Whereas according to today’s physics energy-momentum equation holds only for fast moving particles, this paper proves it to be true for all velocities 0<v<c. More importantly, the algorithm underlying this equation is mimicked in all particleparticle interactions, (gravitational, nuclear, weak, electromagnetic), thus unifying the ‘four forces’. It reveals the existence of Nature’s fifth force– the centrifugal force beyond doubt. The algorithm is based on the relationship pc = mc2 tanθ, between the two left side terms of the equation, prompting right side term to be mc2.sec2θ. Algorithm reveals that the problematic second order term v2/c2 which has hitherto been neglected for the validity of classical mechanics for optical and electromagnetic phenomena has the relational expression sin2θ, which represents a quantum formed in the interaction in empirical reality. In every interaction such quanta are formed by contribution of fractions of, particle’s intrinsic energy mc2 and motive energy pc, together with an influx of kinetic energy and kinetic momentum from the field. On this basis Quantum phenomena and Relativistic phenomena find a unified origin, signalling a new foundation for physics. Even though a photon moves by its own intrinsic energy, and undergoes changes of states without the direct application of external constraints, photon interactions occur by simulation of the fermion algorithm, and quanta are formed, emitted or absorbed by energy effluxes and influxes to and from the field. The veracity of the fermion and photon algorithms are demonstrated in this paper by applying them in combination to the collision of a photon and an electron in Compton’s experiment.