Hamiltonian equations and inertial mass increase

TL;DR

This paper demonstrates that classical Hamiltonian mechanics can model velocity-dependent inertial mass increase, aligning with special relativity predictions when specific functions are chosen, challenging the exclusive relativistic explanation.

Contribution

It introduces a generalized Hamiltonian framework with adjustable parameters to describe inertial mass increase with velocity within classical physics.

Findings

Classical Hamiltonian mechanics can replicate relativistic mass increase.

Derived generalized formulas for kinetic energy, momentum, and force.

Shows classical physics can encompass relativistic effects through parameter choices.

Abstract

It has been shown in the past century that the particle inertia against velocity change has increased at higher velocity values. This increase has been predicted in principle in the framework of special theory of relativity. However, any comparison of the corresponding prediction with experimental data obtained already in the first half of the past century has not been provided until now.It will be shown in the presented paper that quite arbitrary inertia mass increase with velocity may be described also in the framework of the classical physics on the basis of Hamilton's equations if the force law of Newton will be generalized; i.e., if time change of particle momentum (not directly acceleration) will be determined by corresponding force. More general velocity-dependent formulas (containing some free parameters) for kinetic energy, momentum and force will be then derived. It will be further shown that this generalized Hamiltonian mechanics describing general mass increase with velocity may be reduced to known result of classical physics of Newton if mass value is taken to be constant, and also that the result of special theory of relativity may be derived if the given increasing function is taken as predicted in this theory.