Time became a key word in the language of physics during the seventeenth century, notably when Isaac Newton wove the passage of time directly into his equations, as in force = mass acceleration. Today, it is difficult for any physicist to examine the universe without thinking of time in much the same way as the illustrious Britisher did more than three hundred years ago. Most of the laws of physics continue to be written in the style of Newton; they are designed to show how things change from one moment to the next. Each event under study, such as the path of a ball thrown into the air or the thermodynamics of a melting ice cube, is broken down into a series of freeze-frames that, run like a movie, show how nature works.
Newton had placed a clock upon the mantel of the universe. This Newtonian timepiece ticked and tocked, chiming like some cosmic Big Ben, in step with all celestial inhabitants, no matter what their speed or position. That meant that a clock situated at the edge of the universe or zipping about the cosmos at high velocities would register the same passage of time—identical minutes and identical seconds—as an earthbound clock. More important, the Newtonian clock was never affected by the events going on around it. Time was aloof and absolute, alike for all as galaxies collided, solar systems formed, and moons orbited planets. Time led an independent existence, separate from nature itself.
This comfortable notion of time held until the beginning of this century, but then it was shattered with a jolt. Albert Einstein uncovered a glitch in Newton’s cozy clockwork. With his special theory of relativity, published in 1905, Einstein showed that a clock at rest and a clock in motion do not necessarily agree with one another. Each registers a different flow of time. This effect is well documented: a muon particle (a heavy electron) racing in from space at near the speed of light, for instance, lives many times longer than a muon at rest on Earth. What Einstein did was transform time into a true physical entity, one that was changed by what was going on around it. With special relativity, physicists learned that time is not absolute, as Newton had us think. Time, it turns out, is in the eye of the beholder and in the beholder’s surroundings.
Three years after this revelation appeared in print, Einstein’s teacher Hermann Minkowski took Newton’s clock off the mantelpiece and rolled it out like cookie dough to form the cosmic landscape called space-time. Minkowski, wanting to better explain some of special relativity’s unusual properties, glued space and time together to form a seamless canvas, a new absolute framework in which time becomes physically connected to space. If you think of space-time coordinates as the interwoven threads of a blanket, tweaking one set of threads will affect all the others: travel near the speed of light and space will shrink as time expands. “Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows,” remarked Minkowski. Time alone can no longer be separated from the mix.
In 1915, with his revolutionary general theory of relativity, Einstein shook up the classical, Newtonian view of time even further. He took the novel image of space-time and warped it, and in so doing was able to explain the origin of gravity, long a mystery. According to Newton, rocks fell to Earth and planets orbited the Sun because these objects were somehow held by invisible tendrils of force. Why should this be so? No one knew. But with Einstein’s insight, the tendency of one object to attract another object became a simple matter of geometry. It was the natural consequence whenever a mass distorted the space-time canvas. A massive body—the Sun, for example—indents the mat (much the way our bodies can sink into a flexible mattress), and nearby objects must then circle it because they are caught, like cosmic marbles, in the deep space-time basin carved out by the Sun.
General relativity treats time very differently from the way it’s handled in other areas of physics. 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 Imperial College’s Isham. “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.
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 space-time, 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 Kuchař (pronounced KOO-cosh), 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, Kuchař 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, Kuchař’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,” Kuchař 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, Kuchař 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 Kuchař, “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 Kuchař 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 space-time’s changing curvature as the infant universe expands or a black hole forms. Kuchař 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 Kuchař, “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 Kuchař 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 space-time and get one answer,” explains Kuchař. “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.”
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. (To give you an idea how tiny that is, if an atom were blown up to the size of our Milky Way galaxy, which spans some 100,000 light-years, this quantum grain would still be no bigger than a human cell.) On that infinitesimal scale, the space-time 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 timewarps—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 space-time. Kuchař 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 Kuchař has been seeking for so long. And with that hope, Kuchař continues to explore, one by one, the varied possibilities.
Kuchař 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 sixteenth-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.
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. Consider a ball being thrown across a street to your neighbor’s house. There’s a high probability it will take the shortest and straightest route, but others are possible. The ball could steeply arc, for instance; it could swerve to the right or to the left; there’s even a minuscule chance it could go around the Earth in the opposite direction and hit your neighbor’s back door. Each path represents a potential outcome for the particle and contributes to the final result.
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 a
nd 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 space-time 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. At that range, the painting looks like nothing more than a random array of dots. But as you move back, the dots begin to blend together and a recognizable picture slowly comes into focus. Likewise, space-time, the entity so familiar to us, might take form and reveal itself only when we scrutinize larger and larger scales. Time could be simply a matter of perception, present on the large scale but not on the smallest scale imaginable. Physicists talk of the universe “congealing” or “crystallizing” out of the chaotic quantum jumble that lies at the heart of the Big Bang. Time is not a physical entity but rather a notion that emerges.
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