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Cordus Optics: Part 2.2 Reflection

Dirk John Pons, Arion Pons, Ariel M. Pons, Aiden Jasper Pons

Published Apr 1, 2011• 2 citations
OpenAlex

Abstract

Optical effects such as reflection and refraction are conventionally best described by Electromagnetic Wave theory, at least when they involve beams of light. However that theory does not explain why single photons should also show such behaviour. This paper shows that optical effects can also be explained from a cordus particuloid perspective. Several principles are proposed for the interaction of a cordus photon with an optical surface, and these are used to explain reflection and subsequently refraction. The formula for critical angle is derived from a particuloid basis. The cordus and wave theory perspectives are compared and contrasted. The significance of this work is that the cordus mechanics explains the reflection and refraction behaviour of both single photons as well as beams of light, so it is a more universal explanation.

Related papers

Cordus Optics: Part 2.1 Frequency

Dirk John Pons, Arion Pons, Ariel M. Pons +1 more

Conventional particle and wave theories struggle to explain the frequency of photons and matter in a coherent manner using natural physics. This paper applies the cordus conjecture to develop a model for frequency of the photon. The interpretation is that there really is a part of the photon cordus that moves with a frequency. The working model is for a reciprocal motion: the energy alternates between the two reactive ends across the span of the cordus, and the hyff represent the observable electric field. This cordus model for frequency readily explains polarisation and tunnelling, and the concept is fundamental to other developments of the cordus mechanics including the reflection and refraction of particuloids. The implications are that frequency is not just an intrinsic variable, but a physical effect within the photon. The cordus frequency is a fundamental conceptual building-block in creating an integrated solution that unifies wave and particle behaviour. It is a powerful concept that is coherent across many other phenomena too, including matter particuloids and it contributes subsequently to the cordus model for granular fields.

•Apr 1, 2011•2 citations

Cordus Conjecture: Part 1.3 Explanation of Fringes

Dirk John Pons, Arion Pons, Ariel M. Pons +1 more

The cordus concept is shown to be able to explain wave behaviour in gaps, and fringes in the double slit device. This is useful because one of the enigmas of the double-slit device is that single photons form fringe patterns. Cordus explains fringes in terms of force lines called hyperfine fibrils (hyff) and their interaction with the edges of the light path. This also explains beam divergence and near-field effects. The results show that it is conceptually possible to create a solution for fringes based on a particuloid interpretation of light, without using the concept of interference. The biggest difference between Wave theory and the cordus explanation is their interpretation of the mechanism for fringes. Wave theory explains fringes as �interference�: two separate waves of light differing by full (half) fractions of wavelengths and thus constructively (destructively) interfering. From the Cordus perspective photons do not actually interfere or add together, and 'interference' is only a convenient analogy. The Cordus explanation is that fringes are caused instead by interaction of the photon hyff with opaque edges. This bracket of papers therefore offers a resolution of wave-particle duality by anticipating the internal cordus structure of the photon and the associated cordus mechanics. From this perspective wave and particle behaviours are simply the different output behaviours that the internal system shows depending on how it is measured. Thus Cordus offers a deeper mechanics that subsumes both quantum mechanics and wave theory. Surprisingly, Cordus suggests that the next deeper level of reality is deterministic.

•Apr 1, 2011•0 citations

Fresnel Equations Derived Using a Non-Local Hidden-Variable Particle Theory

Dirk John Pons

Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell’s law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.

Journal of Modern Physics•Jan 1, 2024•0 citations

Wave–particle duality: A conceptual solution from the cordus conjecture

DJ Pons, Arion Douglas Pons, Ariel M. Pons +1 more

There are several integration problems of fundamental physics that still lack coherent solutions, the case in point being wave-particle duality. While empiricism and mathematical modelling have served physics well, they have not yet been able to achieve integrated causal models. Conventional theories and approaches have only provided partial solutions, and it is possible that a more radical reconceptualisation of fundamental physics may be required. This work comes at the issue from a totally different approach: it applies design thinking to the problem. The result is the cordus conjecture, which proposes that the photon, and indeed every matter ‘particle’, has an internal structure comprising a 'cordus': two reactive ends that each behave like a particle, with a fibril joining them. The reactive ends are proposed to be a small finite distance apart, and energised [typically in turn] at a frequency. When energised they emit a transient force pulse along a line called a hyperfine fibril [hyff], and this makes up the field. This concept is used to explain the path dilemmas of the single photon in the double-slit device, and the wave behaviour of light including the formation of fringes by single photons and beams of light. In addition it provides a tangible explanation for frequency. It also yields new quantitative derivations for several basic optical effects: critical angle, Snell’s law, and Brewster’s angle. Thus the cordus structure offers an alternative conceptual explanation for wave-particle duality.

