If time travel turns out to be possible, I
hereby invite future time travelers to join me on set I’ll post the address one year from today. Okay. Right now. Well that's a bummer. Time travel stories are cool because both
the past and future are somehow more interesting than the present and because everyone secretly wants a do-over. But so far it appears we are doomed to live
consumed by regret in the eternal, boring present. Time marches on, inexorably and only forward. Or so we thought until Einstein came along. His special and general theories of relativity
changed the way we think about time forever, and believe it or not, their raw equations
permit time travel. They even tell us how to do it. So let’s review the possibilities, and decide
how possible time travel really is. The first approach to time travel uses only
special relativity, which describes how intervals of time and space are stretched or contracted
depending on relative speeds. A fast-moving spaceship appears to experience
a slower rate of time compared to someone waiting back on Earth. Do a trip around the galaxy at close to the
speed of light and very little time might pass from the perspective of the traveler. But they’ll find a minimum of hundreds of
thousands of years have passed when they get back to Earth. However, that’s a one-way trip in time, and is really
just traveling in the same temporal direction at different rates. So the original Planet of the Apes style time
travel is possible. But it’d be nicer to be able to go back
in time. Actually, the math does sort of allow that. The spaceship’s clock slows down as it speeds
up, and it stops completely at the speed of light. And at faster speeds, time should actually
tick backwards. So if you could travel faster than light you
could navigate a path to a point in spacetime before you departed. We saw how to Iconstruct such a path in a
previous challenge episode. Of course we know that the laws of physics
forbid faster than light travel. Or do they? In order for any object with regular mass
to even reach light speed it would need infinite energy – which can never be obtained. But notice I said “regular mass.” We can hack the equations of special relativity
by allowing mass to take values in the weird realm of imaginary or complex numbers. An object with imaginary mass is now restricted
to only traveling FASTER than light, never slower. That means it can only travel backwards in
time, not forwards. We call a particle with imaginary mass a tachyon. If we could control tachyons then perhaps
at least we could send information back in time. But do they exist? Does imaginary mass exist? This is an example where the equations
of a theory technically allow something to be true, but there’s still no good reason
to believe that it is. We’ve seen no evidence of tachyons, and common sense tells us we probably never will. So special relativity isn’t much help. Fortunately we still have the general theory
of relativity, which incorporates special relativity, but also explains the force of
gravity as a result of curvature in the fabric of spacetime due to the presence of mass and
energy. But GR describes a warping of space AND time. So maybe we can warp them enough to take us
back to our own past. The best-known approach is through something
called a wormhole. A wormhole is a particularly bizarre hypothetical
consequence of general relativity. Now, if space can be warped, then perhaps it can
be stretched in such a way as to create a tunnel between two points – and one whose
internal distances could be very short, even if the mouths of the tunnel are far apart. This has the obvious benefit of allowing you
to teleport between distant points in space, but also between distant points in time. This is how you do it: take one stable wormhole
large enough to be traversed. Accelerate one end to close to the speed of
light or drop it into a deep gravity well – its rate of time flow will slow relative
to the other end of the hole. Now bring the two ends back together. They will be offset in time: one portal permanently
stuck in the past of the other by some set interval. Travel through the “future” end
and you’ll exit in the "past." So this all sounds straightforward enough. But can wormholes even exist? There are a number of ways they might – from
connections between universes in the interiors of black holes to miniscule wormholes appearing
and vanishing on the tiniest scales of space and time. Now, these deserve their own episode. But for now, to build a useful time machine a wormhole has to be large enough to fit through and it has to be stable. The equations of GR do permit large wormholes,
but they are definitely not stable. They collapses on themselves instantly, leaving
inescapable black holes. In order to keep our wormhole time machine
operational, its throat needs to be kept open. We need to counter gravity, and to do that
we need another probably-non-existent form of mass – negative mass – also referred
to as exotic matter. As far as we know, mass can only take on positive,
real values, so a requirement of negative mass seems a non-starter. However there may be hope. Really what we need to open the wormhole
is a negative energy density. Some have argued that we already produce this
in the Casimir effect, in which the energy of the vacuum is lowered between two nearby
conducting plates. However there’s no clear path to translating
this to a large-scale negative energy distribution that could keep a wormhole open. And in fact we'd need entire planets – perhaps entire stars converted to negative energy to do this. Some other time travel options also involve
using negative energy densities - for example the Alcubierre warp drive, which we already
covered. In short – if you have exotic matter you
can probably time travel. But is negative mass-energy as much of a non-starter
as imaginary mass? While the actual equations of general relativity
themselves don’t prohibit it, there are a set of secondary rules in GR that do. These are the so-called energy conditions. They’re a set of requirements that do things
like prevent negative energies and enforce energy conservation. But the energy conditions don’t have a really
fundamental basis, and they're seen to be violated in some cases – like with the Casimir effect. We can’t completely rule out wormhole or
warp drive time machines based just on the energy conditions. And as it turns out, there may be other ways to build
time machines without either negative or imaginary masses. One example is the Tipler cylinder, conceived
by Frank Tipler based on a solution to the Einstein equations by Willem van Stockum. It’s simple: just build an infinitely long
cylinder of extreme density and set it rotating insanely quickly about its main axis. It will drag spacetime in its vicinity into
a sort of vortex. This generates sub-lightspeed paths through
spacetime that form closed loops, ending up back where they started in both space and
time. We call such paths closed time-like curves. A spaceship traveling along one of these curves
could return to a point in its own past. If you don’t have the budget for an infinitely
long cylinder, you could try building just a very, very long cylinder… and be horribly
disappointed. Stephen Hawking showed that unless the cylinder
is infinitely long this doesn’t work – unless you also modify the spacetime with negative energy. In which case you might as well just build
a wormhole. So it turns out that it’s not so hard to
find solutions in general relativity with closed timelike curves. Kurt Goedel, famous for his incompleteness
theorem, discovered one and he wasn’t even a physicist. His involved an entire universe, rotating
about a central axis and with matter and dark energy perfectly balancing it against collapse
or expansion. So to build this time machine we just need
construct an entire universe – which allows us to travel back in time only within that
universe. Thanks Goedel. Dragging the fabric of space in a circle
can give us our time-loops in very special, and frankly useless cases. Another one is the interior of a rotating
black hole – a so-called Kerr black hole. The maelstrom of spinning spacetime may generate
closed timelike curves deep down below the event horizon. So that’s fun: you can travel back to your
own past, but never to the time before you fell into the black hole, which is probably
the only thing you really want to do at that point. Unless it’s an Interstellar-style black
hole . . . general relativity doesn’t directly refute black hole time machine libraries. Yet. So it seems we have lots of ways to send things
back in time, but it all seem useless for actually making time machines for one reason or another. But the weird thing is that we don’t know
of one consistent, fundamental law in physics that prohibits true time travel. And yet most physicists still think it’s
impossible because time travel threatens the common-sense chain of cause and effect. It threatens causality. Break causality and you can create paradoxes–
time-travel to kill your grandfather and you would ever be born to time travel in the first
place. But there are no true paradoxes – only seeming
paradoxes that point to a gap in our understanding. Stephen Hawking put it nicely with his Chronology
Protection Conjecture. It states that the laws of physics will always
prevent time travel or allow it only when doesn’t cause paradoxes. In other words, the universe has to make sense,
time-travel or no. One way for a closed timelike curve to exist
without causing a paradox is expressed in the Novikov Self-Consistency Principle. Igor Novikov suggested that closed timelike
curves are fine as long as they’re self-consistent. As long as the backwards time-traveling configuration
of matter always leads to exactly to the same forward-traveling configuration. In other words, the loop creates itself. So I don’t know – you try to kill your
grandfather, only to become your own grandfather? Like Fry, let’s not think too hard about
that. An alternative lies in Hugh Everett’s many-worlds
interpretation of quantum mechanics, in which every possible universe exists, splitting
off in an infinite tree. So if you travel back in time and prevent
yourself being born – no problem - your photo doesn’t slowly fade away because you
were still born in that other timeline. Or time-travel could be genuinely impossible. Kip Thorn suggests there should probably be
one fundamental law of physics that prohibits it - for example, the quantum vacuum may
be unstable in the infinitely iterating loops of a closed timelike curves. On the other hand, Kip was the consultant
in Interstellar, so who knows what to believe? In actual fact we can’t know until we have
a full theory of quantum gravity – until then we’re working with the approximate
theories general relativity and quantum theory. Approximate theories can make bad predictions
– like the possibility of time travel. One final argument that time travel is impossible
is that we don’t see time travelers. Stephen Hawking put this to rigorous test
when he organized a cocktail party for time travelers, only advertising the event after
it ended. Tellingly, no one showed up. Though I don’t know – maybe there was a slightly
better party somewhere else in, like, all of history. For now we seem doomed to time travel only
forwards, and very slowly at that. We remain firmly in the grip of that one dimension
that we can never halt nor reverse it's pace: time.
