The Law of Variable Inertial Mass (LVIM): Vacuum-Dependent Inertial Dynamics as a Testable Extension of Classical and Relativistic Physics

Zenodo Archival Metadata — LVIM Version 2.0 (Final Ultimate Clean Canonical Edition) TitleThe Law of Variable Inertial Mass (LVIM): Vacuum-Dependent Inertial Dynamics as a Testable Extension of Classical, Relativistic, and Quantum Physics AuthorDr. B. MazumdarIndependent Researcher–ScholarFounder, FAIR+D Canon (India, 2025)ORCID: 0009-0007-5615-3558 Canonical DOI10.5281/zenodo.18188109 Publication DateJanuary 2026 — Version 2.0 (Final Ultimate Archival Edition) AbstractThe physical origin of inertial mass remains an unresolved foundational problem across classical mechanics, special and general relativity, and quantum field theory. This work presents the Law of Variable Inertial Mass (LVIM), a minimal, covariant, and renormalization-consistent framework in which inertial mass acquires a weak, local dependence on renormalized quantum vacuum energy density gradients. LVIM introduces no new force, does not modify gravity, does not generate rest mass, and does not permit energy extraction from the vacuum. Instead, inertia is identified as a vacuum-susceptibility property of matter, fully consistent with locality, causality, and effective field theory. The theory is formulated from a fully covariant action principle, preserving exact Lorentz invariance and compatibility with general relativity. Stability, Hamiltonian positivity, ghost-freedom, and radiative naturalness are rigorously established. The weak equivalence principle is preserved within current experimental bounds, with only subleading and controllable deviations arising under engineered vacuum-gradient conditions. LVIM reduces exactly to Newtonian mechanics, special relativity, and standard ΛCDM cosmology in homogeneous vacuum limits. Quantitative, falsifiable predictions are provided for precision laboratory and space-based tests, including interferometric and Casimir-vacuum configurations. This release constitutes the Final Ultimate Clean Canonical Edition, consolidating conceptual foundations, mathematical formulation, relativistic and gravitational consistency, renormalization analysis, numerical validation, and experimental testability into a single, self-contained, archival-grade reference suitable for long-term citation and scholarly evaluation. Key Scientific Features Full Lorentz and general covariance; exact recovery of established limits Proven stability, causality, Hamiltonian positivity, and ghost-freedom Weak equivalence principle preserved within η < 10⁻¹⁵ (current bounds) Explicitly falsifiable predictions at the 10⁻¹⁵ sensitivity level Effective field theory consistency with radiative stability and technical naturalness Reproducible numerical validation with sensitivity mapping Version 2.0 Enhancements Complete covariant action with Bianchi-identity consistency Explicit proofs excluding ghosts and superluminal modes Laboratory and space-based experimental protocols Archival-grade documentation (9 Parts, 22 Chapters) Reproducibility policy and referee-oriented technical appendix Experimental Test Platforms Atom and neutron interferometry Casimir-cavity inertial measurements Space-based equivalence-principle missions Theoretical PositioningNot Machian (purely local); not modified gravity; no vacuum-energy extraction.Exact reduction to Newtonian mechanics, general relativity, and QFT in homogeneous vacuum limits. KeywordsInertial Mass; Quantum Vacuum; Variable Mass; Equivalence Principle; General Covariance; Effective Field Theory; Precision Tests; Casimir Physics LicenseCC BY 4.0 CommunitiesTheoretical Physics; Quantum Field Theory; Gravitation References75+ (Complete bibliography included) Code AvailabilityFull Python implementation for LVIM dynamics and sensitivity analysis Data PolicyFAIR principles compliant (Findable, Accessible, Interoperable, Reusable) Archival StatusDefinitive Version 2.0 reference. All prior versions superseded. Cite the canonical DOI for all future references.