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.
Previous papers have presented an alternative picture for photon diffraction based on a distribution of photon paths through quantized momentum exchange with probabilities defined at the location of scattering, not the point of detection. This contrasted with the picture from classical optical wave theory that describes diffraction in terms of the Huygens-Fresnel principle and sums the phased contributions of electromagnetic waves at the location of detection to determine probabilities. This alternative picture was termed “Momentum Exchange Theory (MET),” replacing the concept of Huygens wavelets with photon scattering (positive and negative dispersions) through momentum exchange with the scattering lattice. MET assumes a momentum representation for diffracted particles and has been applied to several different optical diffraction experimental configurations. Straight edge diffraction has been a particularly revealing experimental configuration as it provides significant clues to the geometric parameters controlling exchange probabilities. Diffraction by an opaque disc is examined to provide further insight to negative (attractive) dispersions. This analysis indicates that the “diffraction force” is an integration of momentum exchange field interactions to derive an exchange probability at interaction points along the photon path – resembling aspects of the QED path integral formulation for particle interactions.
Hestenes has presented an integration of Schrödinger's zitterbewegung with the spin matrices of the Dirac equation, suggesting the electron can be modeled by a rapidly rotating dipole moment and a frequency related to the de Broglie frequency. He presents an elegant spacetime algebra that provides a reformulation of the Dirac equation that incorporates these real spin characteristics. A similar heuristic model for quantum particles has been derived by this author from a different, quasi-classical premise: That the most fundamental subcomponents of quantum particles all travel at a constant speed of light. Time is equated with the spatial displacement of these subcomponents – the speed of light is the speed of time. This approach suggests a means of integrating special relativity and quantum mechanics with the same concept of time. The relativistic transformation of spinning quantum particles create the appearance of additional, compactified spatial dimensions that can be correlated with the complex phase of the spin matrices as in the Dirac formalism. This paper further examines the convergence on such new models for quantum particles built on this rapid motion of particle subcomponents. The modeling leverages a string-like heuristic for particle subcomponents and a revised description for the wave-like properties of particles. This examination provides useful insights to the real spatial geometries and interactions of electrons and photons.
An alternative picture for photon diffraction had been proposed describing diffraction by a distribution of photon paths determined through a Fourier analysis of a scattering lattice. The momentum exchange probabilities are defined at the location of scattering, not the point of detection. This contrasts with the picture from classical optical wave theory that describes diffraction in terms of the Huygens-Fresnel principle and sums the phased contributions of electromagnetic waves to determine probabilities at detection. This revised picture, termed “Momentum Exchange Theory,” can be derived through a momentum representation of the diffraction formulas of optical wave theory, replacing the concept of Huygens wavelets with photon scattering through momentum exchange with the lattice. Starting with the Rayleigh-Sommerfeld and Fresnel-Kirchoff formulas, this paper demonstrates that diffraction results from positive and negative photon dispersions through virtual particle exchange probabilities that depend on the lattice geometry and are constrained by the Heisenberg uncertainty principle. The positive and negative increments of momentum exchange exhibit harmonic probability distributions characteristic of a “random walk,” dependent on the distance of momentum exchange. The analysis produces a simplified prediction for the observed intensity profile for a collimated laser beam diffracted by a long, straight edge that lends conceptual support for this alternative picture.
Particle diffraction can be described by an ensemble of particle paths determined through a Fourier analysis of a
scattering lattice where the momentum exchange probabilities are defined at the location of scattering, not the point of
detection. This description is compatible with optical wave theories and quantum particle models and provides deeper
insights to the nature of quantum uncertainty. In this paper the Rayleigh-Sommerfeld and Fresnel-Kirchoff theories are
analyzed for diffraction by a narrow slit and a straight edge to demonstrate the dependence of particle scattering on the
distance of virtual particle exchange. The quantized momentum exchange is defined by the Heisenberg uncertainty
principle and is consistent with the formalism of QED. This exchange of momentum manifests the "diffraction force"
that appears to be a universal construct as it applies to neutral and charged particles. This analysis indicates virtual
particles might form an exchange channel that bridges the space of momentum exchange.
The wavelength has been a common denominator to the various wave-like and particle-like models of the
photon - this wavelength being inversely proportional to the momentum and energy ascribed to the photon. The Lorentz
transformation has been utilized with both wave-like and particle-like descriptions to generate the relativistic Doppler
Effect and the associated transformation of the wavelength. The relativistic transformation of those models is
reexamined here, noting the common feature that wavelength transforms as a specific time-length projected along the
trajectory of the photon. While in the wave-model this length can be associated with the periodicity of the wave, in the
particle-model this length can be associated with a real, quantized geometric property of the photon. This associated
length can tie the photon to the description of components of other quantum particles modeled variously by strings or
membranes. Whatever description for the structure of light we ultimately converge upon should integrate this real,
geometric property of wavelength. A novel membrane-like model for the photon is discussed that integrates this
geometric time-length and suggests the correlation to mass-energy.
Any discussion of the nature of light must include a reminder that whenever we make the observation of light (photons), we only observe particle-like properties. This paper provides a reiteration that we don't need wave-like properties to scattered photons to describe phenomena such as diffraction or refraction of light. This paper updates the original ideas of Duane, later revived by Lande, which provided a description of light diffraction without making reference to a wave nature. These are updated using terminology more common to quantum electrodynamics which describes the interaction of particles in terms of the exchange of virtual photons. Diffraction is described in terms of an ensemble of distinct, probability weighted paths for the scattered photons. The scattering associated with each path results from the quantized momentum exchange with the scattering lattice attributed to the exchange or reflection of virtual photons. The probability for virtual particle exchange/reflection is dependent upon the allowed momentum states of the lattice determined by a Fourier analysis of the lattice geometry. Any scattered photon will exhibit an apparent wavelength inversely proportional to its momentum. Simplified, particle-like descriptions are developed for Young's double slit diffraction, Fraunhofer diffraction and Fresnel diffraction. This description directly accounts for the quantization of momentum transferred to the scattering lattice and the specific eigenvalues of the lattice based upon the constraints to virtual photon exchange set by the Uncertainty Principle, Δπ_{i} = h/ζ_{i}.
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