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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

The nature of light: a description of photon diffraction based upon virtual particle exchange

Michael J. Mobley

Published Aug 1, 2005• 5 citations
Publisher

Abstract

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, Δπi = h/ζi.

DOI
10.1117/12.637439

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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.

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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, Δπi = h/ζi.
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.
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.
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.
Today, the nature of light is accounted for by one of the jewels of physics, quantum electrodynamics (QED), the fundamental theory of light and matter. Yet owing to its infinite complexity, scientists still debate how its central concept, the photon, can be reconciled with the perceived existence of light waves, emerging 200 years ago in the wake of Young's double slit diffraction experiment. Ever since, the phenomenon of diffraction has been viewed to embody the wave nature of light, leading to the schizophrenic wave-particle duality. The latter does not exist in QED which is photon based without the existence of waves. Here we introduce the new paradigm that diffraction images directly reflect the fundamental quantum states of light. This is revealed by analysis of the evolution of modern versions of Young's experiment performed with differently modified laser light and photon-based detection. In conventional quantum mechanics, corresponding to first order QED, the fundamental photon nature of light remains hidden since different quantum states produce only two basic types of diffraction patterns that may also be explained by coherent and incoherent wave superposition. The true photon based substructure of light is shown to clearly emerge through characteristic diffraction images in second order QED. The degeneracy of the first order images is lifted, the wave-particle equivalence breaks down, and the patterns directly reveal the true quantum substructure of light. This allows the replacement of the conventional concept of wave coherence by a precise order-dependent degree of coherence that quantifies the interference and diffraction behavior of all quantum states of light.
Using the Fresnel–Kirchhoff integral, we express the state of the light that diffracts from an aperture to a point, by superposition of two or more waves. The amplitudes of the waves are determined by the distances of the point from the ray optics borders of the emerging beams. The interference approach to the Fresnel diffraction leads to a universal formulation of the normalized intensity distribution on the diffraction pattern that determines the state of the incident light, the parameters of the aperture, and its distance from the observation plane, uniquely. In the photon approach, according to the uncertainty principle, confining the position of a photon to an aperture changes the probable propagation direction of the photon in an interval that leads to the diffraction of the photon or light. Thus, the normalized intensity distribution on the diffraction pattern is the probability distribution of a photon. To this probability distribution, a probability amplitude distribution is associated that diffracts similar to a wave in Fresnel diffraction. Applying the introduced approach to the study of the diffraction, from different simple apertures and phase steps, we deduce general behaviors of the Fresnel diffraction and show it is involved in all aspects of light phenomena.
The dual wave-particle nature of quantum objects is a notoriously unintuitive feature of quantum theories. However, it is often deemed essential, due to quantum objects exhibiting diffraction and interference. We extend the work of Landé and Lévy-Leblond to demonstrate that de Broglie wavelengths are not relativistically covariant as simultaneous spatial structures, making wave properties an unviable explanation of apparent interference. We then explore whether modern experiments vindicate an alternative view: that apparent waviness in diffraction and interference scenarios emerges as a consequence of quantised interactions between particles. Such a view has historically received very little attention, despite being the exact modern explanation of both the Kapitza-Dirac effect and ultrafast electron diffraction. We then study a photon orbital angular momentum realisation of the double slit to show that quantised exchanges can mimic interference. Finally, we demonstrate that the quantum formalism demands that particle momentum is determined at the point of scattering, contravening wave-based explanations of quantum interference.