Dynamics of a 2x2 Relativistic Matrix Model of the Energy Momentum Equation

The purpose of this note is to investigate dynamical features of the 2x2 matrix approach contained in Einstein´s 1905 energy momentum equation E2 = p2 + m2 (1) In particular, we wish to investigate the existence of physical oscillations consistent with the model. The model was based on conversion of (1) into a 2x2 matrix eigenvalue system with various matrices as operators. The matrices and eigenvectors obey quantum mechanical math with exp(-iHt) as a time evolution operator. It is thus possible to calculate O(t)=exp(iHt) O exp(-iHt) where O is an operator. This leads to oscillatory motion along and perpendicular to the x axis in the one dimensional approach used. This oscillatory motion is considered in sme detail  and comparisons with transformations of light from a stationary to moving frame are made.