Physics Essays•Mar 1, 2012•17 citations

Reflection and refraction of photons

Imants Bersons, Rita Veilande, Ojārs Balcers

Abstract Three linear equations are proposed as quantum-mechanical equations for the free propagating photons. The solution of these equations is the vector potential of the electromagnetic field and it is a product of the Gaussian functions for the transverse coordinates and the eigenfunction of the harmonic oscillator for the longitudinal coordinate. This solutions is used to describe the reflection and refraction of photons on the boundary between two dielectrics. The amplitude of the reflected field coincides with the Fresnel formulae for the plane waves, but the amplitude of the refracted field is different. These amplitudes are the probability’s amplitudes of reflection and refraction of photons—like in the quantum mechanics. The photons propagated from the first into the second medium increase (decrease) their transverse size in the plane of incidence, if the refraction index of the second medium is greater (smaller) than in the first medium. The increasing or decreasing grow when increasing the angle of incidence. The difference between the quantum mechanics of the particles with a mass and the photons, as well as the interpretation of the wave function of photons, is discussed.

Physica Scripta•Feb 1, 2022•5 citations

Deriving the Snel--Descartes law for a single photon

Randy Wayne

The laws of reflection and refraction are typically derived using a dispersion relation that assumes that the angular frequency stays the same across a vacuum--dielectric interface and that the angular wave number increases. At the single photon level, this means that the total energy of the photon is conserved but the linear momentum is not. Here I derive the laws of reflection and refraction for a single photon using a dispersion relation that is consistent with the conservation of both total energy and linear momentum. To ensure that both conservation laws are upheld, the optical path length must be considered to be more fundamental than the geometrical path length when reckoning optical distances. As long as the medium is transparent, the optical path length traveled by a photon in a given duration of time is constant. By contrast, the geometrical path length traveled in a given duration of time is inversely proportional to the index of refraction. A photon propagating across a vacuum--dielectric interface is considered to be an indivisible package whose total energy (and angular frequency) and linear momentum (and angular wave number) remain constant, but whose velocity decreases with refractive index as a result of unspecified electromagnetic interactions.

