For most people, the great mystery of time is that there never seems to be enough of it. If it is any consolation, physicists are having much the same problem. The laws of physics contain a time variable, but it fails to capture key aspects of time as we live it—notably, the distinction between past and future. And as researchers try to formulate more fundamental laws, the little t evaporates altogether. Stymied, many physicists have sought help from an unfamiliar source: philosophers.

From philosophers? To most physicists, that sounds rather quaint. The closest some get to philosophy is a late-night conversation over dark beer. Even those who have read serious philosophy generally doubt its usefulness; after a dozen pages of Immanuel Kant, philosophy begins to seem like the unintelligible in pursuit of the undeterminable. “To tell you the truth, I think most of my colleagues are terrified of talking to philosophers—like being caught coming out of a pornographic cinema,” says physicist Max Tegmark of the Massachusetts Institute of Technology.

It was not always so. Philosophers played a crucial role in past scientific revolutions, including the development of quantum mechanics and relativity in the early 20th century. Today a new revolution is under way, as physicists struggle to merge those two theories into a theory of quantum gravity—a theory that will have to reconcile two vastly different conceptions of space and time. Carlo Rovelli of Aix-Marseille University in France, a leader in this effort, observes that “the contributions of philosophers to the new understanding of space and time in quantum gravity will be very important.”

Two examples illustrate how physicists and philosophers have been pooling their resources. The first concerns the “problem of frozen time,” also known simply as the “problem of time.” It arises when theorists try to turn Einstein's general theory of relativity into a quantum theory using a procedure called canonical quantization. The procedure worked brilliantly when applied to the theory of electromagnetism, but in the case of relativity, it produces an equation—the Wheeler-DeWitt equation—without a time variable. Taken literally, the equation predicts that the universe should be frozen in time, in direct contradiction with what we see.

Don't Lose Any More Time

This unhappy outcome may reflect a flaw in the procedure itself, but some physicists and philosophers argue that it has deeper roots, right down to one of the founding principles of relativity: that the laws of physics are the same for all observers. Physicists think of the principle in geometric terms. Two observers will perceive spacetime to have two different shapes, corresponding to their views of who is moving and what forces are acting. Each shape is a smoothly warped version of the other, in the way that a coffee cup is a reshaped doughnut. Relativity theory says that the difference cannot be meaningful. Therefore, any two such shapes are physically equivalent.

In the late 1980s philosophers John Earman and John D. Norton, both at the University of Pittsburgh, argued that general relativity has startling implications for an old metaphysical question: Do space and time exist independently of stars, galaxies and their other contents (a position known as substantivalism), or are they merely an artificial device to describe how physical objects are related (relationism)? As Norton has written: “Are they like a canvas onto which an artist paints; they exist whether or not the artist paints on them? Or are they akin to parenthood; there is no parenthood until there are parents and children.”

He and Earman revisited a long-neglected thought experiment of Albert Einstein's. Consider an empty patch of spacetime. Outside this hole the distribution of matter fixes the geometry of spacetime, per the equations of relativity. Inside, however, the equations let spacetime take on any of a variety of shapes. Spacetime behaves like a canvas tent. The tent poles, which represent matter, force the canvas to assume a certain shape. If you leave out a pole, however, creating the equivalent of a hole, part of the tent can sag, or bow out, or ripple unpredictably in the wind. A similar ambiguity arises everywhere, not just in holes.

The thought experiment poses a dilemma. If the continuum is a thing in its own right (as substantivalism holds), general relativity must be indeterministic—that is, its description of the world must contain an element of randomness. For the theory to be deterministic, spacetime must be a mere fiction (as relationism holds). At first glance, it looks like a victory for relationism. It helps that other theories, such as electromagnetism, are based on symmetries that resemble relationism.

But relationism has its own troubles. It is the ultimate source of the problem of frozen time: space may morph over time, but if its many shapes are all equivalent, it never truly changes. Moreover, relationism clashes with the substantivalist underpinnings of quantum mechanics. If spacetime has no fixed meaning, how can you make observations at specific places and moments, as quantum mechanics seems to require?

Different resolutions of the dilemma lead to very different theories of quantum gravity. Some, such as Rovelli and English physicist Julian Barbour, are trying a relationist approach; they think time does not exist and have searched for ways to explain change as an illusion. Others, including string theorists, lean toward substantivalism.

“It's a good example of the value of philosophy of physics,” says philosopher Craig Callender of the University of California, San Diego. “If physicists think the problem of time in canonical quantum gravity is solely a quantum problem, they're hurting their understanding of the problem—for it's been with us for much longer and is more general.”

Running on Entropy

A second example of philosophers' contributions concerns the arrow of time—the asymmetry of past and future. Many people assume that the arrow is explained by the second law of thermodynamics, which states that entropy, loosely defined as the amount of disorder within a system, increases with time. Yet no one can really account for the second law.

The leading explanation, put forward by 19th-century Austrian physicist Ludwig Boltzmann, is probabilistic. The basic idea is that there are more ways for a system to be disordered than to be ordered. If the system is fairly ordered now, it will probably be more disordered a moment from now. This reasoning, however, is symmetric in time. The system was probably more disordered a moment ago, too. As Boltzmann recognized, the only way to ensure that entropy will increase into the future is if it starts off with a low value in the past. Thus, the second law is not so much a fundamental truth as historical happenstance, perhaps related to events early in the big bang.

Philosopher Huw Price of the University of Cambridge argues that almost every attempt to explain time asymmetry suffers from circular reasoning—some hidden presumption of time asymmetry. This fallacy also distorts how physicists interpret quantum mechanics. Price's work is an example of how philosophers can serve, in the words of philosopher Richard Healey of the University of Arizona, as the “intellectual conscience of the practicing physicist.” Trained in logical rigor, they are experts at tracking down subtle biases.

Life would be boring if we always listened to our conscience, and physicists have often done best when ignoring philosophers. Yet in the eternal battle against our own leaps of logic, conscience is sometimes all we have to go on.