Science Fiction Studies

#60 = Volume 20, Part 2 = July 1993

Gregory Benford

Time and Timescape

Shortly after finishing my doctoral thesis in 1967, I began doing research at the Lawrence Radiation Laboratory, and resumed my hobby of writing fiction. It had never occurred to me to intertwine the two. Yet as I read recent papers on tachyons, hypothetical faster-than-light particles, I realized that they plainly had a science-fictional feel. In a stroke, my rigorous habits of thought as a physicist mingled with my speculative, artistic aspects. It was my first experience with how hard SF could emerge from the experience of "doing" science.

In Newton's worldview, time ticked off in an absolute way, and space was measured by a rigid universal framework. This image ruled until the late nineteenth century. H.G. Wells, always a quick study, caught the shifting winds and jury-rigged a new analogy which equated time with space—made it a fourth dimension, which a traveller could navigate.

Einstein shattered immutable time, combining space and time into a single continuum. The velocity of an observer served to rotate time into space, so that events which seemed simultaneous to one person would not look so to another who moved with a different speed. None of this was readily apparent to us, because we all move very much slower than light, which is thought to be the ultimate speed limit.

That limit separated two realms which could never interpenetrate, because approaching the barrier from lower speeds took ever-greater energy. Nothing precluded particles moving faster than light if they started out that way. The light barrier was weirdly symmetric, too. Particles moving infinitely fast have zero energy, just like particles with no velocity on our side of the barrier. Infinity mirrors zero.

Einstein's theory allowed these eerie faster-than-light particles, as he himself knew. Nobody paid much attention to their theoretical possibility until the early 1960s, however, when Gerald Feinberg introduced the name "tachyons" ("fast ones" in Greek); by contrast, ordinary matter such as us is made of slow ones, "tardyons." The last time I saw Gerry (he died in 1992) he reminded me that the idea had appealed to him because of James Blish's story, "Beep" (1954; later expanded into The Quincunx of Time, 1973). That tale concerns a faster-than-light communicator (a "Dirac transmitter," which he used in later fiction). It works fine, except that the engineers can't eliminate a beep at the end of each message. It turns out that, stretched out, that beep contains all messages from all future times—because, as Blish knew, anything which travels faster than light can be used to send messages backward in time.

Demonstrating this demands space-time diagrams and a fair amount of physics. You can see it qualitatively by noting that a tachyon covers more space than time in its trajectory, so in a sense it has a net debit in its favor—"time to burn." Several physicists had confronted directly a problem Gerry left for others—the familiar grandfather's paradox.

Most physicists believed then (and still do) that this paradox rules out tachyons or any other such backward-in-time trick. Some tried to maintain that tachyons could still exist; as Richard Feynman pointed out, a particle traveling backward in time can be redefined as its own antiparticle (made of anti-matter) moving forward in time. This "reinterpretation principle" would set everything right: apparently anti-causal events would merely be reinterpreted by other observers as perfectly normal events.

This seemed to me a bold finesse from an empty hand. When this ploy appeared in the scientific literature I discussed it with two friends and we wrote a quick paper refuting it. Published in Physical Review D in 1970 (p. 263) under the title "The Tachyonic Anti-Telephone"—see, even in dry old Phys Rev you can have fun with titles, if you try—it remains the only scientific paper I have written without a single equation in it; the argument was logical, not really technical.

We argued that notions like cause and effect could not be so easily made relative. The Feynman argument worked for one particle but not if you used two or more. With a minimum of two, whoever sent a signal could sign it, clearly establishing the origin.

We regarded the whole thing as rather amusing, so we discussed an example in which Shakespeare sends his newest work backward to Francis Bacon. At the time Bacon was a leading contender for the "true" Shakespeare among those who thought that a mere country boy could not have penned such masterpieces. "If Shakespeare types out Hamlet on his tachyon transmitter, Bacon receives the transmission at some earlier time. But no amount of reinterpretation will make Bacon the author of Hamlet. It is Shakespeare, not Bacon, who exercises control over the content of the message."

He can simply sign it, after all. Behind all the mathematics in the earlier papers lurked this simple, fatal idea.

