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The Inertial Transformations (IT) are a new set of transformations of the space and time variables providing an alterative (but empirically equivalent) approach to the Theory of Special Relativity (TSR). With the IT, the one way velocity of light is isotropic only in a privileged reference frame, S0. In this new theory only a weak form of relativity principle holds. We apply the IT to the collision of an energetic photon with an electron (Compton effect). A theoretical description of the dual quantum mechanical photon having both wave and particle properties is required. From the undulatory point of view we use the IT to deduce the e.m. wave equations in an inertial reference frame S moving with respect to S₀ with (absolute) velocity V. Using the Maxwell equations in the form suitable to S, we show that the e.m. plane waves in S have the same properties as in S₀: the fields are perpendicular to one another and perpendicular to the propagation direction of the field energy. The latter direction, however, does not coincide, in S, with the propagation direction of the e.m. plane wave. From the corpuscular point of view, we show that in the framework of the IT the usual equations relating the photon energy and momentum to frequency also hold. The result of this research on the Compton effect is a complete empirical equivalence between the TSR and the IT approach.

The inertial transformations of the space and time variables have recently been shown to provide a viable alternative description of relativistic phenomena. In the present paper we find the inertial transformations of a force by starting from Newton's law. This allows us to write also the inertial transformations of the electric and magnetic fields. Relative to a moving frame, the Maxwell equations assume a novel velocity-dependent form.