THE LAW OF VARIABLE INERTIAL MASS (LVIM): A Vacuum-Dependent Extension of Classical and Relativistic Dynamics

THE LAW OF VARIABLE INERTIAL MASS (LVIM): A Vacuum-Dependent Extension of Classical and Relativistic Dynamics Authors:Dr. B. MazumdarIndependent Researcher–Scholar | Founder, FAIR+D Canon — India (2025)ORCID: 0009-0007-5615-3558 Description:The Law of Variable Inertial Mass (LVIM) presents a complete, self-consistent, and falsifiable framework in which inertial mass emerges from the interaction between matter and local quantum vacuum energy density. Inertial mass formulation (plain-text math-safe): m_i = m_0 + mu * rho_vac alpha_i = mu * rho_vac / m_0 << 1 Predicted inertial deviations: Delta a / a ≈ mu * |∇rho_vac| / m_0 ~ 1e-15 Experimental signatures: Platform Predicted Sensitivity Atom Interferometry 1e-16 1e-17 Space-Based Precision Tests 1e-15 1e-15 Casimir Vacuum Systems 1e-14 1e-13 Additional Features: Equivalence Principle: Compatible to first order in alpha_i (m_g ≈ m_i) Cosmology: Reduces to standard physics for homogeneous vacua (∇rho_vac ≈ 0) Distinction: LVIM is local, covariant, and testable, unlike Machian, electromagnetic vacuum-drag, or Higgs-based models Accompanying Files: PDF Manuscript (LaTeX): Full derivations, equations, and Appendix A (Numerical Illustration) Python Code: Simulation illustrating vacuum-induced inertial deviations Significance:LVIM provides a minimal, conservative, experimentally accessible extension of inertial dynamics, offering a concrete pathway to resolve the physical origin of inertial mass. DOI: 10.5281/zenodo.18187158 License: CC-BY 4.0 Keywords:Inertial Mass, Quantum Vacuum, Emergent Inertia, Foundations of Physics, Testable Dynamics, Relativistic Dynamics, Covariant Formulation