Paradoxes of Time Travel Philosophy Paper Prompt: What is time travel? Explain the grandfather paradox. Explain David Lewis’s solution to the grandfather paradox. Do you find Lewis’s solution convincing and why?
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（Grading rubric is sent as a screenshot） THE PARADOXES
OF TIME TRAVEL
David Lewis
T
travel, I maintain, is possible. The paradoxes of
time travel are oddities, not impossibilities. They
prove only this much, which few would have doubted:
that a possible world where time travel took place would
be a most strange world, different in fundamental ways
from the world we think is ours.
I shall be concerned here with the sort of time travel
that is recounted in science fiction. Not all science fiction
writers are clear-headed, to be sure, and inconsistent
time travel stories have often been written. But some
writers have thought the problems through with great
care, and their stories are perfectly consistent.1
If I can defend the consistency of some science fiction
stories of time travel, then I suppose parallel defenses
might be given of some controversial physical hypotheses, such as the hypothesis that time is circular or the
hypothesis that there are particles that travel faster than
light. But I shall not explore these parallels here.
What is time travel? Inevitably, it involves a discrepancy between time and time. Any traveler departs and
then arrives at his destination; the time elapsed from departure to arrival (positive, or perhaps zero) is the duration of the journey. But if he is a time traveler, the
separation in time between departure and arrival does
not equal the duration of his journey. He departs; he travels for an hour, let us say; then he arrives. The time he
reaches is not the time one hour after his departure. It
is later, if he has traveled toward the future; earlier, if he
has traveled toward the past. If he has traveled far toward the past, it is earlier even than his departure. How
can it be that the same two events, his departure and his
arrival, are separated by two unequal amounts of time?
It is tempting to reply that there must be two independent time dimensions; that for time travel to be possible, time must be not a line but a plane.2 Then a pair
IME
of events may have two unequal separations if they are
separated more in one of the time dimensions than in
the other. The lives of common people occupy straight
diagonal lines across the plane of time, sloping at a rate
of exactly one hour of time1 per hour of time2. The life
of the time traveler occupies a bent path, of varying
slope.
On closer inspection, however, this account seems not
to give us time travel as we know it from the stories.
When the traveler revisits the days of his childhood, will
his playmates be there to meet him? No; he has not
reached the part of the plane of time where they are. He
is no longer separated from them along one of the two
dimensions of time, but he is still separated from them
along the other. I do not say that two-dimensional time
is impossible, or that there is no way to square it with
the usual conception of what time travel would be like.
Nevertheless I shall say no more about two-dimensional
time. Let us set it aside, and see how time travel is possible even in one-dimensional time.
The world—the time traveler’s world, or ours—is a
four-dimensional manifold of events. Time is one dimension of the four, like the spatial dimensions except that
the prevailing laws of nature discriminate between time
and the others—or rather, perhaps, between various
timelike dimensions and various spacelike dimensions.
(Time remains one-dimensional, since no two timelike
dimensions are orthogonal.) Enduring things are timelike
streaks: wholes composed of temporal parts, or stages,
located at various times and places. Change is qualitative
difference between different stages—different temporal
parts—of some enduring thing, just as a “change” in
scenery from east to west is a qualitative difference between the eastern and western spatial parts of the landscape. If this paper should change your mind about the
From American Philosophical Quarterly, April 1976, pp. 145-152. © 1976 by North American Philosophical Publications. Reprinted by permission.
possibility of time travel, there will be a difference of
opinion between two different temporal parts of you, the
stage that started reading and the subsequent stage that
finishes.
If change is qualitative difference between temporal
parts of something, then what doesn’t have temporal
parts can’t change. For instance, numbers can’t change;
nor can the events of any moment of time, since they
cannot be subdivided into dissimilar temporal parts. (We
have set aside the case of two-dimensional time, and
hence the possibility that an event might be momentary
along one time dimension but divisible along the other.)
It is essential to distinguish change from “Cambridge
change,” which can befall anything. Even a number can
“change” from being to not being the rate of exchange
between pounds and dollars. Even a momentary event
can “change” from being a year ago to being a year and
a day ago, or from being forgotten to being remembered.
But these are not genuine changes. Not just any old reversal in truth value of a time-sensitive sentence about
something makes a change in the thing itself.
A time traveler, like anyone else, is a streak through
the manifold of space-time, a whole composed of stages
located at various times and places. But he is not a streak
like other streaks. If he travels toward the past he is a
zig-zag streak, doubling back on himself. If he travels
toward the future, he is a stretched-out streak. And if he
travels either way instantaneously, so that there are no
intermediate stages between the stage that departs and
the stage that arrives and his journey has zero duration,
then he is a broken streak.
I asked how it could be that the same two events were
separated by two unequal amounts of time, and I set
aside the reply that time might have two independent
dimensions. Instead I reply by distinguishing time itself,
external time as I shall also call it, from the personal time
of a particular time traveler: roughly, that which is measured by his wristwatch. His journey takes an hour of his
personal time, let us say; his wristwatch reads an hour
later at arrival than at departure. But the arrival is more
than an hour after the departure in external time, if he
travels toward the future; or the arrival is before the departure in external time (or less than an hour after), if
he travels toward the past.
