Regularizing Relativistic Singularities through a C ∞ -Smooth Extension of the d'Alembert Invariance: Resolving the Hubble Tension
Description
Manuscript Structure
1. Introduction
2. Baseline Mathematics of the Kinematic Boost
2.1 The Lorentz Function Family: Denition and Kinematic Limit
2.2 The Lorentz Function Family: Intrinsic Geometric Properties
3. Regularized Relativistic Kinematics
3.1 Asymptotic Invariance of the d'Alembert Operator
3.2 The Deviation Factor D(β): Higher-Order Regularization
3.3 Preservation of the Causal Light-Cone Structure
3.4 Inheritance of Classical Relativity
3.4.1 Relativistic Velocity Composition: The Illusion of Group Closure
3.4.2 Hierarchy of Relativities: Truncation of Kinematic Information
4. ALR Dynamics at Light Barrier
4.1 Kinematic Tunneling: Transition at the Light-Barrier
4.2 The Superluminal Regime: Four Stable States
4.3 Convergence of Trajectories and Finite Temporal Flow
4.4 The Architecture of Finite Energy States
4.4.1 Bounded Mass, Energy and Momentum at the β = 1 Limit
4.4.2 Preservation of the Finite Length Contraction
4.5 ALR-Upgrade of Lemaître-Einstein Law
5. First-Principle Application: Resolving the Hubble Tension
5.1 The Kinematic Gap: Signicance of Truncated Energy in the Limit Regime
5.2 Quantifying the Hubble Matching Scale (HMS): The Kinematic Breaking Point
5.3 Corresponding Distances: The Hubble-Lemaître Relation at the HMS
5.4 The Hubble Tension in a Nutshell: No Physical Discrepancies
5.5 The Invariance Boundary: Regime Bifurcation at the HMS
6. Conclusion and Outlook
Methods (English)
he manuscript introduces the Asymptotic Lorentz Relativity (ALR) framework. The core of this work is to present a new, C-infinity smooth regularized relativistic kinematics that remains valid even at the light-speed limit (v -> c). While this framework approximates Einsteinian relativity up to order O(beta^4) in the intermediate velocity regime, it substitutes the standard singular behavior with a regularized description as beta approaches 1, where classical theory ceases to be valid.
Key scientific highlights of this manuscript include:
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First-Principles Resolution of the Hubble Tension: A geometric reconciliation of the 5-sigma Hubble tension between Planck and SH0ES data by identifying the Hubble Matching Scale (HMS) at beta_HMS≈0.527 (z_HMS≈ 0.726).
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d'Alembert Form Invariance: Demonstrates full asymptotic invariance of the differential wave operator across all velocity regimes, eliminating unphysical coordinate and boost divergences without modifying the standard Einsteinian domain at intermediate velocities (beta << 1).
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Finite Physical Observables at the Luminal Boundary: Establishes bounded dynamic energy and momentum states at $\beta = 1$ (E_max = √2 · m · c²) and proves the preservation of a finite temporal flow dτ_ALR = dt / √2 > 0.
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Applications to Foundational Field Theories & Quantum Cosmology: Provides the mathematical basis for an analytically continuous transition at boundary limits, offering a non-singular background compatible with Big Bounce models (Loop Quantum Gravity) and finite vacuum impedance structures (aligning with research on electromagnetic field bounds by Prof. Gerd Leuchs, FAU Erlangen).
Notes (English)
Update Note (July 2026):
Version 2.0: Comprehensive structural update. This version streamlines the core manuscript to focus exclusively on the foundational mathematical physics, C-infinity smooth d'Alembert form-invariance, and the first-principles resolution of the Hubble Tension. Secondary phenomenological applications (such as photon mass heuristics) have been removed to provide the most concise and rigorous formulation of the ALR framework, and are planned for a dedicated future publication.
Note: For the full extended version including Section 6 on the photon mass derivation and particle mechanics comparison, please refer to Version 5 of this repository : https://doi.org/10.5281/zenodo.20348597
Files
ALR_Hubble_Tension_Delinic_2026.pdf
Additional details
Related works
- Is supplement to
- Publication: 10.5281/zenodo.21217485 (DOI)