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February 6, 2023

Killing Time
On the quest for a theory of quantum gravity, Edward Anderson must slay the "dragon" of time.
by Kate Becker
FQXi Awardees: Edward Anderson
June 27, 2012
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Taking Time Out
Can Anderson find equations for a timeless universe?
Edward Anderson is on a quest: one complete with dragons, weapons, and of course a holy grail. For Anderson, of Paris Diderot University, France, as for many other theoretical physicists, that grail is the unification of general relativity and quantum mechanics. To reach it, he’ll have to defeat the dragon—and the dragon, Anderson believes, is time.

Time used to be straightforward. To Isaac Newton, time was an absolute, like the tick-tocking of a great cosmic clock. In his theory of general relativity, though, Einstein threw out that cosmic clock and replaced it with a new and pliable notion of time. To Einstein, time could speed up or slow down, and—so long as "cause" and "effect" remained in the right order—no single experience of time was any more correct than any other.

In the early 20th century, while Einstein was busy dismantling Newton’s clockwork, quantum theorists were tearing apart an even more basic Newtonian notion: that the laws of physics can perfectly predict how the universe will unfold. If "the universe" sounds too grand, consider a much smaller slice of it—say, an apple falling from a tree. Applying his law of gravity and his equations of motion, Newton believed that he could completely describe what would happen to the apple as it plopped down onto the ground (or onto his head).

In quantum mechanics, though, physicists accept that fundamental uncertainties are tucked inside every atom in every molecule in every apple. Even with the best information and the best equations, we can’t predict with 100 per cent certainty what will happen to the apple. It might hit Newton on the head, but there’s also a tiny probability that it could dive straight through the Earth and emerge at the feet of a startled kangaroo in Australia. Because randomness lies at the heart of quantum theory, we can’t promise any particular outcome.

Yet for all this strangeness, quantum theory held on to a thoroughly Newtonian picture of time—"The same one Einstein wanted to get rid of," says Anderson. "General relativity and quantum theory developed at almost the same moment, but they moved in different directions away from Newton," Anderson points out. So while general relativity offered a new and plastic version of time, quantum mechanics adhered to the old standard.

The conflict between the two theories goes beyond time. In situations when both sets of rules should apply—like at the heart of a black hole or in the very early universe—their equations break down and spit out nonsense answers. "Both are very successful theories in their own arena," says Anderson—general relativity in the domain of large-density objects with strong gravitational fields, like neutron stars and black holes, and quantum mechanics in the realm of the very small, like subatomic particles. But their fundamental disagreements leave physicists in a no-win situation: "Do you throw away the beloved axioms of general relativity, or the beloved axioms of quantum theory?"

To sidestep this dilemma, Anderson is attacking what he believes to be one crux of the conflict between general relativity and quantum theory: time. If we can solve the problem of time, says Anderson, we just might discover the path to a unified theory of everything.

Frozen Time

If time is the dragon that stands between physicists and their holy grail, the unification of quantum mechanics and general relativity, Anderson is out to become a zoologist of dragons. After all, to plan an attack on a dragon, you need to know something about what kind of dragon you’re dealing with.

The dragon metaphor, which Anderson uses in his teaching and lecturing, gives "some order to the landscape of approaches to face this problem," says physicist Carlo Rovelli, at the University of Marseille, France, who specializes in quantum gravity. "Even most theoretical physicists don’t know what the properties of time are, beyond the fact that it goes forward," adds Anderson. So he has set out to catalog the properties of his dragon, which he compares to the dragon’s breath, scales, and other attributes.

This suggests that nothing
at all happens in the universe!
- Edward Anderson
The dragon’s breath, says Anderson, is made of ice, not fire, and represents the problem of frozen time. Yoke the equations of quantum theory to those of general relativity, and you get a new equation in which time has dropped out entirely—an equation "frozen" in time. "This suggests, in apparent contradiction with everyday experience, that nothing at all happens in the universe!" writes Anderson in a recent paper. Though Anderson goes on to point out that this apparent paradox can actually be resolved (it arises only when we consider the universe as a whole, rather than focusing on the subsystems that compose our everyday experiences), most physicists balk at these impossible equations and abandon them or "set about unfreezing them," says Anderson. But killing an ice dragon requires more than just warming up its breath.

