Exotic Matter Budget of a Warp Bubble

Bubble Parameters

Coordinate velocity v_s 4.0 c

Bubble radius R 10 m

Wall sharpness σ 0.50 /m

Compare exotic mass to

Live Readouts

Peak energy density

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Shape f(0)

1.00

Total exotic mass |M|c²

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Ratio to benchmark

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How it works

The Alcubierre metric's shape function contracts space ahead of the ship and expands it behind:

f(r_s) = tanh(σ(r_s+R)) − tanh(σ(r_s−R))
         ───────────────────────────────
                  2 tanh(σR)

Its own field equations demand a stress-energy source with negative energy density concentrated in the thin wall, strongest off the direction of travel:

T⁰⁰(r_s,θ) = − c⁴/(32πG) · v_s² sin²θ · (df/dr_s)²

M·c² ≈ ∫ |T⁰⁰| dV   (integrated over the wall shell)

The heatmap below samples T⁰⁰ over the wall: white/orange = strong negative-energy demand, dim blue = negligible. The panel integrates that density numerically over the shell volume every time a slider moves and reports the total mass-equivalent |M| = E/c², then divides it by a real astronomical mass so the scale is tangible — for an everyday bubble radius pushed even a few times past light speed this ratio typically runs into the thousands or far beyond, which is the actual reason the drive stays theoretical: no known matter has negative energy density, let alone this much of it.

v_s — bubble's coordinate velocity in units of c.
R — bubble radius in metres; σ — how sharply the wall transitions from f=1 to f=0 (a sharper wall concentrates the same total curvature into less volume, raising the peak density).

Low |T⁰⁰| High |T⁰⁰| Peak negative energy

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