The de Sitter-Unruh Modified-Inertia Theory: A One-Parameter Account of the MOND Acceleration Scale
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Abstract
I present the de Sitter-Unruh modified-inertia (MI) theory as a self-contained, ONE-PARAMETER physical account of the MOND acceleration scale a0 -- explicitly NOT a theory of everything. The theory rests on two physical inputs. First, an accelerated body immersed in a de Sitter universe sees a thermal bath at the Deser-Levin temperature T(a) = (hbar/2pi k_B c) sqrt(a^2 + (cH_Lambda)^2), which never falls below a universal floor T0 = hbar cH_Lambda/(2pi k_B c) = 2.20e-30 K set by the dark-energy horizon alone. Second, a relational/Machian principle: a body's force-responsive (dynamical) inertia is the EXCESS of its bath response above that universal floor -- a body unaccelerated relative to the cosmic vacuum carries no dynamical inertia. From these two inputs, four structures follow as consequences rather than fits: (i) the SCALE a0 = cH_Lambda/Z ~ sqrt(Lambda); (ii) the INTERPOLATION FORM mu_fw(x) = (sqrt(1+4x^2)-1)/2x, with the strikingly clean inverse mu/(1-mu^2) = a/a0, realized as the minimum of a convex, ghost-free potential; (iii) the MEMORY KERNEL theta(0) = sqrt2 (amplitude-branch selection) with a Lorentzian shape forced by the de Sitter Wightman function; and (iv) the MOND SIGN itself -- the relational principle selects inertia-weakening (MOND) and rejects the passive-bath, inertia-raising (anti-MOND) reading that the influence functional otherwise gives. What remains is a single free number Z = 2 sqrt(8pi/3), provably free (the kappa-closure result), entering exactly as Newton's G enters general relativity. The honesty is explicit and two-sided throughout: the sign is CONDITIONAL on the Machian premise (the honest crux); Z and hence a0's numerical value are NOT derived; and the Standard-Model mass sector stays WALLED (the Koide relation is beyond symmetry, the Yukawa sector kernel-free) -- this is a one-parameter theory of one infrared scale, not a theory of everything. The theory is consistent with, and assembles, the author's previously published effective-field-theory results (DOIs 10.5281/zenodo.20935948, 20938891, 20947913, 20963226) and with the author's 2026 retraction of all earlier theory-of-everything / Standard-Model overclaims. Predictions: an s^TX Lorentz-violation dipole (~1.5x the tightest current bound), an a0(z) 'hostage' tied to the dark-energy equation of state, a modified-gravity-impossible dwarf orbital-history velocity-dispersion signature (+12-14%), and a definite universal floor temperature T0 = 2.20e-30 K. All results are reproducible from the public repository.
Related
- A de Sitter-Unruh Modified-Inertia Field Theory, Complete Up To Its Constants: the Action, Its Radiative Protection, Its Equation Set, and Its Measurements
- Mixed modified-gravity--modified-inertia MOND theories
- The Fourth Horn: Local Pais-Uhlenbeck Modified Inertia Is Excluded by an Exceptional-Point Cap and a Frequency-Selection No-Go
- The MOND Acceleration Scale as a de Sitter Curvature Scale: Gauged SO(4,1) Gravity Reduces a0 = c^2 sqrt(Lambda/32pi) to a Single Free Number
- Cusps, cores, and one acceleration: dark-matter haloes versus modified dynamics across the full SPARC sample
BibTeX
@article{zimmerman2026sitterunruh,
title = {{The de Sitter-Unruh Modified-Inertia Theory: A One-Parameter Account of the MOND Acceleration Scale}},
author = {Carl P. Zimmerman},
journal = {Zenodo (CERN European Organization for Nuclear Research)},
year = {2026},
month = jun,
doi = {10.5281/zenodo.20965015},
url = {https://doi.org/10.5281/zenodo.20965015},
note = {CC BY},
}
RIS
TY - JOUR
TI - The de Sitter-Unruh Modified-Inertia Theory: A One-Parameter Account of the MOND Acceleration Scale
AU - Carl P. Zimmerman
PY - 2026
DA - 2026/06/27
JO - Zenodo (CERN European Organization for Nuclear Research)
DO - 10.5281/zenodo.20965015
UR - https://doi.org/10.5281/zenodo.20965015
AB - I present the de Sitter-Unruh modified-inertia (MI) theory as a self-contained, ONE-PARAMETER physical account of the MOND acceleration scale a0 -- explicitly NOT a theory of everything. The theory rests on two physical inputs. First, an accelerated body immersed in a de Sitter universe sees a thermal bath at the Deser-Levin temperature T(a) = (hbar/2pi k_B c) sqrt(a^2 + (cH_Lambda)^2), which never falls below a universal floor T0 = hbar cH_Lambda/(2pi k_B c) = 2.20e-30 K set by the dark-energy horizon alone. Second, a relational/Machian principle: a body's force-responsive (dynamical) inertia is the EXCESS of its bath response above that universal floor -- a body unaccelerated relative to the cosmic vacuum carries no dynamical inertia. From these two inputs, four structures follow as consequences rather than fits: (i) the SCALE a0 = cH_Lambda/Z ~ sqrt(Lambda); (ii) the INTERPOLATION FORM mu_fw(x) = (sqrt(1+4x^2)-1)/2x, with the strikingly clean inverse mu/(1-mu^2) = a/a0, realized as the minimum of a convex, ghost-free potential; (iii) the MEMORY KERNEL theta(0) = sqrt2 (amplitude-branch selection) with a Lorentzian shape forced by the de Sitter Wightman function; and (iv) the MOND SIGN itself -- the relational principle selects inertia-weakening (MOND) and rejects the passive-bath, inertia-raising (anti-MOND) reading that the influence functional otherwise gives. What remains is a single free number Z = 2 sqrt(8pi/3), provably free (the kappa-closure result), entering exactly as Newton's G enters general relativity. The honesty is explicit and two-sided throughout: the sign is CONDITIONAL on the Machian premise (the honest crux); Z and hence a0's numerical value are NOT derived; and the Standard-Model mass sector stays WALLED (the Koide relation is beyond symmetry, the Yukawa sector kernel-free) -- this is a one-parameter theory of one infrared scale, not a theory of everything. The theory is consistent with, and assembles, the author's previously published effective-field-theory results (DOIs 10.5281/zenodo.20935948, 20938891, 20947913, 20963226) and with the author's 2026 retraction of all earlier theory-of-everything / Standard-Model overclaims. Predictions: an s^TX Lorentz-violation dipole (~1.5x the tightest current bound), an a0(z) 'hostage' tied to the dark-energy equation of state, a modified-gravity-impossible dwarf orbital-history velocity-dispersion signature (+12-14%), and a definite universal floor temperature T0 = 2.20e-30 K. All results are reproducible from the public repository.
ER -