In shape dynamics, falling into a black hole seems an awful lot like falling into a rabbit hole and discovering a strange new world on the other side, just like Alice did in Wonderland. The only problem is that we can’t see down the rabbit hole. Whatever may happen within the event horizon, we have no hope of observing it from the outside. Of course, you could jump into a black hole, and see what’s there—but you could never communicate your findings to those outside.

Putting It To the Test

But Gryb is hopeful. We’ve known since the 1970s that black holes don’t stick around forever—Stephen Hawking showed that, given enough time, they evaporate by a mechanism known as Hawking radiation. “It’s possible that the story about what happens on the other side of the horizon might change the story of what happens when the black hole evaporates,” he says. “If we can make definite predictions for this, then it might provide a way to test our scenario against general relativity.”

Such tests are “just wild fantasies” at the moment, Gryb admits—but then, he notes, so are some of the predictions of other novel approaches, such as the recently-popular firewall hypothesis.

The physicists that I spoke with—the few who have been following what the shape dynamics crew have been up to—are understandably cautious. This new picture of black holes is interesting, of course, but the critical question is whether it can be tested.

“What do black holes look like in their picture?” says Astrid Eichhorn, a physicist at Imperial College London and also a visiting fellow at Perimeter. “Is it just mathematical differences? Or is there something we can really observe—for instance with the Event Horizon Telescope—where we can see a physical difference and make an observation or experiment to see which of the two [shape dynamics or general relativity] is correct?”

Eichhorn has other concerns, too. “I’m skeptical of how this will work out, both on the conceptual side and also on the technical side,” she says. “It seems that, by giving up the space-time picture, they have a lot of technical complications in formulating the theory.” Figuring out how to handle quantum effects, for example, “seems to become much more challenging in their framework than it already is in the standard approach to quantum gravity.”

Indeed, the word “quantum” rarely came up at the Perimeter workshop—although the hope is that the new framework will provide some insight into reconciling gravity and quantum theory.

Gryb, for his part, admits that the problem of unifying these two pillars of modern physics is a daunting one—perhaps as daunting in shape dynamics as it has been in earlier approaches. “We’ve made progress on trying to understand what shape dynamics might have to say about quantum gravity—but we’ve also run into a bunch of dead ends.”

Looking for Clarity

Also attending the workshop was physicist Paul Steinhardt of Princeton University, known for his work on the inflation model of the Big Bang and on alternative cosmological models. Several times during the workshop, Steinhardt would call on a speaker to be more clear, more explicit. Like Eichhorn, Steinhardt is concerned about the seeming lack of anything quantum-mechanical in the shape dynamics picture. And of course there’s the issue of falsifiability—that is, putting the theory to the test.

“My question was, what is scientifically meaningful that you expect to come out of this?” he says. “What’s different about this approach to gravity—as opposed to others—that you could test and experiment with and verify that would change our view about anything?”

The answers he got during the workshop didn’t satisfy him. “Some people said, ‘The discipline is too young, so we don’t know yet. It might bring us something new.’ And my brain is thinking, ‘OK, good—come back when you’ve got that something.’ ”

Others, meanwhile, spoke of the new ontology that shape dynamics offers. Ontology is a word that crops up frequently in the philosophy of science. It refers to the labeling of what’s “real” in a scientific theory, but it doesn’t necessarily change what you actually see when you observe nature. To Steinhardt, a change in ontology isn’t very exciting on its own. It’s just a way of describing something in a different way—a change of narrative, as it were, rather than a change in what we’d expect to see or measure. “Sometimes that’s useful,” Steinhardt says, “but it doesn’t obviously give you anything really new.”

And yet, in the history of physics—and of cosmology in particular—changes in narrative sometimes seem rather profound. Think of the change from the Earth-centered cosmos of the ancient Greeks to the sun-centered cosmos of Copernicus. They were the same observations, but a radically different “story.”

Still, Steinhardt sticks to his guns. Switching from an Earth-centered to a sun-centered description of the cosmos didn’t immediately bring any “new science.” Yes, it gave us a new story, but the new model wasn’t much better than the old one in terms of explaining the observed motion of the planets. That didn’t come until a half century later, when Johannes Kepler worked out the true shape of planetary orbits (they’re ellipses, it turns out, not circles). “I would have been skeptical of Copernicus—but I would have been really blown away by Kepler,” Steinhardt says.

A Risky Pursuit

The resistance to shape dynamics—like the skepticism that surrounds any new idea in physics—is par for the course. Science is, by its nature, a skeptical pursuit. The onus is on those who believe they’ve found something new to convince the community that they’ve really done so. In theoretical particle physics and cosmology, in particular, new ideas are always bubbling up like a tea kettle on the boil. There’s no way to read everything that gets published, so one reads only what seems genuinely promising.

For those with the necessary physics background, Flavio Mercati, a postdoc at Perimeter, has published a 67-page shape dynamics tutorial online; Gryb, meanwhile, has a short introductory essay on his Web page. There’s also a brief description of the theory in Smolin’s recent book, Time Reborn.)

Even for those who find shape dynamics compelling, it may be risky to pursue it.

Most of those working on shape dynamics are young, and shape dynamics, at least for now, lies somewhat toward the fringes of mainstream physics—which means that junior researchers are taking a risk by pursuing it.

When Mercati first expressed an interest in working with Barbour on fundamental physics, his professors tried to talk him out of it. “They said, ‘Look, I suggest you don’t,’” he recalls. “Try something more down to earth.” Because of the vagaries of the job market for academic physicists, there’s pressure to steer clear of deep, foundational issues, Mercati says. Pursue matters that are too esoteric and “you pay a price, career-wise.” Most of these researchers have yet to secure tenured academic positions—and it’s not clear if working on shape dynamics helps or hinders that quest. (At least Mercati will soon have a book to show for his efforts—the first textbook on shape dynamics, to be published by Oxford University Press.)

All of this leaves these young shape dynamics researchers poised uncomfortably on the knife-edge between excitement (a new paradigm!) and humility (we’re probably wrong).

In the end, Barbour, Gryb, Mercati, and their colleagues are taking the only route possible—they’re going where their equations lead them.

“We’re saying something totally different from what everyone else is saying,” Gryb says toward the end of our interview. “Can it possibly be right?”