Still, I rather liked tachyons. My two coauthors were David Book and William Newcomb. Newcomb was the grandson of the famous Simon Newcomb, an astronomer who wrote the infamous paper showing why airplanes could not fly. When he happened to mention this over a beer, my alarm bells went off. Was I signing onto a similar blinkered perspective, to be cited with ridicule generations later?

So I mulled the matter over, with one eye cocked at the steady stream of papers about time. Could tachyons actually exist? I was urged on by a report from Australia in 1972 that two experimenters had observed a tachyon. Their particle detectors, carried aloft in a balloon to catch cosmic rays, had found that a single event occurred at about 2.5 times light speed. I read their paper with astonishment. Dozens of papers followed, proposing theories for tachyons. Other experimenters tried to duplicate the Australian results—and failed. In the twenty years since, nobody has seen any such event, and statistically they should have. The Australian data was probably wrong.

Still, I wondered how tachyons—which Einstein's special theory of relativity clearly allowed—could fit into the world as we knew it. I essayed an approach in a novelette in Epoch, an anthology of the mid-1970s. Then over five years I wrote a novel, Timescape (published 1980), exploring the simplest situation I could imagine—discovery of tachyons, and the first attempts to probe their properties and use. Rather than the convenient Wellsian traveler, I used scientists as I knew them, warts and all, doing what they would—trying to use the new discovery to communicate something they cared about.

But how to deal with the paradox? I had always rather liked another theory which resolved the multiple-outcome property of conventional quantum mechanics. This interpretation of quantum events supposes that when a given particle, say, passes through a hole in a wall, it can go in several directions. The wave-like property of matter says that the same experiment, repeated many times, will give a pattern of impacts on a far screen. The density of impacts corresponds to the probability that a single particle would follow that trajectory and make that impression. But a single particle's trajectory can't be predicted precisely—we can only get the probability distribution.

Enter a fresh view, due to Hugh Everett of Princeton in the 1950s. Everett said that all the possible outcomes predicted by the probability analysis of quantum mechanics are separately real. This means that every time a particle passes through a hole, the entire universe splits into many possible outcomes.

Envision separable worlds peeling off from every microscopic event. In our world, the particle smacks into the wall and that specific outcome defines our world forever more. Other worlds simultaneously appear, with a slightly different impact point. Every event generates great handfuls of other worlds—a cosmic plentitude of astronomical extravagance. I've often wondered whether Everett was influenced by such SF stories as Murray Leinster's "Sidewise in Time" (1934). Certainly he influenced later SF writers, including the Larry Niven of "All the Myriad Ways" (1963).

The Everett view was fun to think about, and logically defensible, but nobody really believed it. But I found it handy. (Writers are magpies.) I said in my novel that the Everett interpretation didn't really apply to every event. Instead, I reserved the Everett picture for only those events which produced a causal paradox. If a physicist sent a tachyon backward in time and it had no grandfather-killing effects, no problem. If it did, though, then the universe split into as many versions as it took to cover all the possibilities. So you could indeed send some grandfather-killing message (or anything else that made a paradox), and grandfather would die. But not in the universe you were doomed to inhabit. Instead, another universe would appear, unknown to you, in which dear old grandfather died, alas, and you never happened at all. No paradox, since the tachyon which killed gramps came from another universe, from another you.

This seemed nifty enough to furnish a solution to my novel, but I did not take it seriously enough to actually work up a formal quantum field theory. I published the novel and was astonished at its success. I thought it was quirky, somewhat self-indulgent and, in its fascination with how it feels to do science, obviously destined for a small audience. Yet this rather private novel has been my most successful. It has been cited in several books about causal problems and some scientific papers. Quite pleasant for a hard SF writer.

Meanwhile, the problem of time continued. Einstein's special relativity applies to regions of space-time which are "flat" in the sense that gravity is not significant. Except for introducing the finite speed of light, the theory feels Newtonian. George Bernard Shaw, in a tongue-in-cheek toast to Einstein, put it this way:

Newton was able to combine a prodigious mental faculty with the credulities and delusions that would disgrace a rabbit. As an Englishman, he postulated a rectilinear universe because the English always use the word "square" to denote honesty, truthfulness, in short: rectitude.

