Historical research guide · 0577 · 2021
Worldline numerics applied to custom Casimir geometry generates unanticipated intersection with Alcubierre warp metric
Harold White · Jerry Vera · Arum Han · Alexander R. Bruccoleri · Jonathan MacArthur
In one minute
Harold White and his co-authors were doing something ordinary when they found something remarkable. Under a DARPA grant they were modelling a Casimir cavity — two mirrors microns apart, with tiny pillars standing on the midplane — to check whether a pillar would shield itself from the vacuum structure the team hoped to measure. They used worldline numerics, a loop-cloud method that handles any shape at all, and validated it against published plate and sphere results. The pillar does not shield itself; if anything the field strengthens around it by a factor of three to five. Then White noticed the shape of that field. Plotted in two dimensions it looks like the energy distribution Alcubierre’s warp metric asks for. A follow-up toy model — a one-micron sphere suspended in a four-micron cylinder — gives a toroidal distribution that correlates well with the warp requirement in three dimensions. The paper ends by proposing a chip you could build and a transit-time measurement you could make.
Connection
This is the paper that carries chapter 4’s warp metric out of pure geometry and into a fabrication drawing: a micron-scale structure whose computed vacuum energy distribution has the shape Alcubierre’s solution requires. It also gives chapters 2 and 5 a working numerical tool for the structured vacuum, and chapter 6 a live DARPA-funded hardware line — the pillar cavity whose predicted signal is a transient of roughly seven tenths of a millivolt.
From the source
Worldline numerics, the loop-cloud method developed for the Casimir effect, predicts spatial structure in the vacuum energy density rather than a single isotropic value, and can be applied to any geometry with effectively no restriction on curvature or smoothness — the authors validated their own implementation against published plate-plate and plate-sphere results before using it.Sections 3 and 3.1; Fig. 6
A 1 µm diameter pillar standing on the midplane of a 4 µm Casimir cavity does not screen itself from the cavity field; the model predicts the vacuum energy density inside the pillar is three to five times larger in magnitude than the level present with no pillar, so the pillar focuses the gradient rather than shielding it.Section 4; Fig. 7 panels (a) and (b)
The two-dimensional distribution of vacuum energy density around the pillar is qualitatively very similar to a two-dimensional representation of the energy density the Alcubierre warp metric requires — with the caveat the authors state themselves, that the Casimir plot is a linear extrusion giving a rod-like concentration while the Alcubierre plot is a revolution giving a toroidal one.Section 4; Fig. 9
A toy model of a 1 µm diameter sphere suspended at the centre of a 4 µm diameter cylinder yields a toroidal Casimir energy density distribution that correlates well with the toroidal requirement of the Alcubierre metric in three dimensions, computed on a 100 by 100 grid with a 2000 unit-loop ensemble.Section 4; Fig. 10 top panel
The cavities themselves are in fabrication: SU-8 permanent epoxy printed on a Nanoscribe 3D printer and then electroless-plated with silver, alongside deep reactive ion etching of high-aspect-ratio cavity planes into silicon, aimed at a predicted transient of about 0.7 mV from vacuum polarisation along the midplane of a 4 µm gap.Section 1; Figs. 1 and 2
The experiment the paper proposes is a chip carrying an array of nano-spheres suspended in nano-tubes, through which a pulse of current, photons or electrons is routed and its transit time compared against an identical path with no external tube — a measured difference would be an empirical confirmation of a real, nanoscale warp bubble.Section 4, closing paragraphs; Fig. 10 bottom panel
The way in
https://doi.org/10.1140/epjc/s10052-021-09484-zHow to cite it
Harold White, Jerry Vera, Arum Han, Alexander R. Bruccoleri, Jonathan MacArthur (2021) Worldline numerics applied to custom Casimir geometry generates unanticipated intersection with Alcubierre warp metric doi:10.1140/epjc/s10052-021-09484-z