# Can Imaginary Numbers Solve the Problem of Faster-Than-Light Travel?

Faster-than-light travel, or "warp speed," is a ubiquitous trope in science fiction, but could the science ever hold up in real life? Physicist and science fiction author Catherine Asaro has found a way to modify Einstein's equations in order to make them compatible with an FTL drive, using a fairly simple solution involving imaginary numbers.

In hard science fiction, the distance between stars and planets presents a conundrum, as it would significantly hinder the plot of a space-bound novel or film if the characters needed centuries to travel to each place. So most works get around that issue by incorporating some kind of "warp drive" that allows for faster-than-light travel, but, as Asaro explained at a panel at the Escape Velocity convention in Washington D.C. this weekend, most of them gloss over the scientific basis for the drive, because based on Einstein's theory of relativity, there isn't one.

But in spite of the fact that FTL travel does not seem scientifically plausible, Asaro was determined to find some kind of mathematical justification for her own sci-fi novels. So instead of ignoring Einstein's equations, she came up with a modified version that made speed an imaginary number, a complex number defined by a real number multiplied by

According to Asaro, this effectively solved the problem of FTL travel, at least in a limited sense. Imaginary numbers don't have a physical equivalent in the real world, which means that as far as we know, the same goes for "complex speed," as she calls it in her paper published in the American Journal of Physics. So it's really just a thought problem, but if there were a physical equivalent, it would theoretically allow FTL travel to work in real life.

As a result of this "inversion," according to Asaro, all of the aforementioned effects that would occur when approaching light speeds would occur when traveling slower than the speed of light, while FTL travel would be perfectly normal.

For now, this is just a thought problem, but could we ever discover the physical analog for complex speed in real life? Probably not, since the science of FTL travel, if it does exist, is likely governed by completely different equations that we can't even fathom yet.

In hard science fiction, the distance between stars and planets presents a conundrum, as it would significantly hinder the plot of a space-bound novel or film if the characters needed centuries to travel to each place. So most works get around that issue by incorporating some kind of "warp drive" that allows for faster-than-light travel, but, as Asaro explained at a panel at the Escape Velocity convention in Washington D.C. this weekend, most of them gloss over the scientific basis for the drive, because based on Einstein's theory of relativity, there isn't one.

"The problem for light speed travel in sci-fi is you can never get to the speed of light," Asaro said. "As you approach the speed of light, your mass becomes infinite... Time dilates until it essentially stops."

But in spite of the fact that FTL travel does not seem scientifically plausible, Asaro was determined to find some kind of mathematical justification for her own sci-fi novels. So instead of ignoring Einstein's equations, she came up with a modified version that made speed an imaginary number, a complex number defined by a real number multiplied by

*i*, or the square root of -1.According to Asaro, this effectively solved the problem of FTL travel, at least in a limited sense. Imaginary numbers don't have a physical equivalent in the real world, which means that as far as we know, the same goes for "complex speed," as she calls it in her paper published in the American Journal of Physics. So it's really just a thought problem, but if there were a physical equivalent, it would theoretically allow FTL travel to work in real life.

"I now had a framework based on relativistic physics that I could use to let my starships break the interstellar speed laws," Asaro wrote in an essay for PBS. "I called the process 'inversion' because if you are going faster than light, relativity predicts the constellations you see will be flipped around (inverted) from their positions as seen at slower than light speeds."

As a result of this "inversion," according to Asaro, all of the aforementioned effects that would occur when approaching light speeds would occur when traveling slower than the speed of light, while FTL travel would be perfectly normal.

Once we're traveling at faster than light speeds, our mass decreases, time contracts, and length dilates. Now we have a lower speed limit! We can't go slower than light. The possibilities for the science fiction writer are wonderfully entertaining.

For now, this is just a thought problem, but could we ever discover the physical analog for complex speed in real life? Probably not, since the science of FTL travel, if it does exist, is likely governed by completely different equations that we can't even fathom yet.

"If it is possible to circumvent that pesky speed limit, it's unlikely the physics would be the same in the faster-than-light realm as in the slower-than-light universe, no more than the physics of relativistic space travel is the same as what we experience day-to-day in our much slower existence.

Someday new scientific developments will undoubtedly revolutionize our understanding of the universe just as Einstein's theories changed our world. We've barely scratched the surface of what the cosmos has to teach us."

Someday new scientific developments will undoubtedly revolutionize our understanding of the universe just as Einstein's theories changed our world. We've barely scratched the surface of what the cosmos has to teach us."