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By Root 1974 0

in quantum field theory comes from one essential fact: there is not a single experimental result that counters its predictions. To the contrary, data confirm that the equations of quantum field theory describe the behavior of particles with astounding accuracy. The most impressive example comes from the quantum field theory of the electromagnetic force, quantum electrodynamics. Using it, physicists have undertaken detailed calculations of the electron’s magnetic properties. The calculations are not easy, and the most refined versions have taken decades to complete. But they’ve been worth the effort. The results match actual measurements to a precision of ten decimal places, an almost unimaginable agreement between theory and experiment.

With such success, you might anticipate that quantum field theory would provide the mathematical framework for understanding all of nature’s forces. An illustrious coterie of physicists shared this very expectation. By the late 1970s, the hard work of many of these visionaries had established that, indeed, the weak and strong nuclear forces fit squarely within the rubric of quantum field theory. Both forces are accurately described in terms of fields—the weak and the strong fields—that evolve and interact according to the mathematical rules of quantum field theory.

But, as I indicated in the historical overview, many of these same physicists quickly realized that the story for nature’s remaining force, gravity, was far subtler. Whenever the equations of general relativity commingled with those of quantum theory, the mathematics balked. Use the combined equations to calculate the quantum probability of some physical process—such as the chance of two electrons ricocheting off each other, given both their electromagnetic repulsion and their gravitational attraction—and you’d typically get the answer infinity. While some things in the universe can be infinite, such as the extent of space and the quantity of matter that may fill it, probabilities are not among them. By definition, the value of a probability must be between 0 and 1 (or, in terms of percentages, between 0 and 100). An infinite probability does not mean that something is very likely to happen, or is certain to happen; rather, it’s meaningless, like speaking of the thirteenth egg in an even dozen. An infinite probability sends a clear mathematical message: the combined equations are nonsense.

Physicists traced the failure to the jitters of quantum uncertainty. Mathematical techniques had been developed for analyzing the jitters of the strong, weak, and electromagnetic fields, but when the same methods were applied to the gravitational field—a field that governs the curvature of spacetime itself—they proved ineffective. This left the mathematics saturated with inconsistencies such as infinite probabilities.

To get a feel for why, imagine you’re the landlord of an old house in San Francisco. If you have tenants who throw raucous parties, it might take effort to deal with the situation, but you don’t worry that the festivities will compromise the building’s structural integrity. However, if there’s an earthquake, you’re facing something far more serious. The fluctuations of the three nongravitational forces—fields that are tenants within the house of spacetime—are like the building’s incessant partyers. It took a generation of theoretical physicists to grapple with their raucous jitters, but by the 1970s they’d developed mathematical methods capable of describing the quantum properties of the nongravitational forces. The fluctuations of the gravitational field, however, are qualitatively different. They’re more like an earthquake. Because the gravitational field is woven within the very fabric of spacetime, its quantum jitters shake the entire structure through and through. When used to analyze such pervasive quantum jitters, the mathematical methods collapsed.5

For years, physicists turned a blind eye to this problem because it surfaces only under the most extreme conditions. Gravity makes its mark when things are very massive,