That is only rough. I do not wish to define personal
time operationally, making wristwatches infallible by
definition. That which is measured by my own wristwatch often disagrees with external time, yet I am no
time traveler; what my misregulated wristwatch measures is neither time itself nor my personal time. Instead
of an operational definition, we need a functional definition of personal time; it is that which occupies a certain
role in the pattern of events that comprise the time traveler’s life. If you take the stages of a common person,
they manifest certain regularities with respect to external
time. Properties change continuously as you go along,
for the most part, and in familiar ways. First come in-
fantile stages. Last come senile ones. Memories accumulate. Food digests. Hair grows. Wristwatch hands move.
If you take the stages of a time traveler instead, they do
not manifest the common regularities with respect to external time. But there is one way to assign coordinates
to the time traveler’s stages, and one way only (apart
from the arbitrary choice of a zero point), so that the
regularities that hold with respect to this assignment
match those that commonly hold with respect to external
time. With respect to the correct assignment properties
change continuously as you go along, for the most part,
and in familiar ways. First come infantile stages. Last
come senile ones. Memories accumulate. Food digests.
Hair grows. Wristwatch hands move. The assignment of
coordinates that yields this match is the time traveler’s
personal time. It isn’t really time, but it plays the role in
his life that time plays in the life of a common person.
It’s enough like time so that we can—with due caution—
transplant our temporal vocabulary to it in discussing
his affairs. We can say without contradiction, as the time
traveler prepares to set out, “Soon he will be in the past.”
We mean that a stage of him is slightly later in his personal time, but much earlier in external time, than the
stage of him that is present as we say the sentence.
We may assign locations in the time traveler’s personal time not only to his stages themselves but also to
the events that go on around him. Soon Caesar will die,
long ago; that is, a stage slightly later in the time traveler’s personal time than his present stage, but long ago
in external time, is simultaneous with Caesar’s death.
We could even extend the assignment of personal time
to events that are not part of the time traveler’s life, and
not simultaneous with any of his stages. If his funeral in
ancient Egypt is separated from his death by three days
of external time and his death is separated from his birth
by three score years and ten of his personal time, then
we may add the two intervals and say that his funeral
follows his birth by three score years and ten and three
days of extended personal time. Likewise a bystander
might truly say, three years after the last departure of
another famous time traveler, that “he may even now—if
I may use the phrase—be wandering on some plesiosaurus-haunted oolitic coral reef, or beside the lonely saline
seas of the Triassic Age.”3 If the time traveler does wander on an oolitic coral reef three years after his departure
in his personal time, then it is no mistake to say with
respect to his extended personal time that the wandering
is taking place “even now”.
We may liken intervals of external time to distances
as the crow flies, and intervals of personal time to distances along a winding path. The time traveler’s life is
like a mountain railway. The place two miles due east
of here may also be nine miles down the line, in the
westbound direction. Clearly we are not dealing here
with two independent dimensions. Just as distance along
the railway is not a fourth spatial dimension, so a time
traveler’s personal time is not a second dimension of
time. How far down the line some place is depends on
its location in three-dimensional space, and likewise the
locations of events in personal time depend on their locations in one-dimensional external time.
Five miles down the line from here is a place where
the line goes under a trestle; two miles further is a place
where the line goes over a trestle; these places are one
and the same. The trestle by which the line crosses over
itself has two different locations along the line, five miles
down from here and also seven. In the same way, an
event in a time traveler’s life may have more than one
location in his personal time. If he doubles back toward
the past, but not too far, he may be able to talk to himself.
The conversation involves two of his stages, separated
in his personal time but simultaneous in external time.
The location of the conversation in personal time should
be the location of the stage involved in it. But there are
two such stages; to share the locations of both, the conversation must be assigned two different locations in personal time.
The more we extend the assignment of personal time
outwards from the time traveler’s stages to the surrounding events, the more will such events acquire multiple
locations. It may happen also, as we have already seen,
that events that are not simultaneous in external time
will be assigned the same location in personal time—or
rather, that at least one of the locations of one will be
the same as at least one of the locations of the other. So
extension must not be carried too far, lest the location of
events in extended personal time lose its utility as a
means of keeping track of their roles in the time traveler’s history.
A time traveler who talks to himself, on the telephone
perhaps, looks for all the world like two different people
talking to each other. It isn’t quite right to say that the
whole of him is in two places at once, since neither of the
two stages involved in the conversation is the whole of
him, or even the whole of the part of him that is located
at the (external) time of the conversation. What’s true is
that he, unlike the rest of us, has two different complete
stages located at the same time at different places. What
reason have I, then, to regard him as one person and not
two? What unites his stages, including the simultaneous
ones, into a single person? The problem of personal identity
is especially acute if he is the sort of time traveler whose
journeys are instantaneous, a broken streak consisting of
several unconnected segments. Then the natural way to regard him as more than one person is to take each segment
as a different person. No one of them is a time traveler,
and the peculiarity of the situation comes to this: all but
one of these several people vanish into thin air, all but another one appear out of thin air, and there are remarkable
resemblances between one at his appearance and another
at his vanishing. Why isn’t that at least as good a description as the one I gave, on which the several segments are
all parts of one time traveler?
