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April 14, 20260 citationsOpen Access

Sphere-in-cylinder Casimir topology in commodity zeolites: negative vacuum energy density 10¹⁰ times denser than engineered micrometer cavities

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BHBradley John HartOre Holdings (United States)

Key Points

  • This research aims to evaluate negative vacuum energy density in zeolite frameworks using Casimir geometries.
  • Applied the Gies-Klingmüller numerical method to sphere-in-cylinder geometry.
  • Reproduced the toroidal negative-energy annulus using two-body subtraction.
  • Evaluated topology at molecular scale with C₆₀ fullerenes in carbon nanotubes.
  • Conducted a Lifshitz screen analysis on 10 zeolite frameworks with a Drude dielectric proxy.
  • All sampled points in the toroidal annulus showed negative vacuum energy density.
  • Cu-SSZ-13 chabazite identified as the highest negative vacuum energy density candidate at |ρ_neg| approximately 8.67×10⁷ J/m³.
  • This density is about 10¹⁰ times greater than the density found in previous engineered cavities.
  • Sodalite shows maximum raw negative energy but is topologically inaccessible for guest species.

Abstract

The Gies-Klingmüller subtracted worldline numerical method 4, 5 is applied to the sphere-in-cylinder Casimir geometry of White, Vera, Han et al. (2021) 2. With shared loop libraries across the three subtraction terms, the toroidal negative-energy annulus reported in 2 is reproduced under proper two-body subtraction: 1220 of 1220 sampled points in the annulus (Rₛph = 1, Rcyl = 4, L = 10, all in arbitrary length units) are negative, and 41 of 41 z-rows have a negative ring minimum. The same topology is then evaluated at molecular scale on a single C₆₀ fullerene encapsulated in a (10, 10) single- wall carbon nanotube — the C₆₀@SWCNT peapod first imaged by Smith, Monthioux, and Luzzi (1998) 8. All 422 of 422 sampled annulus points are negative; the toroidal topol- ogy is preserved at the molecular scale. A Lifshitz screen of 10 zeolite frameworks (LTA, CHA, BEA, MOR, EMT, SOD, RHO, AEI, MFI, FAU) under a single-Drude aluminosilicate dielectric proxy (ωₚ = 12 eV, γ = 3 eV) identifies Cu-SSZ-13 chabazite (CHA topology) as the highest physically realizable negative vacuum energy density candidate, at |ρₙeg| = 8. 67×10⁷ J/m³ (Drude proxy) / 1. 10×10⁸ J/m³ (Cu Rakic upper bound). This is approximately 10¹⁰ times the nega- tive energy density of the White 2021 chip (|ρₙeg| ≈ 4. 5×10⁻³ J/m³), and is realized in an industrial diesel selective-catalytic-reduction catalyst already produced at million- tonnes-per-annum scale. Sodalite (SOD) ranks first in raw |ρₙeg| but is topologically inaccessible: its 2. 8 Å six-ring window admits no guest species without bond breaking. A curved-geometry calibration constant Fcurved = 0. 21 ± 0. 003 is established across d/R ∈ 0. 40, 0. 67, 0. 97. Static negative Casimir energy density is not directly equivalent to the exotic matter T_μν of the Alcubierre 1 metric; the correspondence is suggestive but not proven, and the present paper does not claim otherwise.

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Cite This Study

Bradley John Hart (2026) studied this question.

synapsesocial.com/papers/69ddd9e1e195c95cdefd738bhttps://doi.org/10.5281/zenodo.19522954
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