Einstein's general theory stitches together small regions of locally flat spacetime into a quilt of truly warped structure. Powerfully curved spacetime plays hob with causality. One of Einstein's close friends, Kurt Gödel, produced a model (from Einstein's field theory) for a universe which spins so fast that time and space get radically twisted. Zipping around such a universe can return you to the place and time of your departure. The mathematics, coming from the famous author of Gödel's Proof in mathematical logic, was impeccable.
Could this happen? Many hoped not. With a sign of relief they noted that there is no evidence that our universe rotates. So Gödel's case simply doesn't apply here.

But then in the 1960s several theorists showed that local rotation of stressed spacetime near black holes could do similar tricks. Spin a black hole fast enough and the rotation offsets the gravitational attraction, effectively stripping the guts of the hole bare. The bowels of the beast are not pretty, with exotic zones such as negative spacetime. From such regions a traveler could do as Wells' did, slipping backwards in time. Worse, he might reach a naked singularity, where all physical things (mass, density, gravitational attraction) became indefinitely large.

Mathematics cannot handle singularities, so mathematicians would rather that they be decently clothed. No one has been able to produce suitable garments except by the lo-and-behold method. When I last discussed this with Stephen Hawking, in 1989, he admitted that he suspected that we could merely invoke the clothing of singularities as a rule, beyond proof.

Of course, he pointed out, to explain why we don't see time travelers as everyday visitors, notice the requirements. To make a reasonable time machine with a rotating black hole would take just about the mass of a small galaxy. Generally, time travel seemed to require vast public works projects.

Since then there have been other ideas, such as making quantum "wormholes" stable and large—all quite large orders. So we now have several ideas of how to make such a machine, though we can't afford one right now.

But why should this matter? If a time machine is ever built, in principle we should be receiving visitors now. Yet we haven't seen any. Why?

An adroit answer provided by Larry Niven supposes that there is nothing at all illogical about time travel, but we must remember that causality still works going forward in time. Every paradox-producing message or traveler sent back will change the conditions back at the origin of the time machine.* Remember Ray Bradbury's "A Sound of Thunder" (1952), in which a dinosaur-hunting expedition bagged its quarry, but accidentally trampled a butterfly with a boot—a striking image. They returned to find the politics and language of their era had shifted.

Imagine that people keep using such a time machine until an equilibrium sets in between past changes and future reactions. The simplest steady-state in which no changes occur is one in which no time machine exists any longer. Events conspire—say, science falls forever into disfavor, or humanity dies out—to make the time machine erase itself.

This "Niven's Law" follows directly from a basic picture from wave mechanics. Suppose time signals behave like waves. Looping into the past and back to the future, a wave can interfere with itself. Picture ocean waves intersecting, making chop and froth as they cancel here, reinforce there.

Quantum mechanically, even particles can act like waves, so it makes sense to speak of time loops as channels for the propagation of waves of probability. The wave amplitude gives the probability that a particle will exist. A loop which brings a wave back to exactly cancel itself means that the entire process cannot occur—probability zero at the very beginning, where the trip starts.

This picture actually comes from the history of quantum mechanics. One can predict the energy levels of hydrogen by thinking of its electron as a wave propagating around a circle, its orbit about the nucleus. Only certain wavelengths of the wave will fit on the orbital circumference. This quantizing condition yields the values of energy the electron must have.

Several scientific papers have explored this interest in quantum effects as the key to time travel—a welcome change from the gargantuan gravity machines I've already mentioned. In Timescape I tried to finesse the paradoxes by combining special relativity (tachyons) and quantum mechanics. Then the fashion in time machines had shifted to general relativity (Frank Tipler's rotating cylinders, as used by Poul Anderson in The Avatar [1978]), and then to quantum mechanics (wormholes). What about uniting general relativity and quantum mechanics—a much harder job.

Imagine my surprise when in November of 1992 I came upon a paper in Physical Review D, where our old tachyon paper had appeared. Titled somewhat forbiddingly `"Quantum Mechanics Near Closed Timelike Lines," it constructs a theory for effects in highly curved space-time which contains causal loops—"closed timelike lines," in the jargon. It was written by David Deutsch, who has been studying these matters for a decade at Oxford (not Cambridge, the site of the experiments in Timescape).

