Warp Drive: Alcubierre Metric Simulator

Alcubierre Bubble

Bubble speed 2.0×c

Bubble radius 55 u

Wall sharpness 0.09

θ at front wall

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θ at rear wall

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θ inside bubble

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Coordinate distance

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How it works

The Alcubierre metric moves a small flat region of spacetime — the "bubble" — through the universe by contracting space in front of it and expanding space behind it, rather than moving the ship through space in the usual sense. Inside the bubble the ship sits in ordinary flat spacetime, feels no acceleration, and never locally exceeds the speed of light; only the bubble wall itself distorts the geometry.

ds² = −c²dt² + (dx − v_s·f(r_s)·dt)² + dy² + dz²
f(r_s) = [tanh(σ(r_s+R)) − tanh(σ(r_s−R))] / [2·tanh(σR)]
θ = v_s · (x−x_s)/r_s · ∂f/∂r_s

f(r_s) — the shaping function: 1 deep inside the bubble (flat interior), 0 far outside (undisturbed universe), with a thin transition wall at radius R.
θ — the volume-expansion scalar shown as the heatmap: negative (red) ahead of the ship means space is being contracted; positive (blue) behind means it is being expanded.
Wall sharpness (σ) — how abruptly f transitions; a sharper wall concentrates the curvature — and the exotic negative-energy density the wall requires — into a thinner shell.
This is a genuine 1994 general-relativity solution, not a propulsion design: it requires a wall of matter with negative energy density, which no known material provides. The animation is a real-physics visualization, not a science-fiction depiction.

Contraction (θ<0, ahead) Expansion (θ>0, behind) Ship / bubble wall