Quantum limits on pixel resolution from non-commutative photon coordinates

Dynamics of zero-point energy and two-slit phenomena for photons

“…( 59) has been throughly discussed in Refs. [4,5]. In particular, for a photon of helicity +1 moving along the z-axis, the X 1 , X 2 coordinates of the photon precess about the z-axis with a frequency pc/h and the radius R 2 = (X 2 1 + X 2 2 ) is quantized:…”

“…shall not be discussed here, as it does not enter the discussions to follow. The non-commutativity of the photon position coordinates lying in a plane orthogonal to the direction of its motion equation (61) has been throughly discussed in [4,5]. In particular, for a photon of helicity +1 moving along the zaxis, the X 1 , X 2 coordinates of the photon precess about the z-axis with a frequency pc/ÿ and the radius…”

“…Proceeding further, in [4], using Maxwell's equations the photon Zitterbewegung motion along helical paths was explored and the resulting non-commutative geometry of photon position and, the distance between two photons in a polarized beam of a given helicity was shown to have a discrete spectrum that should become manifest in measurements of two photon coincidence counts. An experiment was proposed and its feasibility examined in [5].…”

“…A dissipative interference phase, due to the inherent non-commutative geometry, closely analogous to the Aharanov-Bohm magnetic field induced phase, was also found. An experiment was proposed and its feasibility examined in [4].…”

“…While the emphasis in [4,5] was upon the noncommutative photon field coordinates and on methods for its revelation through two-photon processes, here in section 4, turning to the second part of our discussion, we shall be focusing on the behavior of a single photon for two-slit arrangements to shed light on forward and backward in time propagation.…”