TURKISH JOURNAL OF PHYSICS•Jan 1, 2014•7 citations
Optical effects such as reflection and refraction are conventionally best described by Electromagnetic Wave theory, at least when they involve beams of light. However that theory does not explain why single photons should also show such behaviour. This paper shows that optical effects can also be explained from a cordus particuloid perspective. Several principles are proposed for the interaction of a cordus photon with an optical surface, and these are used to explain reflection and subsequently refraction. The formula for critical angle is derived from a particuloid basis. The cordus and wave theory perspectives are compared and contrasted. The significance of this work is that the cordus mechanics explains the reflection and refraction behaviour of both single photons as well as beams of light, so it is a more universal explanation.
Conventional particle and wave theories struggle to explain the frequency of photons and matter in a coherent manner using natural physics. This paper applies the cordus conjecture to develop a model for frequency of the photon. The interpretation is that there really is a part of the photon cordus that moves with a frequency. The working model is for a reciprocal motion: the energy alternates between the two reactive ends across the span of the cordus, and the hyff represent the observable electric field. This cordus model for frequency readily explains polarisation and tunnelling, and the concept is fundamental to other developments of the cordus mechanics including the reflection and refraction of particuloids. The implications are that frequency is not just an intrinsic variable, but a physical effect within the photon. The cordus frequency is a fundamental conceptual building-block in creating an integrated solution that unifies wave and particle behaviour. It is a powerful concept that is coherent across many other phenomena too, including matter particuloids and it contributes subsequently to the cordus model for granular fields.
The cordus concept is shown to be able to explain wave behaviour in gaps, and fringes in the double slit device. This is useful because one of the enigmas of the double-slit device is that single photons form fringe patterns. Cordus explains fringes in terms of force lines called hyperfine fibrils (hyff) and their interaction with the edges of the light path. This also explains beam divergence and near-field effects. The results show that it is conceptually possible to create a solution for fringes based on a particuloid interpretation of light, without using the concept of interference. The biggest difference between Wave theory and the cordus explanation is their interpretation of the mechanism for fringes. Wave theory explains fringes as �interference�: two separate waves of light differing by full (half) fractions of wavelengths and thus constructively (destructively) interfering. From the Cordus perspective photons do not actually interfere or add together, and 'interference' is only a convenient analogy. The Cordus explanation is that fringes are caused instead by interaction of the photon hyff with opaque edges. This bracket of papers therefore offers a resolution of wave-particle duality by anticipating the internal cordus structure of the photon and the associated cordus mechanics. From this perspective wave and particle behaviours are simply the different output behaviours that the internal system shows depending on how it is measured. Thus Cordus offers a deeper mechanics that subsumes both quantum mechanics and wave theory. Surprisingly, Cordus suggests that the next deeper level of reality is deterministic.
Problem: The Fresnel equations describe the proportions of reflected and transmitted light from a surface, and are conventionally derived from wave theory continuum mechanics. Particle-based derivations of the Fresnel equations appear not to exist. Approach: The objective of this work was to derive the basic optical laws from first principles from a particle basis. The particle model used was the Cordus theory, a type of non-local hidden-variable (NLHV) theory that predicts specific substructures to the photon and other particles. Findings: The theory explains the origin of the orthogonal electrostatic and magnetic fields, and re-derives the refraction and reflection laws including Snell’s law and critical angle, and the Fresnel equations for s and p-polarisation. These formulations are identical to those produced by electromagnetic wave theory. Contribution: The work provides a comprehensive derivation and physical explanation of the basic optical laws, which appears not to have previously been shown from a particle basis. Implications: The primary implications are for suggesting routes for the theoretical advancement of fundamental physics. The Cordus NLHV particle theory explains optical phenomena, yet it also explains other physical phenomena including some otherwise only accessible through quantum mechanics (such as the electron spin g-factor) and general relativity (including the Lorentz and relativistic Doppler). It also provides solutions for phenomena of unknown causation, such as asymmetrical baryogenesis, unification of the interactions, and reasons for nuclide stability/instability. Consequently, the implication is that NLHV theories have the potential to represent a deeper physics that may underpin and unify quantum mechanics, general relativity, and wave theory.
There are several integration problems of fundamental physics that still lack coherent solutions, the case in point being wave-particle duality. While empiricism and mathematical modelling have served physics well, they have not yet been able to achieve integrated causal models. Conventional theories and approaches have only provided partial solutions, and it is possible that a more radical reconceptualisation of fundamental physics may be required. This work comes at the issue from a totally different approach: it applies design thinking to the problem. The result is the cordus conjecture, which proposes that the photon, and indeed every matter ‘particle’, has an internal structure comprising a 'cordus': two reactive ends that each behave like a particle, with a fibril joining them. The reactive ends are proposed to be a small finite distance apart, and energised [typically in turn] at a frequency. When energised they emit a transient force pulse along a line called a hyperfine fibril [hyff], and this makes up the field. This concept is used to explain the path dilemmas of the single photon in the double-slit device, and the wave behaviour of light including the formation of fringes by single photons and beams of light. In addition it provides a tangible explanation for frequency. It also yields new quantitative derivations for several basic optical effects: critical angle, Snell’s law, and Brewster’s angle. Thus the cordus structure offers an alternative conceptual explanation for wave-particle duality.
Abstract Three linear equations are proposed as quantum-mechanical equations for the free propagating photons. The solution of these equations is the vector potential of the electromagnetic field and it is a product of the Gaussian functions for the transverse coordinates and the eigenfunction of the harmonic oscillator for the longitudinal coordinate. This solutions is used to describe the reflection and refraction of photons on the boundary between two dielectrics. The amplitude of the reflected field coincides with the Fresnel formulae for the plane waves, but the amplitude of the refracted field is different. These amplitudes are the probability’s amplitudes of reflection and refraction of photons—like in the quantum mechanics. The photons propagated from the first into the second medium increase (decrease) their transverse size in the plane of incidence, if the refraction index of the second medium is greater (smaller) than in the first medium. The increasing or decreasing grow when increasing the angle of incidence. The difference between the quantum mechanics of the particles with a mass and the photons, as well as the interpretation of the wave function of photons, is discussed.
The laws of reflection and refraction are typically derived using a dispersion relation that assumes that the angular frequency stays the same across a vacuum--dielectric interface and that the angular wave number increases. At the single photon level, this means that the total energy of the photon is conserved but the linear momentum is not. Here I derive the laws of reflection and refraction for a single photon using a dispersion relation that is consistent with the conservation of both total energy and linear momentum. To ensure that both conservation laws are upheld, the optical path length must be considered to be more fundamental than the geometrical path length when reckoning optical distances. As long as the medium is transparent, the optical path length traveled by a photon in a given duration of time is constant. By contrast, the geometrical path length traveled in a given duration of time is inversely proportional to the index of refraction. A photon propagating across a vacuum--dielectric interface is considered to be an indivisible package whose total energy (and angular frequency) and linear momentum (and angular wave number) remain constant, but whose velocity decreases with refractive index as a result of unspecified electromagnetic interactions.