Time Travel - Dr. Sean Carroll

Traveling to the Past?
 We travel through time every day, but we travel to the future.
Special relativity allows us to talk about changing the rate at which
we travel to the future. Because the amount of time that passes
depends on our trajectory through the world, we can actually get to
the future faster but not slower.
 The real question most people are interested in, however, is: Can
we travel to the past? If Newton had been right that space and time
were absolute, then the answer would be no. The laws according
to Newton are that there are separate moments in the history of the
universe, and you march forward through them; you cannot help
but do that.
 In special relativity, the answer is also no. Special relativity replaces
the Newtonian division of space and time with spacetime structured
by light cones. You are forced to move into the interior of your light
cone—that’s the same as saying that you must move slower than
light—and the light cones point into the future. They don’t go into
the past.
 In general relativity, the answer is probably not, but at least we can
wonder whether we could tilt the light cones enough to travel into
our personal futures and nevertheless end up in the past. In general
relativity, a time machine would be a twisting of light cones,
focusing them back on themselves so far that we could go into the
past while still moving forward in time.
A Realistic Time Machine
 If time travel were possible, it would not be what we generally
see in science fi ction movies. It would not involve some kind of
dematerialization in the present and rematerialization in a different
time. Real time travel would be a journey through spacetime, and a
true time machine would be some vehicle that moves you through
space and time but in a spacetime that allows you to visit your past.
 The most realistic version of time travel we can imagine is not
about building a machine but about building spacetime. Our goal
as potential time travelers is to warp spacetime so much that we can
personally move forward in time and nevertheless visit ourselves in
the past.
 To think about spacetime, we need to think locally, in this case,
about what is happening to you.

o What’s happening to you is that you’re growing older; you are
moving locally forward in time. In other words, you are staying
inside your light cone.
o As we said, general relativity tells us that light cones can be
twisted. Thus, we can imagine a light cone twisting so that you
could locally move forward but visit your past self because the
light cone had closed in on itself.
o This formation is called a closed timelike curve. A timelike
curve is simply a path through spacetime that is moving slower
than the speed of light. We ordinarily move on open timelike
curves, but a time machine would be a closed timelike curve.
 There are spacetimes that allow closed timelike curves, but is that
our universe? If we started in a universe that didn’t have closed
timelike curves, could we create them? Could we warp space
and time so much that we were able to visit our own past? These
questions remain open.
Kurt Gödel’s Version of Spacetime
 The most famous example of a kind of spacetime that has the
possibility of time travel built into it comes from Kurt Gödel, a
German mathematician. Gödel dabbled in general relativity and was
curious about Laplacian determinism, just as we are. He wondered
whether it was possible to start with one moment in time, evolve it
forward, and then evolve it backward.
 Neither quantum mechanics nor special relativity gets in the way of
doing that, but what about general relativity?
o In Gödel’s cosmological answer to this question, instead
of expanding, the universe is rotating. The stuff that sits
inside Gödel’s hypothetical universe is vacuum energy—the
cosmological constant energy that is inherent in space itself—
and swirling matter particles. The energy and particles cause
the curvature of spacetime to be light cones that are tilting
gradually as we travel through the universe.

o Every event in this universe sits on a closed timelike curve.
Everywhere you start, you can travel through some trajectory
in spacetime and eventually visit your past.
 It’s not diffi cult to write solutions to Einstein’s equation in general
relativity that look like time machines, such as an infi nite rotating
cylinder or cosmic strings, but all these examples in Gödel’s
universe have the property that they are infi nitely large.
o If we ask whether we can start with a universe that doesn’t
have time travel built in and create a situation that resembles
any of these, the answer seems to be no.
o The naïve solutions require an infi nite amount of energy. If
we try to make a fi nite cylinder or fi nite cosmic strings or a
fi nite amount of dust rotating, we don’t seem to get closed
timelike curves.
o These solutions are curiosities, but they are not realistic ways
to go about engineering a time machine.
Wormholes
 The most well-known way to construct a time machine in a fi nite
region of space is to use wormholes. A wormhole is a tube through
spacetime. It’s as if you enter some sphere locally and you are spit
out somewhere else arbitrarily far away. Wormholes can connect
different regions of spacetime, and you can use them to travel in
much shorter time periods than if you went the ordinary route.
negative energy—something that supplies us with a repulsive
gravitational force.
o Everything we know about in the universe has the gravitational
effect of pulling things toward it—positive energy—but to
keep a wormhole from collapsing, negative energy is needed
to push it apart.
o The mathematical physicist and cosmologist Frank Tipler,
as well as Stephen Hawking, have posited that manipulating
matter and energy in such a way as to create any form of closed
timelike curve will inevitably create some sort of singularity.
The density of curvature and energy in the universe would go
to infi nity somewhere.
The Paradoxes of Time Travel
 The grandfather paradox is one of the most famous problems that
arises from the idea of time travel: What stops me from traveling
backward in time and killing my grandparents before they ever met
so that neither my parents nor I were born? In that situation, who
committed the murders?
 One problem with this scenario is that we can’t pick the time we
travel back to. The entrance to a wormhole is like a portal; you go
in one end, and you come out somewhere else and some when else.

It’s also true that if you can go backward, then someone else can
come forward.
 Logic must still work even if there is time travel. You cannot kill
your grandparents and then be born to go back in time and kill your
grandparents. You can’t change the present moment because you
are in the present moment and you know what the present moment
has. It has you, for example, so nothing you do can truly prevent
you from coming into existence.
 If time travel were possible, the most likely scenario is that even
if you made it into the past, something would prevent you from
changing things that really happened.
 What is truly bothering us here is the arrow of time, which is
absolutely built into how we think about the past, present, and
future. As we said, we believe that we can make choices that affect
the future but not choices that affect the past. The past is tied down
in our epistemic knowledge because of the past hypothesis. If you
have a memory of something happening and your memory is valid,
then that is what happened and you can’t change it.
 If you put the possibility of time travel into this situation, then your
personal future becomes mixed up with the past of the universe.
You personally always age into your future light cone, but you go
off in a spaceship, zoom around a closed timelike curve, and come
to the past. Now, something that you thought was fi xed—the past—
gets mixed up with something you thought was alterable—your
personal future.
 It’s likely that time travel isn’t possible, but the many-worlds
interpretation of quantum mechanics offers a tiny loophole to the
impossibility of time travel.
o It is conceivable that if we had a closed timelike curve, we
could imagine going back into the past, truly changing the past,
and by doing so, bringing into existence a new world, a new
branch of the wave function of quantum mechanics.

o You could travel back in time from one branch of the wave
function, in which your grandparents did exist and you were
born, into another branch of the wave function, in which your
grandparents were killed and you were never born.
Conceptual Implications of Time Travel
 For our purposes, the most signifi cant implication of time travel is
that it would destroy the universality of the arrow of time.
 When we have the possibility of time travel, we no longer have
Laplace’s demon. We cannot slice the universe into moments of
time. The moments of time intersect with each other in complicated
ways, so that we cannot record the data of the universe at any one
moment and imagine running it forward and backward.
 If it is possible to build a wormhole connecting two different regions
of space, it is also possible to build a wormhole that connects two
different moments in time. Again, it’s relatively easy to write down
the equations to qualify this as a solution to Einstein’s theory
of relativity.
 The problem here is that wormholes involve physics that we
don’t think works in our world. In particular, wormholes collapse
instantly into black holes. To get around this problem, we need