Time Travel: A History (25 page)

*6
Rosenfeld then started a blog,
The Counterfactual History Review,
and embarked on a collection to be titled
If Only We Had Died in Egypt!: What Ifs of Jewish History.

*7
In an odd coincidence, Le Guin had gone to high school with Philip K. Dick, as she realized later. “
Nobody
knew Phil Dick,” she told
The Paris Review.
“He was the invisible classmate.”

*8
She said to an interviewer, Bill Moyers, “The book is full of dreams and visions, and you are never sure which is which.”

*9
Indeed, it is the essence of doublethink. “This demands a continuous alteration of the past.” The literal rewriting of history was Winston Smith’s day job, remember, in the Minitrue RecDep (Ministry of Truth Records Department).

ELEVEN

The Paradoxes

This seems to be a paradox. But one must not think ill of the paradox, for the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion: a mediocre fellow.

—Søren Kierkegaard (1844)

PROPOSITION:
Time travel is impossible, because you’d be able to go back and kill your grandfather, in which case you, the murderer, would never have been born;
and so on, and so on.

We’ve been here before. We are in the domain of logic, which is, let’s remember, a country distinct from the domain of reality. Its inhabitants speak a dialect of their own, resembling natural language and often quite understandable, but full of pitfalls. A thing can be
logically possible
yet
empirically impossible.
If the logicians give us permission to build a time machine, we may still not be able to build it.

I doubt that any phenomenon, real or imagined, has inspired more perplexing, convoluted, and ultimately futile philosophical analysis than time travel has. (Some possible contenders, determinism and free will, are bound up anyway in the arguments over time travel.) The disputation was well under way while H. G. Wells was still alive to be bemused by it. In his classic textbook,
An Introduction to Philosophical Analysis,
John Hospers tackles the question: “Is it logically possible to go back in time—say, to 3000 B.C., and help the Egyptians build the pyramids? We must be very careful about this one.” The possibility is easy to state—we habitually use the same words to talk about time as we do when talking about space—and it’s easy to imagine. “In fact, H. G. Wells did imagine it in
The Time Machine,
and every reader imagines it with him.” (Hospers misremembers
The Time Machine:
“a person in 1900 pulls a lever on a machine and suddenly is surrounded by the world of many centuries earlier.”) Hospers was a bit of a kook, actually, who achieved the distinction, unusual for a philosopher, of having received one electoral vote for president of the United States.
^*1
His textbook, first published in 1953, remained standard through four editions and forty years.

His answer to the rhetorical question is an emphatic no. Time travel à la Wells is not just impossible, it is
logically
impossible. It is a contradiction in terms. In an argument that runs for four dense pages, Hospers proves this by power of reason.

“How can we be in the 20th century A.D. and the 30th century B.C.
at the same time
? Here already is one contradiction….It is
not
logically possible to be in one century of time and in another century of time at the same time.” You may pause to wonder (though Hospers doesn’t) whether a trap is lurking in that deceptively common expression “at the same time.” The present and the past are different times, therefore they are not the same time, nor
at
the same time. Q.E.D.

That was suspiciously easy. The point of the time-travel fantasy, however, is that the lucky time travelers have their own clocks. Their time can keep running forward, while they travel back to a different time as recorded by the universe at large. Hospers sees this but resists it. “People can walk backward in space, but what would ‘going backward in time’ literally mean?” he asks.

And if you continue to live, what can you do but get one day older every day? Isn’t “getting younger every day” a contradiction in terms—unless, of course, it is meant figuratively, as in “My dear, you’re getting younger every day,” where it is still taken for granted that the person, while
looking
younger every day, is still
getting older
every day?

(He gives no hint of being aware of F. Scott Fitzgerald’s short story in which Benjamin Button does precisely that. Born as a seventy-year-old, Benjamin grows younger every day, until infancy and oblivion. Fitzgerald admitted the logical impossibility. The story has many offspring.)

Time is simple for Hospers. If you imagine that one day you are in the twentieth century and the next day your time machine carries you back to ancient Egypt, he retorts, “Isn’t there a contradiction here again? For the next day after January 1, 1969, is January 2, 1969. The day after Tuesday is Wednesday (this is analytic—‘Wednesday’ is defined as the day that follows Tuesday)” and so on. And he has one final argument, the last nail in time travel’s logical coffin. The pyramids were built before you were born. You didn’t help. You didn’t even watch. “This is an unchangeable fact,” says Hospers and adds, “You can’t change the past. That is the crucial point: the past is what happened, and you can’t make what happened not have happened.” We’re still in a textbook about analytical philosophy, but you can almost hear the author shouting:

Not all the king’s horses or all the king’s men could make what
has
happened
not
have happened, for this is a logical impossibility. When you say that it is logically possible for you (literally) to go back to 3000 B.C. and help build the pyramids, you are faced with the question: did you help them build the pyramids or did you not? The first time it happened you did
not:
you weren’t there, you weren’t yet born, it was all over before you came on the scene.

