The Coherence That Must Be Decreed: Kopczyński's Bounce and the Price of Alignment

In 1972 W. Kopczyński produced the first torsion bounce: in Einstein–Cartan gravity, a spin fluid's repulsion halts collapse at a finite maximum density and the singularity is avoided. The bounce as published runs on a Weyssenhoff spinning dust with S_23 = σ the only nonzero spin component — perfect alignment, everywhere, by decree. Trautman's own review calls the aligned estimate "(unrealistic)". No derivation of the coherence from the matter sector has ever been supplied, by Kopczyński's programme or by mine: in my own corpus's census of dead ends, the coherence of the spin density σ at the crossing is a premise of the frame, not an output, and it is printed that way. This paper asks the question my problem board poses in its cheapest form — whether drag-accretion onto a twinned, spinning seed aligns what it gathers — and answers it completely, in the negative, with the price attached. I prove a precession-invariance theorem: the torsion torque I own, ds/dt = Ω(n̂ × s), preserves every spin's angle to the seed axis identically, so owned torsion cannot align at any strength. I derive a seed-coherence dilution law, C_rms = √(N_0² + M)/(N_0 + M): a perfectly coherent seed falls to C ≈ 0.011 after growth by a factor of 100, so coherence must be re-made continuously or lost. I then price what producing it would cost: a dissipative spin-alignment law of the constitutive/binding species, which I do not own, plus two unpriced numbers — the coupling κ = E_T/D in the equilibrium law C_eq = L(κ) = coth κ − 1/κ (κ = 1.7968 for C = 0.5; κ = 10 for C = 0.9), and the rate ratio Γ/r in the steady state C_ss = C_eq · Γ/(Γ + r). Finally I exhibit the separation the 1972 ansatz conflated: the bounce magnitude is independent of coherence, ⟨|s|²⟩/s_0² = 1.00000 at every κ from 0 to 10, so the bounce numbers never needed the decree — only a signed, macroscopic spin axis does, and that remains unproduced. The honesty line of this paper, at full size: coherence at the crossing remains a premise of the frame; this paper prices what producing it would cost — it does not produce it. Verdict: NO PRODUCEMENT / PRICED. My programme headline stands unmoved: the vacuum catastrophe is NOT SOLVED / PARTIAL, producing-count 0.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-31
DOI
https://doi.org/10.5281/zenodo.23837435
Primary Topic
Cosmology and Gravitation Theories
Type
preprint
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preprint

The Coherence That Must Be Decreed: Kopczyński's Bounce and the Price of Alignment

William Alexander Aldred
Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
preprint

The Coherence That Must Be Decreed: Kopczyński's Bounce and the Price of Alignment

William Alexander Aldred
preprint en

Abstract

In 1972 W. Kopczyński produced the first torsion bounce: in Einstein–Cartan gravity, a spin fluid's repulsion halts collapse at a finite maximum density and the singularity is avoided. The bounce as published runs on a Weyssenhoff spinning dust with S_23 = σ the only nonzero spin component — perfect alignment, everywhere, by decree. Trautman's own review calls the aligned estimate "(unrealistic)". No derivation of the coherence from the matter sector has ever been supplied, by Kopczyński's programme or by mine: in my own corpus's census of dead ends, the coherence of the spin density σ at the crossing is a premise of the frame, not an output, and it is printed that way. This paper asks the question my problem board poses in its cheapest form — whether drag-accretion onto a twinned, spinning seed aligns what it gathers — and answers it completely, in the negative, with the price attached. I prove a precession-invariance theorem: the torsion torque I own, ds/dt = Ω(n̂ × s), preserves every spin's angle to the seed axis identically, so owned torsion cannot align at any strength. I derive a seed-coherence dilution law, C_rms = √(N_0² + M)/(N_0 + M): a perfectly coherent seed falls to C ≈ 0.011 after growth by a factor of 100, so coherence must be re-made continuously or lost. I then price what producing it would cost: a dissipative spin-alignment law of the constitutive/binding species, which I do not own, plus two unpriced numbers — the coupling κ = E_T/D in the equilibrium law C_eq = L(κ) = coth κ − 1/κ (κ = 1.7968 for C = 0.5; κ = 10 for C = 0.9), and the rate ratio Γ/r in the steady state C_ss = C_eq · Γ/(Γ + r). Finally I exhibit the separation the 1972 ansatz conflated: the bounce magnitude is independent of coherence, ⟨|s|²⟩/s_0² = 1.00000 at every κ from 0 to 10, so the bounce numbers never needed the decree — only a signed, macroscopic spin axis does, and that remains unproduced. The honesty line of this paper, at full size: coherence at the crossing remains a premise of the frame; this paper prices what producing it would cost — it does not produce it. Verdict: NO PRODUCEMENT / PRICED. My programme headline stands unmoved: the vacuum catastrophe is NOT SOLVED / PARTIAL, producing-count 0.

Zenodo (CERN European Organization for Nuclear Research)
Cosmology and Gravitation Theories
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