Using TARDIS to Mathematically Travel Through Time

Marty McFly, TARDIS and Albert Einstein
Marty and Albert ponder the intricacies of time travel. UNIVERSAL/SHIRLAINE FORREST/BETTMANN/GETTY

Will we ever be able to travel through time? Well, according to a new mathematical theory, it might be possible — assuming we can find some exotic matter.

Ever since H. G. Wells popularized the concept of the time machine with his 1895 novel, popular culture has been fascinated with the idea of building a machine that could magically slip through history. When Wells wrote "The Time Machine," science viewed time as a relentless river, forever flowing forward at a constant pace.

Then, more than 20 years later, Albert Einstein flipped our view of the universe on its head by introducing the world to his groundbreaking theory of general relativity. Suddenly, we realized that space and time were not as rigid as classical theories predicted. In Einstein's universe, space and time are unified to create spacetime and it can be warped, bent and even create ripples – a phenomenon known as gravitational waves.

General relativity opened the floodgates for time travel possibilities. In 1949, mathematician Kurt Gödel presented Einstein with the first mathematical model within which a rotating universe may allow time travel. More recently, physicists such as Kip Thorne have proposed the use of wormholes (another general relativity prediction) to facilitate time travel.

In 2013, Ben Tippett and colleague David Tsang formulated a mathematical model for time travel. The method was called TARDIS.

Of course, the name "TARDIS" – an acronym for traversable acausal retrograde domains in spacetime – was no coincidence.

"My work on this started right around the 50th anniversary of 'Doctor Who,'" says Tippett, who works as a mathematics and physics instructor at the University of British Columbia. "I've been doing analysis and rewriting of the paper on weekends and vacations since then, and finally got it published."

Published in the journal Classical and Quantum Gravity, TARDIS describes a different way to look at the dimension of time itself and how it might be manipulated to create a time machine — or, at least, a mathematical construction of a hypothetical time machine.


Space and Time

Although Einstein unified space and time over a century ago, too often we see time as a separate dimension, points out Tippett, an expert in general relativity.

 A common way to think of spacetime is to imagine a suspended sheet of rubber. If you roll a heavy object, like a bowling ball, across the sheet, the sheet will warp around the mass. This is one of the key tenets of general relativity; the curvature of spacetime (the warped rubber) around massive objects (bowling ball) creates gravity. The larger the mass, the greater the gravitational effects on spacetime. Mass and gravity are therefore intimately related.

This model may be a great way to imagine how the three dimensions of space get warped by mass, but what about time?

All four dimensions – the three dimensions of space and one of time – should be seen as a spacetime continuum. In this case, it's not only the three dimensions of space that are warped; time is, also.

Of course, we already know this. To keep the clocks on satellites in sync with clocks on Earth, a small correction for the effects of general relativity must be included in the satellites' software – satellites orbit Earth in a lower gravity environment than on Earth's surface. Therefore, time runs slower (albeit infinitesimally so) down here, deep in Earth's gravitational well.

Now take this reasoning to the extreme: Imagine you have a twin sister who is bravely traveling toward a black hole's event horizon – the point at which spacetime is so warped that not even light can escape the black hole's gravity. As she gets closer to the event horizon, spacetime becomes increasingly warped, gravity increases and time slows down. Assuming her spaceship has enough fuel, she pulls out before reaching the event horizon and zooms back to Earth. When she returns, having only aged a day, you're not there to welcome her. You're dead. In fact, the time dilation was so extreme during her mission that everyone grew old and died, human civilization is extinct and Earth is overrun with giant cockroaches.

This is a variation of what is known as the "Twin Paradox."


The Need for Exotic Matter

Rather than punching through spacetime (traveling through a wormhole) or traveling close to an impossibly massive object to warp spacetime (a black hole), TARDIS requires a type of spacetime curvature that cannot be produced by regular matter. According to general relativity, large masses of regular matter can only cause curvature that is gravitationally attractive. According to Tippett, the curvature required to build TARDIS can only be created using a bizarre, and currently unknown, type of matter known simply as "exotic matter" that has the opposite effect.

If, in the future, we find this exotic matter and work out how to harness it, the TARDIS "time machine" might send a time traveler backward and forward in time. The time traveler would be contained within a bubble of "normal" spacetime and exotic matter would then be applied to the bubble, making it travel through spacetime on a large, circular path. The traveler inside the bubble would feel a constant acceleration during their journey. The larger the circle, the further back and forward in time they would go.

But there's a catch.

"As far as I understand, we have never detected, observed, or interacted with exotic matter," Tippett tells HowStuffWorks. "Exotic matter is a class of matter which is gravitationally repulsive – or rather, it causes a type of spacetime curvature associated with gravity pushing things apart – and we've never seen it."


Paradoxes Galore?

Now, let's just assume that we overcome the exotic matter problem and achieve time travel, wouldn't traveling back in time cause all kinds of "Back to the Future"-like spacetime continuum paradoxes? Could Marty traveling back to 1955 really jeopardize his own life by accidentally becoming his own mother's love interest?

If traveling back in time can change history, just like Marty's existential crisis predicts, we have a paradox. In this case, it is known as the "Grandfather Paradox," and it's a good way to visualize this problem. The paradox basically asks: If you traveled back in time and killed your grandfather (or your mother never ends up marrying your biological father), would you cease to exist?

"As Doc Brown reminds us: the resolution of the Grandfather Paradox is to think four-dimensionally," says Tippett.

According to Einstein's theory, all past, present and future history is laid out in spacetime, like threads woven into a four-dimensional tapestry. If you went back in time and met your younger self, a relativistic situation called a "closed timelike curve," could you give your younger self the Grays Sports Almanac, thereby dramatically changing your financial future?

To address this paradox, Russian theoretical physicist Igor Novikov proposed the universe has a failsafe and, while it might allow closed timelike curves (i.e., time travelers), the tapestry of spacetime cannot be changed no matter how hard you try. Whenever you try to give your past self the almanac, some situation will arise to prevent a paradox from occurring. The universe will adapt and counter your paradoxical (and, frankly, reckless) actions.

"The Grandfather Paradox, in my mind, is resolved with the Novikov self-consistency condition: you can't change the past," says Tippett. "All events, past and future, are laid out on the four-dimensional spacetime, and cannot change.

"While an object can interact with its own past, it cannot do so in a way which is inconsistent with its own history," he adds.

Tippett likens the idea to the plot of the movie and TV series "12 Monkeys" – the universe will prevent you from altering historic events. But, he admits, we probably wouldn't be able to test any of these hypotheses until we actually do achieve time travel.

That said, although a fun idea to ponder, turning a mathematical model into a fully operational time machine is unlikely.

"The emphasis here is on 'mathematically possible, but physically improbable. Very, very, very improbable,'" concludes Tippett.