Time Travel. A History

Besides religious conviction, Newton was motivated by mathematical necessity: he needed absolute time, as he needed absolute space, in order to define his terms and express his laws. Motion is defined as the change in place over time; acceleration is the change in velocity over time. With a backdrop of absolute, true, and mathematical time, he could build an entire cosmology, a System of the World. This was an abstraction; a convenience; a framework for calculating. But for Newton it was also a statement about the world. You may believe it, or not.^*2

Albert Einstein believed it. Up to a point.

He believed in an edifice of laws and computation that had grown from a bare stone church into a grand ornate cathedral, supported by colonnades and flying buttresses, layered with carving and tracery—work still in progress, with hidden crypts and ruined chapels. In this edifice time t played an indispensable part. No one could grasp the whole structure, but Einstein understood more than most and had encountered a problem. There was an internal contradiction. The great achievement of the last century’s physics was James Clerk Maxwell’s unification of electricity, magnetism, and light—the achievement that was so visibly wiring the whole world. Electric currents, magnetic fields, radio waves, and light waves were one and the same. Maxwell’s equations made it possible to calculate the speed of light, for the first time. But they were not meshing perfectly with the laws of mechanics. Those light waves, for example—so clearly waves, according to the mathematics, but waves in what? Sound needs air or water or other substance to carry the vibrations. Light waves likewise implied an unseen medium, the so-called ether—“luminiferous,” or light bearing. Naturally experimentalists were trying to detect this ether, with no success. Albert Michelson and Edward Morley came up with a clever experiment in 1887 to measure the difference between the speed of light in the direction of the earth’s motion and the speed of light at right angles to it. They couldn’t find any difference at all. Was the ether necessary? Or was it possible to think purely of an electrodynamics of moving bodies, through empty space?

We know now that the speed of light in empty space is constant, 299,792,458 meters per second. No rocket ship can overtake a flash of light or reduce that number in the slightest. Einstein struggled (“psychic tension”; “all sorts of nervous conflicts”) to make sense of that: to discard the luminiferous ether, to accept the speed of light as absolute. Something else had to give. On a fine bright day in Bern (as he told the story later), he talked it over with his friend Michele Besso. “Next day I came back to him again and said to him, without even saying hello, ‘Thank you. I’ve completely solved the problem.’ An analysis of the concept of time was my solution.” If light speed is absolute, then time itself cannot be. We must abandon our faith in perfect simultaneity: the assumption that two events can be said to happen at the same time. Multiple observers experience their own present moments. “Time cannot be absolutely defined,” said Einstein—it can be defined, but not absolutely—“and there is an inseparable relation between time and signal velocity.”

The signal carries information. Suppose six sprinters line up at the start line for the hundred-meter run, with their hands and one knee touching the ground and their feet in the starting blocks, awaiting the sound of the gun. The signal velocity in this case will be about a few hundred meters per second, the speed of sound through air. That’s slow nowadays, so Olympic events have scrapped starting pistols in favor of signals wired (at light speed) into loudspeakers. To think about simultaneity more carefully, it becomes necessary also to consider the signal velocity of light traveling to the eyes of the runners, the judges, and the spectators. In the end, there is no one instant, no “point in time,” that can be the same for everyone.

Suppose lightning strikes a railway embankment (trains are more usual than horses in these stories) at two different points, distant from each other. Can you—a physicist, with the most excellent modern equipment—establish whether the two flashes were simultaneous? You cannot. It turns out that a physicist riding the train will disagree with a physicist standing at the station. Every observer owns a reference frame, and each reference frame has its own clock. There is no one cosmic clock, no clock of God or Newton.