The mathematical basis of physical laws: Relativistic mechanics,quantum mechanics,the Lorentz force,Maxwell's equations and non-electromagnetic forces for spin zero particles

We show that defining the observed proper velocity and acceleration of a spin zero particle as the first and second derivatives of the classical expectation value for the space-time position vector, defined on a manifold carrying the Lorentz metric, with respect to a conditioning parameter , yields directly: a Lorentz and gauge invariant quantum mechanics, the Lorentz force, Maxwell's equations and a field equation for a non-electromagnetic potential. This also provides a new basis for gauge conditions in the field theory and shows that only the Lorentz gauge condition is admissible in electromagnetic theory.