ENE-4: Van Den Broeck's pocket

Does not remove the negative energy, only its quantity.

Kind: constraint · Family: ENE (Energy) · Last reviewed: 2026-09-12

The result

A bubble whose interior is a 200 m pocket behind a femtometre-sized outer bubble reduces the Alcubierre negative energy from universe scale to about −2 × 10^30 kg, roughly a solar mass, with about 4.9 × 10^30 kg of positive energy alongside. The wall stays within about a hundred Planck lengths and the minimum curvature radius is about ten Planck lengths

What it forbids or costs

Does not remove the negative energy, only its quantity. Structure a few orders of magnitude above the Planck scale is its own bill

Escape hatches

None needed; this is itself an escape from ENE-3

Who it bites

Physics proposals

• SATISFIES: Bobrick and Martire 2021: physical warp drives. Its own pocket variant, equation (17), still carries negative density, in line with the entry's finding that the pocket changes the quantity not the sign; its appendix A.2 claim that Van Den Broeck's metric is a coordinate transformation of Alcubierre, which would undercut the entry's solar-mass figure, is shown by Santiago, Schuster and Visser (App. B) not to be a coordinate transformation, so the register figure stands
• SATISFIES: Van Den Broeck 1999: the pocket geometry. This paper is the entry: about $-2 \times 10^{30}$ kg negative, $4.9 \times 10^{30}$ kg positive, wall within about a hundred Planck lengths, minimum curvature radius about ten Planck lengths, all verified against the text.
• SATISFIES: Warp drives in modified gravity. DeBenedictis and Ilijic carry the Van Den Broeck pocket as their second case and find ENE-4's trade reproduced in spin: a higher peak density (about $10^{84}$ spin-one particles per cubic metre) in a far smaller volume.
• SILENT: Alcubierre 1994: the warp drive metric. The pocket geometry postdates the letter and is a modification of it; the original bubble has its interior and its wall at the same radius and pays the full ENE-3 bill. The reduction is scored in the Van Den Broeck dossier.
• SILENT: Everett and Roman 1997: the superluminal subway. No pocket-style reduction is attempted for the tube, and the paper predates Van Den Broeck; whether the trick transfers is unexamined here.
• SILENT: Fell and Heisenberg 2021: positive energy from hidden geometric structure. Van Den Broeck's pocket is cited as prior art and not used
• SILENT: Krasnikov 1998: the tube laid on the way out. Van Den Broeck's pocket trick is for bubbles; no analogous reduction is proposed for the tube here, and whether a conformal blow-up inside a tube could cut its bill has not been analysed in the sources this dossier could verify.
• SILENT: Lentz 2021: hyper-fast positive-energy solitons. Cites Van Den Broeck as a saving that "may provide significant savings in energy for the positive-energy soliton" and never applies it
• SILENT: Natário 2002: warp drive with zero expansion. The pocket trick (a conformal factor on the slices) is outside the class as defined, since it makes the slices non-flat; Natário does not use it and does not say whether a zero-expansion pocket exists.

Sources

• Van Den Broeck, Class. Quantum Grav. 16, 3973 (1999), arXiv:gr-qc/9905084 ✓