To find common ground on time, theorists often strip away some of the structure of our universe, as if they were dismantling a building part by part and piling its support beams, pipes, wiring, and drywall in a heap for examination. But this creates yet another problem—the scaly armor of Anderson’s dragon—how to reconstruct space and time as we know them from a pile of parts. Many attempts "make spaghetti" instead of spacetime, says Anderson, spitting out universes with the wrong number of dimensions.

If that spaghetti weren’t bad enough, quantum theorists also have other culinary problems to contend with. Picture spacetime as a loaf of bread, says Anderson—backing away from the dragon metaphor for a moment. Imagine slicing through it at a spot that corresponds to a specific and constant point in time. That slice represents one instant of time for the observers (say, raisins) who occupy that slice. "Given a fixed initial and final slice, classical general relativity has the striking feature that the outcome on the final slice does not care about how the slicing in between was done," says Anderson. But this essential feature is lost in the translation to quantum mechanics.

These are just three elements of the dragon’s defenses. To kill the dragon, one must crack them all—and not one by one, but in a single great blow.

Raiding the Arsenal

To do that, theorists will need more than one weapon. "It used to be the case that people would only consider one strategy," says Anderson. Now, however, physicists are beginning to see the value of combining them. Diverse strategies can "deal with each other’s problems," says Anderson. In fact, "They’re quite good friends."

Anderson has selected three weapons from this arsenal. First, he considers a world that is more like our everyday one than it is like the quantum world, where strange events—like the exceedingly unlikely apple that popped up in Australia, or the more familiar phenomenon of radioactive decay—are not allowed. As an added simplification, he considers scenarios in which the universe does not change over time. The universe does not become; it just is. Finally, instead of a ticking cosmic clock, he investigates sequences of cause-and-effect events, or histories.

The problem is to kill the
dragon with a mirror that
will show him how ugly and
absurd he is.
- Carlo Rovelli
That is not to say that Anderson studies systems entirely devoid of time. "The timelessness is at a primary level," he explains. "Such models had better end up looking like change is happening within them" or else they will never harmonize with the universe we live in. But in these systems, time is not fundamental; it emerges from deeper laws of physics.

Even with this armful of weapons, the dragon is formidable. So Anderson gives his dragon a handicap. Instead of considering the full universe, in all its complexity, Anderson works with "toy models" that contain just three or four particles.

Many of the important qualities of the problem of time can be addressed in these very simple systems, says Anderson. "It has the good fortune of having easy mathematics as well," he adds. "These calculations can be done by any smart undergraduate" and prove that it is possible to "address difficult conceptual questions using simple math."

What does time look like in a universe of three particles? "My approach follows what the astronomers did," explains Anderson. They "abstracted time from observations of the earth, moon and sun’s relative positions." Even in this simple universe, though, the problem of time is a formidable one. "It’s very difficult to defeat a dragon," says Anderson, even when that dragon is playing with a significant handicap.

Beyond the Dragon

Will defeating the dragon reveal the key to uniting quantum mechanics with general relativity? Not everyone is convinced. "Time is one of the difficult problems with joining general relativity and quantum mechanics," says Don Page, a theoretical physicist at the University of Alberta, "but I am not sure that it is at the crux." Page argues that if time emerges from deeper quantum physics, as he believes, then the dragon is the puppet of a more powerful master. Yet, he says, Anderson’s approach is useful. "I do think his work has fundamental importance, even though I do not think that even if the…picture he is building becomes completely understood, we will then have the full solution to the mysteries of quantum gravity."

Anderson agrees with Page’s points: "I don’t believe it"—time—"is the only crux. It is one such that I happen to have been working on." The dragon, it seems, may not be the only creature in the bestiary that stands between physicists and an understanding of quantum gravity.

The Dragon of Time
Anderson’s analogy relates each aspect of the problem of time to a different part of the dragon’s anatomy.
Credit: Edward Anderson
Rovelli, meanwhile, is optimistic that a peaceful solution to the dragon conundrum may be at hand. "I think that the problem is not to cut the heads of the dragon one after the other faster than their reappearing," says Rovelli, a point with which Anderson heartily agrees. "The problem is to kill the dragon with a mirror that will show him how ugly and absurd he is, so he will instantly fall down dead," Rovelli adds. (To learn more about Rovelli’s strategy for handling time, read his prize-winning FQXi essay, "Forget Time.")

"The complexity is due to our own difficulty of thinking without time," he continues. "I think that if we get rid of the prejudice that we have to find what is time at the fundamental quantum level, everything will become clear, and the dragon will vanish."

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