Admit it: you didn’t help build the pyramids. That’s a fact, but is it a logical fact? Not every logician finds these syllogisms self-evident. Some things cannot be proved or disproved by logic. The words Hospers deploys are more slippery than he seems to notice, beginning with the word
time.
And in the end, he’s openly assuming the thing he’s trying to prove. “The whole alleged situation is riddled with contradictions,” he concludes. “When we say we can imagine it, we are only uttering the words, but there is nothing in fact even logically possible for the words to describe.”

Kurt Gödel begged to differ. He was the century’s preeminent logician, the logician whose discoveries made it impossible ever to think of logic in the same way. And he knew his way around a paradox.

Where a logical assertion of Hospers sounds like this—“It is logically impossible to go from January 1
to any other day
except January 2 of the same year”—Gödel, working from a different playbook, sounded more like this:

That there exists no one parametric system of three-spaces orthogonal on the
x
₀
-lines follows immediately from the necessary and sufficient condition which a vector field
v
in a four-space must satisfy, if there is to exist a system of three-spaces everywhere orthogonal on the vectors of the field.

He was talking about world lines in Einstein’s space-time continuum. This was in 1949. Gödel had published his greatest work eighteen years earlier, when he was a twenty-five-year-old in Vienna: mathematical proof that extinguished once and for all the hope that logic or mathematics might assemble a complete and consistent system of axioms, powerful enough to describe natural arithmetic and either provably true or provably false. Gödel’s incompleteness theorems were built on a paradox and leave us with a greater paradox.
^*2
We know that complete certainty must always elude us. We know that for certain.

Now Gödel was thinking about time—“that mysterious and self-contradictory being which, on the other hand, seems to form the basis of the world’s and our own existence.” Having escaped Vienna after the Anschluss by way of the Trans-Siberian Railway, he settled at the Institute for Advanced Study in Princeton, where he and Einstein intensified a friendship that had begun in the early thirties. Their walks together, from Fuld Hall to Olden Farm, witnessed enviously by their colleagues, became legendary. In his last years Einstein told someone that he still went to the Institute mainly
um das Privileg zu haben, mit Gödel zu Fuss nach Hause gehen zu dürfen,
to have the privilege of walking home with Gödel. For Einstein’s seventieth birthday, in 1949, his friend presented him with a surprising calculation: that his field equations of general relativity allow for the possibility of “universes” in which time is cyclical—or, to put it more precisely, universes in which some world lines loop back upon themselves. These are “closed timelike lines,” or as a physicist today would say, closed timelike curves (CTCs). They are circular highways lacking on-ramps or off-ramps. A closed timelike curve loops back on itself and thus defies ordinary notions of cause and effect: events are their own cause. (The universe itself—entire—would be rotating, something for which astronomers have found no evidence, and by Gödel’s calculations a CTC would have to be extremely large—billions of light-years—but people seldom mention these details.)
^*3

If the attention paid to CTCs is disproportionate to their importance or plausibility, Stephen Hawking knows why: “Scientists working in this field have to disguise their real interest by using technical terms like ‘closed timelike curves’ that are code for time travel.” And time travel is sexy. Even for a pathologically shy, borderline paranoid Austrian logician. Almost hidden inside the bouquet of computation, Gödel provided a few words of almost-plain English:

In particular, if
P,
Q
are any two points on a world line of matter, and
P
precedes
Q
on this line, there exists a time-like line connecting
P
and
Q
on which
Q
precedes
P;
i.e., it is theoretically possible in these worlds to travel into the past, or otherwise influence the past.

Notice, by the way, how easy it had already become for physicists and mathematicians to speak of alternative universes. “In these worlds…,” Gödel writes. The title of his paper, when he published it in
Reviews of Modern Physics,
was “Solutions of Einstein’s Field Equations of Gravitation,” and a “solution” is nothing less than a possible universe. “All cosmological solutions with non-vanishing density of matter,” he writes, meaning
all possible universes that aren’t empty.
“In this paper I am proposing a solution” =
Here’s a possible universe for you.
But does this possible universe actually exist? Is it the one we’re living in?

Gödel liked to think so. Freeman Dyson, then a young physicist at the Institute, told me many years later that Gödel would ask him, “Have they proved my theory yet?” There are physicists today who will tell you that if a universe has been proved not to contradict the laws of physics, then yes, it is real. A priori. Time travel is possible.

That’s setting the bar fairly low. Einstein was more cautious. Yes, he acknowledged, “such cosmological solutions of the gravitation equations…have been found by Mr. Gödel.” But he added mildly, “It will be interesting to weigh whether these are not to be excluded on physical grounds.” In other words, don’t follow the math out the window.
^*4
Einstein’s caution did little to diminish the popularity of Gödel’s closed timelike curves among fans of time travel—and in their number we must count logicians, philosophers, and physicists. They wasted little time in launching the hypothetical Gödel rocket ships.

“Suppose our Gödelian spacetime traveller decides to visit his own past and talk to his younger self,” wrote Larry Dwyer in 1973. He specifies:

at
t
₁
,
T
talks to his younger self

at
t
₂
,
T
enters his rocket to begin his journey to the past.

Let
t
₁
= 1950;
t
₂
= 1974

Not the most original start, but Dwyer is a philosopher writing in
Philosophical Studies: An International Journal for Philosophy in the Analytic Tradition,
a far cry from
Astounding Stories.
Dwyer has done his homework: