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 .

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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.