A common force law for the four interactions Gravity, electromagnetism, the strong force and the weak force in one law of motion

This work asks whether one law of motion, dX/dt = ∂E/∂P, dP/dt = −∂E/∂X + F, covers gravity, electromagnetism, the strong force and the weak force, so that the four interactions differ only in the energy function E and in a force F applied from outside E. It is a companion to “The ether theory of gravity” (doi: 10.5281/zenodo.23536684). The energy content of each force is taken from current physics; the law supplies the dynamics and the dependence on the ether potential φ. Chapter 1 states the law, shows that it contains the work–energy theorem, and places every interaction inside the internal energy of the body, so that the weight and the inertia of a bound system equal its total energy. Chapters 2–5 take one force each and test the law numerically against standard results: orbits, light deflection, Shapiro delay and redshift (gravity); the Lorentz force, Maxwell’s equations, radiation reaction and the Larmor power (electromagnetism); quarkonium level spacings (strong force); the neutrino potential in matter and the muon lifetime (weak force). Every chapter ends with a table setting each result against the equation or measurement of current physics, with a number for the agreement. Status: the law itself is a postulate. Where it differs from current physics, the size of the difference is stated (for example, second-order light bending, 4π against 15π/4 in units of (μ/b)²). The φ-dependence of the strong and weak energies rests on an assumed scaling map with no data behind it. Quantum phenomena are not treated. Constants recalled from memory are marked †. Files: the text (PDF and Word) and sixteen Python scripts with their logs, which reproduce every number in the text