Faster-Than-Light

For several decades, science fiction media (TV, film, and novels) began to adopt traversable wormholes, and more recently “stargates,” for interstellar travel schemes that allowed their heroes to travel throughout the galaxy. In 1985, CalTech physicist Kip Thorne and coworkers discovered the principle of traversable wormholes based on Einstein’s General Theory of Relativity. They did this as an academic exercise, and in the form of problems for a physics final exam, at the request of Carl Sagan who had then completed the draft of his novel Contact. This little exercise led to a continuous line of insights and publications in general relativity research – the study of traversable wormholes and time machines. Wormholes are hyperspace tunnels through spacetime connecting together either remote regions within our universe or two different universes; they even connect together different dimensions and different times. Space travelers would enter one side of the tunnel and exit out the other, passing through the throat along the way. The travelers would move at ≤ c (c is the speed of light, 3 × 108 m/s) through the wormhole and therefore not violate Special Relativity, but external observers would view the travelers as having traversed multi-light year distances through space at faster-than-light (FTL) speed. A “stargate” was later found to be a very simple special class of traversable wormhole solutions to Einstein’s general relativistic field equation.

This development was later followed by M. Alcubierre’s formulation in 1994 of the “warp drive” spacetime metric, which was another solution to the general relativistic field equations. Alcubierre derived a metric motivated by cosmological inflation that would allow arbitrarily short travel times between two distant points in space. The behavior of the warp drive metric provides for the simultaneous expansion of space behind the spacecraft and a corresponding contraction of space in front of the spacecraft. The warp drive spacecraft would appear to be “surfing on a wave” of spacetime geometry. A spacecraft can be made to exhibit an arbitrarily large apparent FTL speed (>> c) as viewed by external observers, but its moving local rest frame never travels outside of its local comoving light cone, and thus does not violate Special Relativity.

How does one study the physics of FTL spacetimes within the framework of general relativity theory? When studying spacetime physics, the normal philosophy is to take the general relativistic field equations, add some form of matter, make simplifying assumptions, and then solve to deduce what the geometry of spacetime will be. This is very difficult to do because there are ten nonlinear second-order partial differential equations with four redundancies (arbitrary choice of spacetime coordinates) and four constraints (stress-energy conservation). There is a tremendous body of research that takes exactly this approach, either analytically or numerically. However, this is not the best strategy for understanding FTL spacetimes. The appropriate strategy is to decide beforehand on a definition of the traversable wormhole or warp drive that you desire and decide what the spacetime geometry should look like. Given the desired geometry, use the general relativistic field equations to calculate the distribution of matter required to produce this geometry. Then one needs to assess whether the required distribution of matter is physically reasonable and whether it violates any basic rules of physics – performing sanity checks is a good thing to do in physics.

The implementation of FTL interstellar travel via traversable wormholes, warp drives, or other FTL spacetime modification schemes generally requires the engineering of spacetime into very specialized local geometries. The analysis of these via the general relativistic field equations plus the resultant source matter equations of state demonstrate that such geometries require the use of “exotic” matter in order to produce the requisite FTL spacetime modification. Exotic matter is generally defined by general relativity physics to be matter that possesses (renormalized) negative energy density or negative energy flux, negative pressure, or both – this matter must also violate the general relativistic Hawking-Ellis energy conditions. Negative energy and negative pressure produce gravitational repulsion or what is often called antigravity. Exotic matter is a very misunderstood and misapplied term by the non-general relativity community. We clear up this misconception by defining what negative energy is, where it can be found in nature, and we also review the experimental concepts that have been proposed to generate negative energy in the laboratory. Also, it has been claimed that FTL spacetimes are not plausible because exotic matter violates the Hawking-Ellis energy conditions. However, it has been shown that this is a spurious issue. The identification, magnitude, and production of exotic matter is seen to be a key technical challenge, however. FTL spacetimes also possess features that challenge the notions of causality and there are alleged constraints placed upon them by quantum effects. These issues are summarized in the links in the left column.