2x2 Matrix Model and X and Y Direction Motion of Bouncing Photons
In a series of notes, it was seen that Einstein’s 1905 energy momentum equation
E2 = p2 + m2 (1) can be written as an eigenvalue equation linear in E, p and m. This equation applies to particles and leads to zitterbewegung results which appear in the literature. [
In a note, it was seen how the 2x2 matrix eigenvalue equation was general and could be applied to a photon moving in the y direction in a frame moving along the x axis with speed v. It was then argued that zitterbewegung should be applied to photons as well. In this note, we try to investigate this further. In addition, we attempt to clarify x and y direction motion of photons and their relation to the 2x2 model. We also examine zitterbewegung in EM energy density equations such as: energy density= .5(E2 +B2) and try to apply it to the cases of a photon moving in the y direction in a box moving in the x direction and to a photon moving in the x direction in a similar box. In such cases, the E field carries effects of the translational motion which are part of the zitterbewegung.