Saturday, July 18, 2015

The Nonexistent Paradoxes of Time Travel

A clock that has seen a lot of time go by. (Photo by Cami.)

This clock has seen a lot of time go by. (Photo by Cami.)

Apparently the first story to hint at the paradoxes of time travel was Edward Page Mitchell’s “The Clock that Went Backward,” which appeared in a New York newspaper, The Sun, in 1881. Most of the action takes place in Leyden, the Netherlands, where a 300-year-old clock made by one Jan Lipperdam sends the narrator, his cousin Harry, and their professor, Von Stott, back in time to the historic siege of 1574. Events suggest, although with much uncertainty, that Von Stott is Lipperdam, and that Harry is his own great-grandfather.

These are foreshadowings of the by-now traditional grandfather paradox and bootstrap paradox (or causal loop), the latter named for Robert Heinlein’s 1941 short story “By His Bootstraps.” The causal loop is often illustrated with the tale of an inventor of a time machine who uses it to return to his past, where he teaches his younger self how to build it; where, except from himself, did he get the information? The grandfather paradox raises the possibility that a man returns to the past and kills his own grandfather, an act that should have pre-erased him.

Some kinds of time travel are commonplace. Imagine a scientist who brings an atomic clock aboard a jet plane and flies around the world; velocity makes her clock run slower than an identical clock on the ground, which is tended by her twin sister; she thus returns to Earth in her sister’s future.

This is a version of the so-called twin paradox, which is not a paradox at all but a straightforward result of Special Relativity. (Gravity also has an effect on the passage of time, but for now we can ignore it.) The clocks aren’t necessary; they’re just there to prove that people in the speeding plane, or space shuttle, or some future rocket to Andromeda, really do travel into the future of those they leave behind, whether by nanoseconds or centuries. Many such experiments have been performed.

Even if travel to the past is not impossible, it would require tremendous energy and expense—not to mention unlikely circumstances, such as wormholes that don’t annihilate everything that falls into them. So far, visits to the past happen only in fiction. If the protagonist gets whacked on the head or runs into a chronosynclastic infundibulum, it’s probably a work of satire. If the author hand-waves about time machines, black holes, spacetime continua, or genetic disorders, it’s a science fiction story. However much real science there may be in the story, there’s none in the mechanism for traveling back in time.

Philosophers love it anyway. In 1976 David Lewis published an essay titled “The Paradoxes of Time Travel.” With typical bluntness, he begins, “Time travel, I maintain, is possible. The paradoxes of time travel are oddities, not impossibilities.” He’s not talking about practical difficulties but logical ones. “I shall be concerned here with the sort of time travel that is recounted in science fiction.”

Lewis is beloved of fiction writers, at least this one, because of his argument—stated in his 1978 essay, “Truth in Fiction”—that “worlds where the fiction is told, but as known fact rather than fiction,” are not only possible worlds but real ones.

Unlike the twin paradox, however, the paradoxes of travel to the past are widely thought to render these fictional worlds impossible. In a subtle retort, Lewis deals with the objection by distinguishing two kinds of time, external and personal. External time deals with the real world, personal time with the time traveler’s experience. “We can say without contradiction, as the time traveler prepares to set out, ‘Soon he will be in the past.’”

No matter how many loops or leaps, a time traveler's personal time is always continuous. (M.C. Escher, red ants on a Mobius strip)

A time traveler’s personal time is always continuous. (M.C. Escher, red ants on a Mobius strip)

With this simple distinction, Lewis demolishes the grandfather paradox. In neither the linear passage of external time nor the loops and  leaps of the time traveler’s personal time is continuity ever interrupted. “Tim [a time traveler who is motivated and able to kill his grandfather] cannot kill Grandfather. Grandfather lived, so to kill him would be to change the past. But the events of a past moment… cannot change.”

There’s no such simple solution to the bootstrap paradox, since it too respects the demands of both external and personal time. Causal loops are possible, says Lewis, but they don’t matter.

Where did the information come from in the first place…? There is simply no answer. The parts of the loop are explicable, the whole of it is not. Strange! But not impossible, and not too different from the inexplicabilities we are already inured to. Almost everyone agrees that God, or the Big Bang, or the entire infinite past of the universe, or the decay of a tritium atom, is uncaused and inexplicable. Then if these are possible, why not also the inexplicable causal loops that arise in time travel?

In this blithe paragraph, Lewis puts his finger on one of the central tenets of real science, namely, that there is a profound difference between the inexplicable and the impossible.

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