"Contrary to what has usually been assumed," Deutsch says, "there is no reason in what we know of fundamental physics why closed timelike lines should not exist." In twenty pages of quantum logic calculations, he shows that no obstacle to free will or even grandfather murder really exists.

It's all done with the Everett interpretation. In quantum cosmology there is no single history of space-time. Instead, all possible histories happen simultaneously. For the vast preponderance of cases, this doesn't matter—the ontological bloat of an infinitude of worlds has no observable consequences. It's just a way of talking about quantum mechanics.

Not so for time machines. Then a quantum description requires a set of `"classical" (ordinary) space-times which are similar to each other—except in the important history of the paradox-loop. The causal loop links all the multiple histories.

Think of unending sheets stacked on end and next to each other, like the pages in this magazine. Timelines flow up them. A causal loop snakes through these sheets, so the parallel universes become one. If the grandson goes back in time, he crosses to another time-sheet. There he shoots granddad, and lives thereafter in that universe. His granddad lived as before and had grandchildren, one of whom disappears, period.

Quantum mechanics always furnishes as many linked universes as there would be conflicting outcomes; it's quite economical. In this view, "it is only ever an approximation to speak of things happening 'in a universe'. In reality the 'universes' form part of a larger object...which, according to quantum theory, is the real arena in which things happen." Cosmic stuff, indeed.

Just now, writing this three months after Deutsch's paper appeared, I opened Timescape and tracked down my old thinking. "When a loop was set up, the universe split into two new universes.... The grandson reappeared in a second universe, having traveled back in time, where he shot his grandfather and lived out his life, passing through the years which were forever altered by his act. No one in either universe thought the world was paradoxical."

I framed my fictional theory this way because it seemed at least a plausible escape hatch from the genuine problems of time machines, using quantum logic. But my deeper motivation was to capture the eerie sense of having altered the past, the age-old dream . . . but for someone else.

If you know this, then such an act is the ultimate altruism: you cannot then benefit in any way from usefully adjusting the past (or suffer, either). Someone exactly like you does benefit (yes, a twin; and I wonder how much my being an identical twin has led to my interest in these ideas)—but you will never see him, and cannot know this except in theory. Most of all, I was struck in writing the closing pages of the novel with that glimpse of vistas unknown, whole universes beyond our grasp, times untouched. To me that is the essential SF impulse. Much critical attention paid the book (such as Susan Stone-Blackburn's, who contributed a critical summary to the new Bantam edition of the novel) lauds its characterization, perhaps because the scientific content and metaphors are less obvious and not traditional.

To me, though, beyond the book's puzzles and plots lurks its central driver: a sense of unchanging immensity, the timescape glimpsed with the flitting attention of a mortal being. This touches on the often-invoked emotions behind much hard SF—awe and thinly veiled transcendence. They are the core passions of Clarke and Stapledon.

In most of my writing I do try to portray humans as they really are, because I am uncomfortably aware that real science is done by people with dirt under their fingernails. In hard SF there is an inevitable tension between conventional short-focus realism and the impact of the larger landscape (humanity foregrounded against the universe) that is central to hard SF's ideology and affect.

The usual hard SF protagonist is an Everyman, who believes in reason and his/her ability to fathom the unknown. Hard SF is not about ironic distance or individual failure, though that may play a part in a particular hard SF work. Still less is it about the symptoms of narrative exhaustion which some term post-modern—pastiche, borrowing, self-aware recycling of genre materials, and the rearrangement of conceptual deck chairs on a cultural Titanic. Titles like Mission of Gravity, Gateway, and Childhood's End are about the great ol' up and out.

It was quite strange to read Deutsch's neatly couched arguments in Physical Review D. There is a certain wrenching sensation in having anticipated the qualitative aspects—not the thickets of equations; Deutsch's quantum logic calculations I find quite daunting—of a theory which seems to open the way to actual use of time machines, if we should ever devise them.

Will we? Perhaps. But hard SF is not about exactly predicting the future. It is about the beauty of a small, reasoning reed, which can see past its own mortality and wonder at the vistas beyond. Its essential drama lies in that huge leap of scale.

23 February 1993

*Larry Niven, "The Theory and Practice of Time Travel," All the Myriad Ways (NY: Ballantine, 1971), 110-23..

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