I answer that what unites the stages (or segments) of
a time traveler is the same sort of mental, or mostly mental, continuity and connectedness that unites anyone else.
The only difference is that whereas a common person is
connected and continuous with respect to external time,
the time traveler is connected and continuous only with
respect to his own personal time. Taking the stages in
order, mental (and bodily) change is mostly gradual
rather than sudden, and at no point is there sudden
change in too many different respects all at once. (We
can include position in external time among the respects
we keep track of, if we like. It may change discontinuously with respect to personal time if not too much else
changes discontinuously along with it.) Moreover, there
is not too much change altogether. Plenty of traits and
traces last a lifetime. Finally, the connectedness and the
continuity are not accidental. They are explicable; and
further, they are explained by the fact that the properties
of each stage depend causally on those of the stages just
before in personal time, the dependence being such as
tends to keep things the same.4
To see the purpose of my final requirement of causal
continuity, let us see how it excludes a case of counterfeit
time travel. Fred was created out of thin air, as if in the
midst of life; he lived a while, then died. He was created
by a demon, and the demon had chosen at random what
Fred was to be like at the moment of his creation. Much
later someone else, Sam, came to resemble Fred as he
was when first created. At the very moment when the
resemblance became perfect, the demon destroyed Sam.
Fred and Sam together are very much like a single person: a time traveler whose personal time starts at Sam’s
birth, goes on to Sam’s destruction and Fred’s creation,
and goes on from there to Fred’s death. Taken in this
order, the stages of Fred-cum-Sam have the proper connectedness and continuity. But they lack causal continuity, so Fred-cum-Sam is not one person and not a time
traveler. Perhaps it was pure coincidence that Fred at his
creation and Sam at his destruction were exactly alike;
then the connectedness and continuity of Fred-cum-Sam
across the crucial point are accidental. Perhaps instead
the demon remembered what Fred was like, guided Sam
toward perfect resemblance, watched his progress, and
destroyed him at the right moment. Then the connectedness and continuity of Fred-cum-Sam has a causal explanation, but of the wrong sort. Either way, Fred’s first
stages do not depend causally for their properties on
Sam’s last stages. So the case of Fred and Sam is rightly
disqualified as a case of personal identity and as a case
of time travel.
We might expect that when a time traveler visits the
past there will be reversals of causation. You may punch
his face before he leaves, causing his eye to blacken centuries ago. Indeed, travel into the past necessarily involves reversed causation. For time travel requires
personal identity—he who arrives must be the same person who departed. That requires causal continuity, in
which causation runs from earlier to later stages in the
order of personal time. But the orders of personal and
external time disagree at some point, and there we have
causation that runs from later to earlier stages in the order of external time. Elsewhere I have given an analysis
of causation in terms of chains of counterfactual dependence, and I took care that my analysis would not rule
out casual reversal a priori.5 I think I can argue (but not
here) that under my analysis the direction of counterfactual dependence and causation is governed by the direction of other de facto asymmetries of time. If so, then
reversed causation and time travel are not excluded altogether, but can occur only where there are local exceptions to these asymmetries. As I said at the outset, the
time traveler’s world would be a most strange one.
Stranger still, if there are local—but only local—causal
reversals, then there may also be causal loops: closed
causal chains in which some of the causal links are normal in direction and others are reversed. (Perhaps there
must be loops if there is reversal: I am not sure.) Each
event on the loop has a causal explanation, being caused
by events elsewhere on the loop. That is not to say that
the loop as a whole is caused or explicable. It may not
be. Its inexplicability is especially remarkable if it is
made up of the sort of causal processes that transmit
information. Recall the time traveler who talked to himself. He talked to himself about time travel, and in the
course of the conversation his older self told his younger
self how to build a time machine. That information was
available in no other way. His older self knew how because his younger self had been told and the information
had been preserved by the causal processes that constitute recording, storage, and retrieval of memory traces.
His younger self knew, after the conversation, because
his older self had known and the information had been
preserved by the causal processes that constitute telling.
But where did the information come from in the first
place? Why did the whole affair happen? 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 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 the time travel?
I have committed a circularity in order not to talk
about too much at once, and this is a good place to set
it right. In explaining personal time, I presupposed that
we were entitled to regard certain stages as comprising
a single person. Then in explaining what united the
stages into a single person, I presupposed that we were
given a personal time order for them. The proper way
to proceed is to define personhood and personal time
simultaneously, as follows. Suppose given a pair of an
aggregate of persona-stages, regarded as a candidate for
personhood, and an assignment of coordinates to those
stages, regarded as a candidate for his personal time. If
the stages satisfy the conditions given in my circular explanation with respect to the assignment of coordinates,
then both candidates succeed: the stages do comprise a
person and the assignment is his personal time.
I have argued so far that what goes on in a time travel
story may be…
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