Null geodesics in the Alcubierre warp-drive spacetime: the view from the bridge

Abstract

The null geodesic equations in the Alcubierre warp drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the "warp drive" bubble to reach an observer at the origin of the warp effect. We find that for a starship with an effective warp speed exceeding the speed of light, stars in the forward hemisphere will appear closer to the direction of motion than they would to an observer at rest. This aberration is qualitatively similar to that caused by special relativity. Behind the starship, a conical region forms from within which no signal can reach the starship, an effective "horizon". Conversely, there is also an horizon-like structure in a conical region in front of the starship, into which the starship cannot send a signal. These causal structures are somewhat analogous to the Mach cones associated with supersonic fluid flow. * e-mail: chadc@orion.physics.montana.edu † e-mail: hiscock@montana.edu ‡ e-mail: shane@orion.physics.montana.edu 1The existence of these structures suggests that the divergence of quantum vacuum energy when the starship effectively exceeds the speed of light, first discovered in two dimensions, will likely be present in four dimensions also, and prevent any warp-drive starship from ever exceeding the effective speed of light.Typeset using REVT E X 2 Alcubierre [1] has described a spacetime which has features reminiscent of the "warp drive" common in science fiction lore. The Alcubierre solution allows a "starship" to have an apparent speed relative to distant observers which is much greater than the speed of light, an effect caused by the spacetime expanding behind and contracting in front of the starship.In such a spacetime, passengers on the starship can travel arbitrarily large distances in small amounts of proper time; further, there is no time dilation effect between the starship and clocks outside the region affected by the warp drive.If a technology based on such a spacetime could be realized, space travel to distant points in our Universe could seem almost plausible. The Alcubierre warp drive spacetime has properties, however, which make it unlikely to be physical. As Alcubierre himself pointed out, in order to create the distortion of spacetime which produces the warp drive effect, "exotic" matter is required, which violates the weak, strong, and dominant energy conditions. Although quantized fields can locally violate the energy conditions, an analysis by Pfenning and Ford [2] has shown that the distribution of exotic matter needed to generate the warp 'bubble' around the starship appears quite implausible. Additional work has shown that any spacetime that permits apparent superluminal travel will inevitably violate the weak and averaged null energy conditions [3][4][5]. On the other hand, Van Den Broeck has recently shown how to significantly reduce the amount of negative energy density matter required for the warp drive to the order of grams [6].Even if one could somehow obtain the ...

Detailed study of null and timelike geodesics in the Alcubierre warp spacetime

“…As already found by Clark et al [3] there is no aberration for ξ = 90 • . Hence, light rays that originate precisely at 90 • to the direction of motion of the warp bubble will be seen by an observer at the bridge at an angle ξ = 90 • (see also "Appendix D").…”

“…The bending of light as well as the frequency shift for an observer at the center of the warp bubble (view from the bridge) was already discussed in detail by Clark et al [3]. What is not known so far is how the warp bubble influences the lensing of point-like objects.…”

“…A detailed discussion of the paths of null geodesics and their frequency shift as observed from inside the Alcubierre warp bubble, in particular the emergence of an apparent horizon behind the warp bubble, was given by Clark et al [3]. The influence of a warp bubble passing between the observer and a distant object onto the visual distortion was studied by Weiskopf [4] using four-dimensional raytracing.…”

Weak Energy Condition Violation and Superluminal Travel

“…Reminiscence of an Event Horizon: The appearance of an event horizon becomes evident in the 2-dimensional model of the Alcubierre space-time, with ρ = 0 [10,11,12]. The axis of symmetry coincides with the line element of the spaceship.…”

Fundamental limitations on ‘warp drive’ spacetimes

“…We will take the bubble velocity to be non-relativistic, v ≪ 1. Thus we are not focussing attention on the "superluminal" aspects of the warp bubble, such as the appearance of horizons [27,28,29], and of closed timelike curves [30], but rather on a secondary unremarked effect: The warp drive (if it can be realised in nature) appears to be an example of a "reaction-less drive" wherein the warp bubble moves by interacting with the geometry of spacetime instead of expending reaction mass.…”