Abstract
Momentum exchange theory (MET) provides an alternative picture for optical diffraction based on a distribution of photon paths through momentum transfer probabilities determined at the scattering aperture. This is contrasted with classical optical wave theory that uses the Huygens–Fresnel principle and sums the phased contributions of wavelets at the point of detection. Single-slit, multiple-slit (Talbot effect), and straight-edge diffraction provide significant clues to the geometric parameters controlling momentum transfer probabilities and the relation to Fresnel zone numbers. Momentum transfer is primarily dependent on preferred momentum states at the aperture and the specific location and distance for momentum exchange. Diffraction by an opaque disc provides insight to negative (attractive) dispersions. MET should simplify the analysis of a broadened set of aperture configurations and experimental conditions.
Highlights
Momentum exchange theory (MET) provides an alternative picture for optical diffraction based on a distribution of photon paths through momentum transfer probabilities determined at the scattering aperture
MET starts from a momentum representation for scattered particles and postulates the probability distribution for diffraction scattering is determined by at least two important factors: (1) the momentum transfer states of the scattering lattice and (2) the distance over which momentum is transferred between the lattice and scattered particle
Classical optical wave (COW) theory leaves us with an erroneous understanding of diffraction in suggesting that the probability for detecting a diffracted photon is determined on observation at the point of detection.[2,5]
Summary
COW was built on the Huygens–Fresnel principle that assumes a spherical dispersion of the light as wavelets in the vicinity of the aperture with phase summation and interference determining the light intensity at detection. COW has been very successful in describing the diffraction of light.[26,27] Physicists have translated optical wave theory into the mathematical formalism of quantum mechanics that better reflects the statistical foundations of QM (see Ref. 28). This established a common theoretical foundation for the diffraction of photons, electrons, and other fundamental particles based upon the interference for a particle wave. There remains a significant gap between the conceptual foundations of wave theory and the descriptions of particle scattering we obtained from both classical mechanics and the more recent formulations of quantum theory that invoke quantized momentum exchange, such as quantum electrodynamics (QED).[29]
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