How Long a Warp Bubble Can Persist: Crossing Times and the Quantum-Inequality Clock

Three clocks govern a warp bubble of radius one hundred metres: light crosses the bubble in 3.34e-07 seconds and a one-metre wall in 3.34e-09 seconds, while the quantum-inequality sampling bound, evaluated schematically, licenses wall-density negative energy for about 2.62e+08 seconds at one-metre wall thickness, 1.48e+02 seconds at ten to the minus five metres, and 8.30e-05 seconds at ten to the minus ten metres. The licence therefore exceeds the bubble's own crossing time by fifteen orders of magnitude for the thick wall and still exceeds it at the thinnest tabulated wall, crossing below it only on extrapolation near a picometre. The verdict is deliberately two-sided: persistence is not the thick-wall bubble's problem, since its energy is, and persistence becomes binding only in the extreme thin-wall corner, where it adds an independent exclusion to a region already excluded on other grounds. All times are computed schematically from stated assumptions, not measured.