You could say that this is exactly what Isaac Newton’s picture of gravity does—giving a relation between an object’s mass and the gravitational force it exerts. And you would be right. But the concept of space-time curvature gives rise to a much richer range of phenomena than a simple force. It allows a kind of repulsive gravity that drives our universe to expand, creates time dilation around massive objects and gravitational waves in space-time, and—in theory at least—it makes warp drives possible.
Alcubierre tackled his problem from the opposite direction to the usual one. He knew what kind of space-time curvature he wanted. It was one in which an object could surf on a region of warped space-time. So, he worked backwards to determine the kind of matter configuration you would need to create this. It wasn’t a natural solution of the equations, but rather something “made to order.” It wasn’t exactly what he would have ordered though. He found he needed exotic matter, something with a negative energy density, to warp space in the right way.
Exotic matter solutions are generally viewed with skepticism by physicists, and rightly so. While mathematically, one can describe material with negative energies, almost everything we know appears to have a positive energy. But in quantum physics, we have observed that small, temporary violations of energy positivity can occur, and so, “no negative energy” can’t be an absolute, fundamental law.
From Warp Drives to Waves
Given Alcubierre’s model of the warp drive space-time, we can begin to answer our original question: What would a signal from it look like?
One of the cornerstones of modern gravitational wave observations, and one of its greatest achievements, is the ability to accurately predict waveforms from physical scenarios using a tool called “numerical relativity.”
This tool is important for two reasons. First, because the data we get from detectors is still very noisy, which means we often have to know roughly what a signal looks like to be able to pull it out of the data stream. And second, even if a signal is so loud that it stands out above the noise, we need a model in order to interpret it. That is, we need to have modeled many different types of event, so we can match the signal to its type; otherwise we might be tempted to dismiss it as noise, or mislabel it as a black-hole merger.
One problem with the warp drive space-time is that it doesn’t naturally give gravitational waves unless it starts or stops. Our idea was to study what would happen when a warp drive stopped, particularly in the case of something going wrong. Suppose the warp drive containment field collapsed (a staple storyline in sci-fi); presumably there would be an explosive release of both the exotic matter and gravitational waves. This is something we can, and did, simulate using numerical relativity.
What we found was that the collapse of the warp drive bubble is indeed an extremely violent event. The enormous amount of energy needed to warp space-time gets released as both gravitational waves and waves of positive and negative matter energy. Unfortunately, it’s most likely the end of the line for the ship’s crew, who would be torn apart by tidal forces.
