Faster-Than-Light: Antigravity and Exotic Matter

It is almost universally believed among experts that traveling faster-than-light (FTL) is impossible. But if it weren’t, how would we do it?

Relativity and the Speed of Light

The speed of light is special. The reason it is special has nothing to do with light; it is the fixed feature of the universe against which we measure space and time. Our human brains naturally think of space and time as absolute. It makes sense to us to believe that if two things happen at the same place but different times, or two things happen at the same time but different places, then that’s the way it is no matter how you look at them.

But space and time are not absolute, they are relative. Space is easier to comprehend. Suppose you are standing by a train track. As I pass by in a train car, you snap your fingers twice. To you, in the reference frame of the surface of the Earth, the two snaps happen at the same place. But to me, in the reference frame of the train car, the snaps happen at different places.

In the station's frame the snaps happen at the same place, but in the train's frame the snaps happen in different places.

There is no objective reference frame by which to determine whether something is stationary or moving. Everything is stationary from its own viewpoint.

What about time? The relativity of time is harder to wrap our heads around, because it only appears when observers are moving significantly close to the speed of light relative to each other.

Let’s go back to the train example. You hold your arms out to their full length, and snap both your hands at once as I pass by. In my reference frame, however, you snap the fingers of the hand that points forward along the track first, and the hand that points backward second.

We aren’t talking about the difference in how long it takes for sound and light to get to our eyes and ears. The discrepancy is still there after we account for that. In your reference frame, you snap the fingers of both of your hands at once, but in my reference frame, you snap them at different times.

In the station's frame the snaps happen at the same time, but in the train's frame the snaps happen at different times. This is not because of light lag; it is found to be true after we account for light lag.

It is a fact baked into the fabric of the universe that there is no objective “here,” and there is no objective “now.” The speed of light is the absolute which ties together all perspectives of space and time. It does not matter where you are, nor what speed or acceleration you are going, the speed of light is the same for you as it is for everyone else.

Chasing Light Beams

Suppose you turn a flashlight on and off, sending a pulse of light out into space, and then chase after it. You accelerate and accelerate and accelerate, but no matter how fast you go, that light pulse is still retreating away from you at the speed of light. You can never catch it.

What is your trip like in the reference frame of Earth? It is an objective fact that you never catch the flashlight’s pulse. Therefore, in the reference frame of Earth, you speed up and speed up, but the closer you get to the speed of light, the less you speed up. No matter how much you accelerate, you never reach light speed.

This is the trajectory of an object with constant proper acceleration under Special Relativity. The shape is a hyperbola, and it never becomes parallel with the light beam it chases. The dashed line is the asymptote, shown as a visual aid.

However, you can, in fact, travel across the universe. In Earth’s reference frame, you are experiencing time dilation. Time is running slower on your ship than it is on Earth. In your reference frame, the universe is undergoing space contraction. The distance to the stars in front of you is shrinking—not just that you’re getting closer, but there is less total space for you to go through. The distance from Earth to your destination is shorter in the ship’s reference frame than it is in Earth’s reference frame.

In a sense, this can almost feel like traveling faster than light, even though light always races ahead of you. But because of the way the time dilation and space contraction work out, it still takes years to travel light-years according to your departure and destination reference frames. We don’t just want to visit Alpha Centauri, we want to get back in time for work the next week. How do we do that?

Both science fiction writers and scientists have pondered this conundrum. I myself wrote my undergraduate thesis on the topic. There are three families of FTL methods: space warping, wormholes, and hyperspace. Space warping involves shortening the distance between the beginning and end of the journey. A wormhole is a shortcut between points in space. And hyperspace is a hypothetical more-than-three-dimensional space, in which our 3D universe is just a slice. All of these deserve their own discussions, so today we will focus on an essential ingredient for making and using these things, exotic matter.*

Negative Energy and Imaginary Mass

Exotic matter sounds exciting. What is it? If we put the space-time curvature for a warp drive or a traversable wormhole into the Einstein field equations, we find we need to generate antigravity. In order to get antigravity, we need negative energy. You might think negative energy means negative mass, because E = mc², but that equation is just a special case of the real equation,

As you can see, the mass in this equation is squared, so in order to end up with a negative energy, the mass must be complex. I don’t mean difficult to explain, we’re talking imaginary numbers, the square roots of negative numbers. Yeah, now you know why it’s called exotic matter.

Dark Energy

All right, so how do we make exotic matter? Do we have any clues to suggest it exists? Yes, in fact. Just a hint, but it’s more than nothing (or should I say, less than nothing?). The universe is expanding, and not only that, it is speeding up. Under attractive gravity, it should be slowing down. But because it is speeding up, we know there is a repulsive antigravity, some kind of “dark energy,” pushing everything apart.

We don’t know what this dark energy is. It is one of the biggest unsolved mysteries in physics. It could turn out to be completely useless. Or, it may be that it can be used to create exotic matter, or harnessed directly as negative energy.

Zero-Point Energy

There is one phenomenon people often point to as negative energy in the lab: the Casimir effect. So let’s talk about it, and see if it really is the magic ticket that will get us to the stars.

To begin, a little background knowledge. What we think of as empty space is not, strictly speaking, nothing. It has a number of quantum fields overlapping one another. For a deeper discussion of quantum fields, check out part 1 of our quantum physics series.

As it turns out, even when there are no particles, the quantum fields aren’t at 0 energy. An energy of absolute 0 leads to a contradiction in the math. Thus, the fields always have a buzz of vibrations far smaller than any particle. This is zero-point energy, also known as quantum foam.

The quantum foam is influenced by objects. If, for instance, there are two metal plates with empty space between them, these plates act as boundary conditions for the zero-point waves in the quantum fields. It’s like the harmonics of a guitar string, except instead of a string, it’s empty space. In empty space without the plates, there are no limits on the frequencies allowed in the quantum foam, but between the plates, only the harmonics are allowed.

If that was confusing, here is the bottom line: between the plates, the energy of the empty space is less than the energy of the empty space surrounding them. This is the Casimir effect.

The argument goes, if there is less energy between the plates than in normal empty space, that’s negative energy, so it should be usable for space warping and stuff like that. Here’s the problem, though. When it comes to gravity, it’s not the relative energy that matters, it’s the absolute energy. The zero-point energy in the Casimir effect may be less than the normal zero-point energy, but it is still more than absolute zero. Thus, although the Casimir effect looks like it creates negative energy, it is really still positive energy, and cannot be used for FTL technology.


As it turns out, getting negative energy is really, really hard. When it comes to FTL travel, we’re pretty much dead in the water. Of course, we don’t have any proof that exotic matter can’t exist, so there’s the possibility it’s hiding out somewhere in what’s left of the unknown. Maybe dark energy can provide a thread to follow, but that’s a big maybe. As things stand, it looks pretty certain that we’ll be stuck taking the slow route. Of course, that doesn’t mean we can’t use our imagination, and you can bet we will return to the topic of FTL in the future.

*We currently have no reason to believe hyperspace exists, nor any idea how to use it if it does. Exotic matter may be necessary, or may not be of any use at all.