by Norbert Nopper
A synthesis programme extending the Quaternion–Hypersphere Theory of Spacetime to quantum mechanics.
A monograph that develops a synthesis programme aimed at unifying general
relativity and quantum mechanics through the structural identity
- A Euclidean spectral triple on the static product $S^{1}{\beta} \times S^{3}{a}$ whose spectral action reproduces the Einstein–Hilbert plus cosmological-constant action and the Standard Model kinetic terms to machine precision (a Wick-rotated check on a stationary background, not yet a Lorentzian Krein triple on time-dependent FLRW).
- An ADM reduction of that action to a Wheeler–DeWitt constraint operator on minisuperspace including matter.
- Construction of the physical inner product on the
homogeneous-minisuperspace Wheeler–DeWitt kernel via the conserved
Wronskian / Klein–Gordon form, identified with the Marolf–Giulini
group-averaging inner product in 1D, with the conservation law
$\partial_R W = 0$ verified numerically to relative precision$1.2 \times 10^{-12}$ — rigorous, but restricted to the homogeneous sector. - A consistency relation between two moments of the spectral cutoff
function and the two Reuter asymptotic-safety fixed-point values
$(g_\star, \lambda_\star)$ . - A tree-level EFT identity
$\delta\lambda = -\lambda_\sigma^2 / (4 \lambda_2)$ that, combined with a one-parameter Yukawa-ratio fit, reproduces the σ-threshold value$|\delta\lambda| = 0.141$ at$\alpha = y_\nu / y_t \approx 1.24$ . - A numerical illustration of the Cheeger–Müller–Schrader action-level
convergence theorem on three regular triangulations of
$S^3$ , with an amplitude-level continuum limit for spin foams left open. - A falsifiable forecast on
$(\Omega_K, r, n_s)$ with joint significance$\sigma_{\mathrm{disc}} \in [2, 13]$ across the predicted band at CMB-S4 + LiteBIRD sensitivity.
Throughout, a strict distinction is maintained between rigorously established results, controlled numerical evidence, and conjectural extensions; the calibrated frontier-by-frontier honest assessment is in Part Honest review and open problems, which should be read before any of the "closed" or "resolved" labels elsewhere in the text.
Status. A synthesis programme, not a proof of unification.
- 📄 paper.pdf — typeset PDF (≈ 236 pp)
- 📝 paper.tex — master document
- LaTeX sections:
paper/sections/ - Bibliography:
refs.bib
Rebuild with any modern LaTeX engine:
latexmk -pdf paper.texScripts under scripts/ reproduce the figures and tables cited
in the paper. In particular, scripts/wdw_inner_product.py realises the
Marolf–Giulini refined algebraic quantisation of the Wheeler–DeWitt
constraint.
Builds on the Quaternion–Hypersphere Theory of Spacetime.
Code: MIT. Paper text and figures: CC BY 4.0. See LICENSE and
CONTRIBUTING.md.