• Choose a category
• All
• Classic-Fiction

The empty space of the physicist’s imagination—the chalkboard on which every motion, every force, every interaction played itself out—had undergone a transformation in less than a generation. A ball pursued a trajectory through the everyday space of three dimensions. The particles of Feynman’s reckoning forged paths through the four-dimensional space-time so indispensable to the theory of relativity, and through even more abstract spaces whose coordinate axes stood for quantities other than distance and time. In space-time even a motionless particle followed a trajectory, a line extending from past to future. For such a path Minkowski coined the phrase world-line—“an image, so to speak, of the everlasting career of the substantial point, a curve in the world… . The whole universe is seen to resolve itself into similar world-lines.” Science-fiction writers had already begun to imagine the strange consequences of world-lines twisting back from the future into the past. No novelist was letting his fantasies roam as far as Wheeler was, however. One day he called Feynman on the hall telephone in the Graduate College. Later Feynman remembered the conversation this way:

—Feynman, I know why all the electrons have the same charge and the same mass.

—Why?

—Because they are all the same electron! Suppose that all the world-lines which we were ordinarily considering before in time and space—instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world-lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world-line, in the section in which it reversed itself and is coming back from the future we have the wrong sign … and therefore, that part of a path would act like a positron.

The positron, the antiparticle twin of the electron, had been discovered (in cosmic-ray showers) and named (another modern -tron, short for positive electron) within the past decade. It was the first antiparticle, vindicating a prediction of Dirac’s, based on little more than a faith in the loveliness of his equations. According to the Dirac wave equation, the energy of a particle amounted to this: ±√something. Out of that plus-or-minus sign the positron was born. The positive solution was an electron. Dirac boldly resisted the temptation to dismiss the negative solution as a quirk of algebra. Like Wheeler in making his leap toward advanced waves, he followed a mirror-image change in sign to its natural conclusion.

Feynman considered the wild suggestion coming through the earpiece of his telephone—that all creation is a slice through the spaghetti path of a single electron—and offered the mildest of the many possible rebuttals. The forward and backward paths did not seem to match up. An embroidery needle pulling a single thread back and forth through a canvas must go back as many times as it goes forth.

—But, Professor, there aren’t as many positrons as electrons.

—Well, maybe they are hidden in the protons or something.

Wheeler was still trying to make the electron the basis of all other particles. Feynman let it pass. The point about positrons, however, reverberated. In his first published paper two years before, on the scattering of cosmic radiation by stars, he had already made this connection, treating antiparticles as ordinary particles following reversed paths. In a Minkowskian universe, why shouldn’t the reversal apply to time as well as to space?

Mr. X and the Nature of Time

Twenty years later, in 1963, the problem of time having given up none of its mystery, a group of twenty-two physicists, cosmologists, mathematicians, and others sat around a table at Cornell to discuss the matter. Was time a quantity entered in the account books of their equations to mark the amount of before and after? Or it was an all-enveloping flow, carrying everything with it