Lorentz force law in invariant formulation under Galilean transformations

This paper proposes a generalized formulation of the Lorentz force law that achieves full invariance under Galilean transformations across all inertial reference frames and for any velocity of the charged particle relative to the magnetic field source. Traditionally, the Lorentz force is considered non-invariant under Galilean relativity, a discrepancy that historically led to the development of Special Relativity. It is demonstrated that this formulation rests on two fundamental pillars. First, by defining the particle velocity as the explicit physical relative velocity between the charged particle and the magnetic field source, frame independence is restored for all inertial observers; under this formulation, the standard textbook Lorentz force is revealed to be a special operational case valid only when the field source is at rest in the laboratory reference frame and at non-relativistic speeds . Second, by incorporating electrodynamic field dynamics and Heaviside contraction, the invariant law is generalized to arbitrary velocities, naturally accounting for particle accelerator data while keeping the particle rest mass strictly constant . Furthermore, analyzing the limit demonstrates that represents the physical threshold where electromagnetic interaction efficiency drops to zero, rather than an absolute speed barrier of nature. This approach restores physical symmetry to the interaction and aligns directly with classical Newtonian mechanics . The implications for high-energy electrodynamics and crucial experimental tests are discussed.