The unphysical nature of "Warp Drive"

TL;DR

This paper analyzes the physical viability of the Alcubierre warp drive by applying flat-space quantum inequalities to the warp-bubble metric in a locally flat regime. By deriving the resulting bounds on the wall thickness and the total negative energy, the authors show that macroscopic warp bubbles would require unimaginably large amounts of negative energy, effectively making them unphysical under these quantum constraints. The analysis links the thickness of the bubble wall to the sampling time and local curvature, yielding wall thickness on the order of hundreds of Planck lengths and prohibitive energy budgets for practical travel. While extremely tiny (sub-atomic) bubbles could, in principle, reduce the energy demands, the quantum inequalities still impose severe limitations, suggesting that warp drive remains physically implausible for human-scale travel.

Abstract

We will apply the quantum inequality type restrictions to Alcubierre's warp drive metric on a scale in which a local region of spacetime can be considered ``flat''. These are inequalities that restrict the magnitude and extent of the negative energy which is needed to form the warp drive metric. From this we are able to place limits on the parameters of the ``Warp Bubble''. It will be shown that the bubble wall thickness is on the order of only a few hundred Planck lengths. Then we will show that the total integrated energy density needed to maintain the warp metric with such thin walls is physically unattainable.

Figures (3)

• Figure 1: The path of an observer who passes through the outer region of the bubble, shown in the bubble's rest frame. As viewed from the interior of the bubble, the observer is moving to the left.
• Figure 2: The worldline (the dark line) of the geodesic observer passing through the outer region of a warp bubble, plotted in the observer's initial rest frame. The two lighter diagonal lines are the worldlines of the center of the bubble wall on the front and rear edges of the bubble, respectively. The bubble has a radius of 3, a velocity of 1, and the $\sigma$ parameter is also 1. The plot shows an observer who begins at rest at $x=10$, $y^2+z^2 = \rho^2 = 4$. The shape function is of the form given by Alcubierre, Equation (\ref{['eq:alcub']}).
• Figure 3: The negative energy density is plotted for a longitudinal cross section of the warp metric traveling at constant velocity $v_s = 1$ to the right for the Alcubierre shape function. Black regions are devoid of matter, while white regions are maximal negative energy.