Is Time Travel Impossible?

If time travel turns out to be possible, Ihereby 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 boththe 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 liveconsumed 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 relativitychanged the way we think about time forever, and believe it or not, their raw equationspermit time travel.

They even tell us how to do it.

So let’s review the possibilities, and decidehow possible time travel really is.

The first approach to time travel uses onlyspecial relativity, which describes how intervals of time and space are stretched or contracteddepending on relative speeds.

A fast-moving spaceship appears to experiencea slower rate of time compared to someone waiting back on Earth.

Do a trip around the galaxy at close to thespeed of light and very little time might pass from the perspective of the traveler.

But they’ll find a minimum of hundreds ofthousands of years have passed when they get back to Earth.

However, that’s a one-way trip in time, and is reallyjust traveling in the same temporal direction at different rates.

So the original Planet of the Apes style timetravel is possible.

But it’d be nicer to be able to go backin time.

Actually, the math does sort of allow that.

The spaceship’s clock slows down as it speedsup, and it stops completely at the speed of light.

And at faster speeds, time should actuallytick backwards.

So if you could travel faster than light youcould navigate a path to a point in spacetime before you departed.

We saw how to Iconstruct such a path in aprevious challenge episode.

Of course we know that the laws of physicsforbid faster than light travel.

Or do they? In order for any object with regular massto 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 relativityby allowing mass to take values in the weird realm of imaginary or complex numbers.

An object with imaginary mass is now restrictedto only traveling FASTER than light, never slower.

That means it can only travel backwards intime, not forwards.

We call a particle with imaginary mass a tachyon.

If we could control tachyons then perhapsat least we could send information back in time.

But do they exist? Does imaginary mass exist? This is an example where the equationsof a theory technically allow something to be true, but there’s still no good reasonto 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 theoryof relativity, which incorporates special relativity, but also explains the force ofgravity as a result of curvature in the fabric of spacetime due to the presence of mass andenergy.

But GR describes a warping of space AND time.

So maybe we can warp them enough to take usback to our own past.

The best-known approach is through somethingcalled a wormhole.

A wormhole is a particularly bizarre hypotheticalconsequence of general relativity.

Now, if space can be warped, then perhaps it canbe stretched in such a way as to create a tunnel between two points – and one whoseinternal distances could be very short, even if the mouths of the tunnel are far apart.

This has the obvious benefit of allowing youto teleport between distant points in space, but also between distant points in time.

This is how you do it: take one stable wormholelarge enough to be traversed.

Accelerate one end to close to the speed oflight or drop it into a deep gravity well – its rate of time flow will slow relativeto the other end of the hole.

Now bring the two ends back together.

They will be offset in time: one portal permanentlystuck in the past of the other by some set interval.

Travel through the “future” endand 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 – fromconnections between universes in the interiors of black holes to miniscule wormholes appearingand 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, leavinginescapable black holes.

In order to keep our wormhole time machineoperational, its throat needs to be kept open.

We need to counter gravity, and to do thatwe need another probably-non-existent form of mass – negative mass – also referredto 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 wormholeis a negative energy density.

Some have argued that we already produce thisin the Casimir effect, in which the energy of the vacuum is lowered between two nearbyconducting plates.

However there’s no clear path to translatingthis 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 involveusing negative energy densities – for example the Alcubierre warp drive, which we alreadycovered.

In short – if you have exotic matter youcan probably time travel.

But is negative mass-energy as much of a non-starteras imaginary mass? While the actual equations of general relativitythemselves 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 thingslike prevent negative energies and enforce energy conservation.

But the energy conditions don’t have a reallyfundamental basis, and they're seen to be violated in some cases – like with the Casimir effect.

We can’t completely rule out wormhole orwarp drive time machines based just on the energy conditions.

And as it turns out, there may be other ways to buildtime machines without either negative or imaginary masses.

One example is the Tipler cylinder, conceivedby Frank Tipler based on a solution to the Einstein equations by Willem van Stockum.

It’s simple: just build an infinitely longcylinder of extreme density and set it rotating insanely quickly about its main axis.

It will drag spacetime in its vicinity intoa sort of vortex.

This generates sub-lightspeed paths throughspacetime that form closed loops, ending up back where they started in both space andtime.

We call such paths closed time-like curves.

A spaceship traveling along one of these curvescould return to a point in its own past.

If you don’t have the budget for an infinitelylong cylinder, you could try building just a very, very long cylinder… and be horriblydisappointed.

Stephen Hawking showed that unless the cylinderis infinitely long this doesn’t work – unless you also modify the spacetime with negative energy.

In which case you might as well just builda wormhole.

So it turns out that it’s not so hard tofind solutions in general relativity with closed timelike curves.

Kurt Goedel, famous for his incompletenesstheorem, discovered one and he wasn’t even a physicist.

His involved an entire universe, rotatingabout a central axis and with matter and dark energy perfectly balancing it against collapseor expansion.

So to build this time machine we just needconstruct an entire universe – which allows us to travel back in time only within thatuniverse.

Thanks Goedel.

Dragging the fabric of space in a circlecan give us our time-loops in very special, and frankly useless cases.

Another one is the interior of a rotatingblack hole – a so-called Kerr black hole.

The maelstrom of spinning spacetime may generateclosed timelike curves deep down below the event horizon.

So that’s fun: you can travel back to yourown past, but never to the time before you fell into the black hole, which is probablythe only thing you really want to do at that point.

Unless it’s an Interstellar-style blackhole .

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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 thingsback 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 knowof one consistent, fundamental law in physics that prohibits true time travel.

And yet most physicists still think it’simpossible 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 firstplace.

But there are no true paradoxes – only seemingparadoxes that point to a gap in our understanding.

Stephen Hawking put it nicely with his ChronologyProtection Conjecture.

It states that the laws of physics will alwaysprevent 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 existwithout causing a paradox is expressed in the Novikov Self-Consistency Principle.

Igor Novikov suggested that closed timelikecurves are fine as long as they’re self-consistent.

As long as the backwards time-traveling configurationof 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 yourgrandfather, only to become your own grandfather? Like Fry, let’s not think too hard aboutthat.

An alternative lies in Hugh Everett’s many-worldsinterpretation of quantum mechanics, in which every possible universe exists, splittingoff in an infinite tree.

So if you travel back in time and preventyourself being born – no problem – your photo doesn’t slowly fade away because youwere still born in that other timeline.

Or time-travel could be genuinely impossible.

Kip Thorn suggests there should probably beone fundamental law of physics that prohibits it – for example, the quantum vacuum maybe unstable in the infinitely iterating loops of a closed timelike curves.

On the other hand, Kip was the consultantin Interstellar, so who knows what to believe? In actual fact we can’t know until we havea full theory of quantum gravity – until then we’re working with the approximatetheories general relativity and quantum theory.

Approximate theories can make bad predictions– like the possibility of time travel.

One final argument that time travel is impossibleis that we don’t see time travelers.

Stephen Hawking put this to rigorous testwhen he organized a cocktail party for time travelers, only advertising the event afterit ended.

Tellingly, no one showed up.

Though I don’t know – maybe there was a slightlybetter party somewhere else in, like, all of history.

For now we seem doomed to time travel onlyforwards, and very slowly at that.

We remain firmly in the grip of that one dimensionthat we can never halt nor reverse it's pace: time.

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