You could say that this is exactly what Isaac Newton’s diagram of gravity does – show the relationship between the mass of an object and the gravitational force it exerts. And that would be correct. But the concept of space-time curvature gives rise to much richer phenomena than simple forces. It allows for a kind of repulsive gravity, expanding the universe, creating time dilation around massive objects and gravitational waves in space-time, and, at least in theory, making warp drive possible.
Alcubierre approached the problem from the opposite direction: he knew the type of space-time curvature he was looking for: one that would allow objects to surf a warped region of space-time. So he worked backwards to determine the type of material configuration needed to produce this. It wasn’t a natural solution to the equations, but rather something “bespoke.” But it wasn’t exactly what he ordered. He discovered that to warp space correctly, he needed an exotic material with negative energy density.
Among physicists, the exotic matter solution is generally viewed with skepticism, and rightly so. Mathematically, it is possible to describe matter with negative energy, but almost everything we know seems to have positive energy. However, it has been observed in quantum physics that the positivity of energy can be violated slightly and temporarily, and “there is no negative energy” is not an absolute fundamental law.
From warp drive to waves
Considering Alcubierre’s warp drive space-time model, we can answer the original question: what would the signal from there look like?
One of the cornerstones of modern gravitational wave observations, and one of their 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, the data coming from the detectors is still very noisy, so to extract a signal from the data stream, we need to have a rough idea of what that signal looks like. Second, even if the signal is very large and stands out above the noise, we still need a model to interpret it. This means we need to model different types of events and match the signal with its type; otherwise we might ignore it as noise or misclassify it as a black hole merger.
One of the problems with warp drive space-time is that gravitational waves don’t naturally occur unless you start or stop it. Our idea was to explore what would happen if the warp drive were to stop, specifically if something went wrong. Suppose the containment field of the warp drive collapsed (a classic sci-fi storyline). There would likely be an explosion of both exotic matter and gravitational waves. This is something that can be simulated using numerical relativity, and we have done so.
What we discovered is that the collapse of the warp drive bubble would be a very violent event indeed. The enormous energy required to distort space-time would be released as gravitational waves and waves of positive and negative matter-energy. Unfortunately, it would likely be the end for the crew of the ship; they would be ripped apart by tidal forces.
