Nothing can travel faster than the speed of light. But if it
*
could
*
, the conventional wisdom goes, it would travel back in time. Is the conventional wisdom right? Earlier this year, I was part of a team of researchers that
decided to find out whether “superluminal” travel—that is, going faster than the speed of light—really does take you back in time
.

To find out, we imagined a souped-up spacecraft that could somehow go faster than the speed of light and sent it on an (imaginary) journey out to a distant planet and back again. We started the ship up at the speed of light—denoted in physics equations as
*
c
*
—then gradually hit the gas pedal, accelerating past the universal “speed limit” to see how long the trip took at various different velocities. We used only the velocity addition formula from special relativity, as the other ones (time dilation, length contraction, etc.) all gave us goofy, imaginary answers. (Also, those formulas apply to what’s going on
*
inside
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of the spaceship, which is a whole other space-ball game.) We pictured what the trip would look like to an observer waiting back on Earth and watching the ship’s progress through a powerful super-telescope.

When the spaceship goes exactly at the speed of light, from the point of view of the observer back on Earth, everything appears normal as the ship speeds away. But just when the spaceship appears to reach the planet, it instantly materializes back on its landing pad on Earth, and the observer sees a huge flash of light containing an “instantaneous movie” of the spaceship’s trip back! Here’s why: imagine that it takes the ship ten years to get to the planet and ten years to get home. The light that the spaceship emits, say, five years into the journey will be seen by the Earthbound observer ten years after the ship took off, because it takes it five more years for it to get all the way back to Earth. Light the spaceship emits when it reaches the planet, ten years into its journey, makes it back to Earth twenty years after take-off. Now the ship turns around and heads home. As it gets closer to Earth, the light it emits has a shorter distance to backtrack. So, light from year 15 of the trip only has to travel for five years before it reaches the observer, 20 years after launch day. In fact, because the spaceship is “riding along” at the speed of light with the light it emits on the way back, the observer sees both the landed ship and the “movie” of its return journey, all at the same time, when it arrives back on Earth. Traveling at the speed of light, half of the journey appears to be instantaneous, but the ship hasn’t actually traveled back in time.

But what if the spaceship breaks the speed of light? Now, we are entering the purely theoretical realm of superluminal travel. The spaceship is outracing the light it emits, so when the spaceship takes off, it leaves its own light in the space-dust. At some point later, the spaceship arrives back on the landing pad, but since the light emitted closer to Earth is what the observer there will see first, the spacecraft’s journey will appear to her as a series of images retracing the ship’s journey in reverse, like a movie on rewind. Meanwhile, images from the spaceship’s outbound trip are still coming in, so the observer can see three versions of the spaceship: one image going forward towards the planet, one image heading in reverse towards the planet, and the real spaceship on the landing pad. We call this an “image pair creation event,” because the real ship is accompanied by two images.

You can think of it like mailing selfies home from long, round-trip vacation. Just as the spaceship was traveling faster than light, you are traveling faster than snail-mail, so you beat some (or all) of your mailed selfies home. The day after your homecoming, the mail carrier delivers two of your pictures: one from the trip out, and a second from your trip back. It’s a more mundane kind of image pair creation event: There are three versions of you there at the mailbox, but only one is real.

In the case of the faster-than-light spaceship, though, something very strange happens that our snail-mail analogy can’t account for: Eventually, as someone watches the two moving images, they will see them meet up and disappear at the planet at the same time in what is called an image pair annihilation event.

This is all very peculiar, but it doesn’t actually take you back in time. So, we imagined pushing the ship even faster. As the ship’s velocity increases, what the observer sees looks the same, but the reality is very different. The observer watches the spaceship leave the launch pad and head out to the planet, just as before; however, a
*
real
*
pair of spaceships appears on the landing pad, not simply one and an image! Then, one of the ships immediately takes off for the planet, again in reverse, and annihilates with the original ship in a
*
real
*
pair annihilation event at the planet.

Now, you may be wondering: Where did the extra spaceship come from? We wondered the same thing. Though our equations seem to be telling us that this second, physically-real ship should appear on the landing pad, the equations don’t give us many clues about where it came from or how it got there. Our guess is that one of the pair-created ships is made of exotic negative mass, if only to conserve the mass in the problem.

This is definitely weird and needs further research. But to achieve true backward time travel, we’ll have to go even faster!

So, we imagined nudging the ship’s velocity up once again. Finally, we pass the critical speed limit
^{
1
}
at which the total trip time is a negative number—we’ve gone back in time! In this scenario, a certain time before the spaceship takes off for the planet from the launch pad, a new pair of real spaceships is created on the landing pad, and one takes off toward the planet. Then, the original spaceship takes off at its normal time, and they annihilate as before at the planet. At this point, we could conjecture any time-travel related paradox imaginable, but since this post is about how we got to travel backwards in time and not time travel itself, we will leave those to the reader’s imagination.

So, simply going faster than light does not inherently lead to backwards time travel. Very specific conditions must be met—and, of course, the speed of light remains the maximum speed of anything with mass.

There is a lot more to this fascinating topic than this blog post can cover, so if you have any questions, comments, or concerns whatsoever, leave a comment, and I will do my best to address it!

^{
1
}
To travel backward in time, the spacecraft’s velocity must exceed:

where
*
u
*
is the velocity of the planet relative to Earth, and
*
c
*
is the speed of light.

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Go Deeper
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Picks for further reading
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The Nature of Reality:
Trap Doors in Time and Space: Teleportation, Time Travel, and Escape from Black Holes

Seth Lloyd, professor of quantum-mechanical engineering at MIT, investigates hypothetical methods of time travel, both forward and back.

The Open University:
The Grandfather Paradox – 60-Second Adventures in Thought

A brief video introduction to the grandfather paradox and its troubling implications for backward time travel.

Relativity for the Questioning Mind

In this friendly introduction to Einstein’s special and general relativity, Oberlin College physicist Daniel Styer provides a rigorous but non-technical look at time dilation, the twin paradox, and more.

Wikipedia:
The Tachyonic Antitelephone

A modest proposal for a way to send messages back in time.