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Poets often think of time as a river, a free-flowing stream that carries us from the radiant morning of birth to the golden twilight of old age. It is the span that separates the delicate bud of spring from the lush flower of summer.
Physicists think of time in somewhat more practical terms. For them, time is a means of measuring change—an endless series of instants that, strung together like beads, turn an uncertain future into the present and the present into a definite past. The very concept of time allows researchers to calculate when a comet will round the sun or how a signal traverses a silicon chip. Each step in time provides a peek at the evolution of nature’s myriad phenomena.
In other words, time is a tool. In fact, it was the first scientific tool. Time can now be sliced into slivers as thin as one ten-trillionth of a second. But what is being sliced? Unlike mass and distance, time cannot be perceived by our physical senses. We don’t see, hear, smell, touch, or taste time. And yet we somehow measure it. As a cadre of theorists attempt to extend and refine the general theory of relativity, Einstein’s momentous law of gravitation, they have a problem with time. A big problem.
“It’s a crisis,” says mathematician John Baez, of the University of California at Riverside, “and the solution may take physics in a new direction.” Not the physics of our everyday world. Stopwatches, pendulums, and hydrogen maser clocks will continue to keep track of nature quite nicely here in our low-energy earthly environs. The crisis arises when physicists attempt to merge the macrocosm—the universe on its grandest scale—with the microcosm of subatomic particles.
Under Newton, time was special. Every moment was tallied by a universal clock that stood separate and apart from the phenomenon under study. In general relativity, this is no longer true. Einstein declared that time is not absolute—no particular clock is special—and his equations describing how the gravitational force works take this into account. His law of gravity looks the same no matter what timepiece you happen to be using as your gauge. “In general relativity time is completely arbitrary,” explains theoretical physicist Christopher Isham of Imperial College in London. “The actual physical predictions that come out of general relativity don’t depend on your choice of a clock.” The predictions will be the same whether you are using a clock traveling near the speed of light or one sitting quietly at home on a shelf.
The choice of clock is still crucial, however, in other areas of physics, particularly quantum mechanics. It plays a central role in Erwin Schrödinger’s celebrated wave equation of 1926. The equation shows how a subatomic particle, whether traveling alone or circling an atom, can be thought of as a collection of waves, a wave packet that moves from point to point in space and from moment to moment in time.
According to the vision of quantum mechanics, energy and matter are cut up into discrete bits, called quanta, whose motions are jumpy and blurry. They fluctuate madly. The behavior of these particles cannot be worked out exactly, the way a rocket’s trajectory can. Using Schrödinger’s wave equation, you can only calculate the probability that a particle—a wave packet—will attain a certain position or velocity. This is a picture so different from the world of classical physics that even Einstein railed against its indeterminacy. He declared that he could never believe that God would play dice with the world.
We don’t see, hear, smell, touch, or taste time. And yet we somehow measure it.
You might say that quantum mechanics introduced a fuzziness into physics: You can pinpoint the precise position of a particle, but at a trade-off; its velocity cannot then be measured very well. Conversely, if you know how fast a particle is going, you won’t be able to know exactly where it is. Werner Heisenberg best summarized this strange and exotic situation with his famous uncertainty principle. But all this action, uncertain as it is, occurs on a fixed stage of space and time, a steadfast arena. A reliable clock is always around—is always needed, really—to keep track of the goings-on and thus enable physicists to describe how the system is changing. At least, that’s the way the equations of quantum mechanics are now set up.
And that is the crux of the problem. How are physicists expected to merge one law of physics—namely gravity—that requires no special clock to arrive at its predictions, with the subatomic rules of quantum mechanics, which continue to work within a universal, Newtonian time frame? In a way, each theory is marching to the beat of a different drummer (or the ticking of a different clock).
That’s why things begin to go a little crazy when you attempt to blend these two areas of physics. Although the scale on which quantum gravity comes into play is so small that current technology cannot possibly measure these effects directly, physicists can imagine them. Place quantum particles on the springy, pliable mat of spacetime, and it will bend and fold like so much rubber. And that flexibility will greatly affect the operation of any clock keeping track of the particles. A timepiece caught in that tiny submicroscopic realm would probably resemble a pendulum clock laboring amid the quivers and shudders of an earthquake. “Here the very arena is being subjected to quantum effects, and one is left with nothing to stand on,” explains Isham. “You can end up in a situation where you have no notion of time whatsoever.” But quantum calculations depend on an assured sense of time.
For Karel Kucha, a general relativist and professor emeritus at the University of Utah, the key to measuring quantum time is to devise, using clever math, an appropriate clock—something he has been attempting, off and on, for several decades. Conservative by nature, Kucha believes it is best to stick with what you know before moving on to more radical solutions. So he has been seeking what might be called the submicroscopic version of a Newtonian clock, a quantum timekeeper that can be used to describe the physics going on in the extraordinary realm ruled by quantum gravity, such as the innards of a black hole or the first instant of creation.
