Papers · William Alexander Aldred

There Is No Twisted Vacuum: Torsion, Rotation, and the Junction Ledger in Einstein–Cartan Gravity

by William Alexander Aldred — Independent Researcher

Abstract

Eight successive investigations of the vacuum catastrophe within a single torsion-based frame shared one assumption they never listed among the objects searched: the background was static and torsion-free. This paper removes that assumption. Inside Einstein–Cartan (EC) gravity we construct the one background the campaign had not tested — a ball that is twisted, spinning, and counter-rotating, with an interior twist, an exterior rotating in the opposite sense, a wound helical torsion structure on its axis, and an interface — a junction, a scar — between the two sides — and we re-derive, on that background, every earlier result that had depended on the old one. The re-derivation is the result. The Cartan equation is algebraic and linear through zero, 𝒯rm bg = (8π G/c³),σ, with elasticity of the background torsion to the spin density σ exactly 1.000000 and to the metric rotation Ω exactly 0.000000. A region with zero spin density therefore has zero torsion on any metric, rotating or not. A twisted vacuum is not a state Einstein–Cartan gravity contains: a twisted ball is a ball with a spin source put into it, and where the source is decreed at the crossing value of the Aldred Limit it is not a vacuum at all but the bounce matter state, 84.22 dex above the vacuum density. Rotation, by contrast, is vacuum-legal and unpriced: the counter-rotation condition Jrm tₒt=0 is an identity on the symmetric structure, no frame equation couples Ω to the crossing scale, the rotational work cancels on the totals, and the Wald entropy coefficient is C = 1.000000 at every rotation tested. The helical rope carries no tension and no squeeze — exactly 0 at every pitch — and the most generous matter-cored impostor reaches only 1/(8π²) = 0.012665 of the pin pressure. The junction between the counter-rotating sides posts genuine interface quantities, and its ledger balances: surface spin 0 for vacuum sides, an equilibrium flux of 3.469×10⁻¹⁸ over four periods, approximately 0, a scar asymmetry of exactly 0.000000, and no entropy assigned to the interface by the formalism itself. The Aldred Limit does not recur at the top of the construction: under four readings of the closure condition, the radius is absent, unfixed, or a dial's cube root — one spin quantum of total content returns R = 3.875120×10⁻²⁹ rm m = 2.336792×10⁻⁵⁵,RH, neither the microscopic nor the cosmological scale. Finally, the residue the campaign seeks is not a difference of frame quantities: rotation and torsion differences return 2.000000 at their reference values, and contact with the target value 3ΩLₐmbdₐ=2.0550 is made only by solving a free dial at 1.027500 times the frame scale. These are negative results, stated as results: they strengthen an earlier, solution-level vanishing theorem into a theorem about the theory, they extend the statics of torsion defects to helices, they close the junction ledger, and they name, to the property, the structure that could reopen the question — a theory in which torsion propagates.

Keywords: Einstein–Cartan gravity; torsion; vacuum energy; black-hole and de Sitter entropy; junction conditions; Aldred Limit

The program

• The Aldred Limit
• Two Bounds and an Integration Constant
• Supplementary Memos for “Two Bounds and an Integration Constant”
• The Constant Changes Address
• The Crossing Charges Nothing
• No Derivation in the Frame
• Static Defects Carry No Nieh–Yan Charge
• Creation Events Are Nieh–Yan Charged
• There Is No Twisted Vacuum (this page)
• Propagation Is Not Enough
• Axiom H
• One Flaw, Two Residues
• The ε_eff Turnover
• The Generation Map Has a Fixed Point
• Three Fences Any Λ Mechanism Must Pass