Towards the Unity of Classical Physics

The unity of classical mechanics and electromagnetism is proposed to be established through putting both on equal footing. The special-relativistic equations of motion for the particles and fields, the Maxwell-Lorentz force, and the Yukawa potential are derived exploiting Newton’s and Euler’s (stationary-)state descriptions, Newton’s decomposition of forces into bodyand position-dependent factors, and Helmholtz’s analysis of the relationships between forces and energies. For instance, the magnetic MaxwellLorentz force is a special case of the Lipschitz force being a general class of forces that leave the kinetic energy constant. Adding this force to Newton’s force of gravity leads to self-standing fields representing the mediating agent of interaction sought by Newton. Thus, equal footing is realized through a foundation on common principles, but not through a reduction to mechanical models.