Unlike the clocks used in everyday physics, Kucha’s hypothetical clock would not stand off in a corner, unaffected by what is going on around it. It would be set within the tiny, dense system where quantum gravity rules and would be part and parcel of it. This insider status has its pitfalls: The clock would change as the system changed—so to keep track of time, you would have to figure out how to monitor those variations. In a way, it would be like having to pry open your wristwatch and check its workings every time you wanted to refer to it.
The most common candidates for this special type of clock are simply “matter clocks.” “This, of course, is the type of clock we’ve been used to since time immemorial. All the clocks we have around us are made up of matter,” Kucha points out. Conventional timekeeping, after all, means choosing some material medium, such as a set of particles or a fluid, and marking its changes. But with pen and paper, Kucha mathematically takes matter clocks into the domain of quantum gravity, where the gravitational field is extremely strong and those probabilistic quantum-mechanical effects begin to arise. He takes time where no clock has gone before.
But as you venture into this domain, says Kucha, “matter becomes denser and denser.” And that’s the Achilles heel for any form of matter chosen to be a clock under these extreme conditions; it eventually gets squashed. That may seem obvious from the start, but Kucha needs to examine precisely how the clock breaks down so he can better understand the process and devise new mathematical strategies for constructing his ideal clock.
More promising as a quantum clock is the geometry of space itself: monitoring spacetime’s changing curvature as the infant universe expands or a black hole forms. Kucha surmises that such a property might still be measurable in the extreme conditions of quantum gravity. The expanding cosmos offers the simplest example of this scheme. Imagine the tiny infant universe as an inflating balloon. Initially, its surface bends sharply around. But as the balloon blows up, the curvature of its surface grows shallower and shallower. “The changing geometry,” explains Kucha, “allows you to see that you are at one instant of time rather than another.” In other words, it can function as a clock.
Unfortunately, each type of clock that Kucha has investigated so far leads to a different quantum description, different predictions of the system’s behavior. “You can formulate your quantum mechanics with respect to one clock that you place in spacetime and get one answer,” explains Kucha.
“But if you choose another type of clock, perhaps one based on an electric field, you get a completely different result. It is difficult to say which of these descriptions, if any, is correct.”
It would be like having to pry open your wristwatch and check its workings every time you wanted to refer to it.
More than that, the clock that is chosen must not eventually crumble. Quantum theory suggests there is a limit to how fine you can cut up space. The smallest quantum grain of space imaginable is 10-33 centimeter wide, the Planck length, named after Max Planck, inventor of the quantum. On that infinitesimal scale, the spacetime canvas turns choppy and jumbled, like the whitecaps on an angry sea. Space and time become unglued and start to wink in and out of existence in a probabilistic froth. Time and space, as we know them, are no longer easily defined. This is the point at which the physics becomes unknown and theorists start walking on shaky ground. As physicist Paul Davies points out in his book About Time, “You must imagine all possible geometries—all possible spacetimes, space warps and time warps—mixed together in a sort of cocktail, or ‘foam.’ ”
Only a fully developed theory of quantum gravity will show what’s really happening at this unimaginably small level of spacetime. Kucha conjectures that some property of general relativity (as yet unknown) will not undergo quantum fluctuations at this point. Something might hold on and not come unglued. If that’s true, such a property could serve as the reliable clock that Kucha has been seeking for so long. And with that hope, Kucha continues to explore, one by one, the varied possibilities.
Kucha has been trying to mold general relativity into the style of quantum mechanics, to find a special clock for it. But some other physicists trying to understand quantum gravity believe that the revision should happen the other way around—that quantum gravity should be made over in the likeness of general relativity, where time is pushed into the background. Carlo Rovelli is a champion of this view.
Forget time,” Rovelli declares emphatically. “Time is simply an experimental fact.” Rovelli, a physicist at the Center of Theoretical Physics in France, has been working on an approach to quantum gravity that is essentially timeless. To simplify the calculations, he and his collaborators, physicists Abhay Ashtekar and Lee Smolin, set up a theoretical space without a clock. In this way, they were able to rewrite Einstein’s general theory of relativity, using a new set of variables so that it could more easily be interpreted and adapted for use on the quantum level.
Their formulation has allowed physicists to explore how gravity behaves on the subatomic scale in a new way. But is that really possible without any reference to time at all? “First with special relativity and then with general relativity, our classical notion of time has only gotten weaker and weaker,” answers Rovelli. “We think in terms of time. We need it. But the fact that we need time to carry out our thinking does not mean it is reality.”
Rovelli believes if physicists ever find a unified law that links all the forces of nature under one banner, it will be written without any reference to time. “Then, in certain situations,” says Rovelli, “as when the gravitational field is not dramatically strong, reality organizes itself so that we perceive a flow that we call time.”
Getting rid of time in the most fundamental physical laws, says Rovelli, will probably require a grand conceptual leap, the same kind of adjustment that 16th-century scientists had to make when Copernicus placed the sun, and not the Earth, at the center of the universe. In so doing, the Polish cleric effectively kicked the Earth into motion, even though back then it was difficult to imagine how the Earth could zoom along in orbit about the sun without its occupants being flung off the surface. “In the 1500s, people thought a moving earth was impossible,” notes Rovelli.
But maybe the true rules are timeless, including those applied to the subatomic world. Indeed, a movement has been under way to rewrite the laws of quantum mechanics, a renovation that was spurred partly by the problem of time, among other quantum conundrums. As part of that program, theorists have been rephrasing quantum mechanics’ most basic equations to remove any direct reference to time.
On the smallest of scales time would have no meaning, just as a pointillist painting, built up from dabs of paint, cannot be fathomed close up.
The roots of this approach can be traced to a procedure introduced by the physicist Richard Feynman in the 1940s, a method that has been extended and broadened by others, including James Hartle of the University of California at Santa Barbara and physics Nobel laureate Murray Gell-Mann.
Basically, it’s a new way to look at Schrödinger’s equation. As originally set up, this equation allows physicists to compute the probability of a particle moving directly from point A to point B over specified slices of time. The alternate approach introduced by Feynman instead considers the infinite number of paths the particle could conceivably take to get from A to B, no matter how slim the chance. Time is removed as a factor; only the potential pathways are significant. Summing up these potentials (some paths are more likely than others, depending on the initial conditions), a specific path emerges in the end.
The process is sometimes compared to interference between waves. When two waves in the ocean combine, they may reinforce one another (leading to a new and bigger wave) or cancel each other out entirely. Likewise, you might think of these many potential paths as interacting with one another—some getting enhanced, others destroyed—to produce the final path. More important, the variable of time no longer enters into the calculations.
Hartle has been adapting this technique to his pursuits in quantum cosmology, an endeavor in which the laws of quantum mechanics are applied to the young universe to discern its evolution. Instead of dealing with individual particles, though, he works with all the configurations that could possibly describe an evolving cosmos, an infinite array of potential universes. When he sums up these varied configurations—some enhancing one another, others canceling each other out—a particular spacetime ultimately emerges. In this way, Hartle hopes to obtain clues to the universe’s behavior during the era of quantum gravity. Conveniently, he doesn’t have to choose a special clock to carry out the physics: Time disappears as an essential variable.
Of course, as Isham points out, “having gotten rid of time, we’re then obliged to explain how we get back to the ordinary world, where time surrounds us.” Quantum gravity theorists have their hunches. Like Rovelli, many are coming to suspect that time is not fundamental at all. This theme resounds again and again in the various approaches aimed at solving the problem of time. Time, they say, may more resemble a physical property such as temperature or pressure. Pressure has no meaning when you talk about one particle or one atom; the concept of pressure arises only when we consider trillions of atoms. The notion of time could very well share this statistical feature. If so, reality would then resemble a pointillist painting. On the smallest of scales—the Planck length—time would have no meaning, just as a pointillist painting, built up from dabs of paint, cannot be fathomed close up.
Quantum gravity theorists like to compare themselves to archeologists. Each investigator is digging away at a different site, finding a separate artifact of some vast subterranean city. The full extent of the find is not yet realized. What theorists desperately need are data, experimental evidence that could help them decide between the different approaches.
It seems an impossible task, one that would appear to require recreating the hellish conditions of the Big Bang. But not necessarily. For instance, future generations of “gravity-wave telescopes,” instruments that detect ripples in the rubberlike mat of spacetime, might someday sense the Big Bang’s reverberating thunder, relics from the instant of creation when the force of gravity first emerged. Such waves could provide vital clues to the nature of space and time.
“We wouldn’t have believed just [decades] ago that it would be possible to say what happened in the first 10 minutes of the Big Bang,” points out Kucha. “But we can now do that by looking at the abundances of the elements. Perhaps if we understand physics on the Planck scale well enough, we’ll be able to search for certain consequences—remnants—that are observable today.” If found, such evidence would bring us the closest ever to our origins and possibly allow us to perceive at last how space and time came to well up out of nothingness some 14 billion years ago.
Marcia Bartusiak is an author, journalist, and a professor of the graduate program in science writing at the Massachusetts Institute of Technology. She writes about astronomy and physics.
Excerpted from Dispatches from Planet 3: Thirty-Two (Brief) Tales on the Solar System, the Milky Way, and Beyond by Marcia Bartusiak, new from Yale University Press. Copyright © 2018 by Marcia Bartusiak.
Lead image credit: viki2win / Shutterstock.
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