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Quantum Electronics

What is a photon: structure and wave function

Andrey P. Kanavin, Oleg N Krokhin

Published Aug 5, 2018• 4 citations
Publisher

Abstract

Based on the model of a photon as a 'radiation oscillator' of a field moving in space with the speed of light and having a zero rest mass, we have constructed a wave function that describes the photon states of the electromagnetic field. It has been suggested that the entire space where the field is present splits into separate regions of the order of the radiation wavelength, within which the field is coherent and the total field energy is equal to the photon energy.

DOI
10.1070/qel16698

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This paper reviews humanity's understanding of the photon, the evolution of quantum mechanics and quantum electrodynamics (QED), and analyzes their physical interpretations and philosophical implications. It seeks to elucidate the true nature of the photon by examining the possibility of hidden variables in the double-slit experiment. The wave-particle duality of the photon, as posited by quantum mechanics, appears to me to be less than entirely convincing. By designing a thought experiment involving a photon double-slit setup, I aim to refute the notion that photons generate Coherence, or so-called wave-function superposition, within the light field between the slits and the screen. This endeavour aims to demonstrate the pure particle nature of photons. Furthermore, by examining the wavelength of electromagnetic waves, this paper explores the intrinsic relationship between electromagnetic waves and photons, positing that electromagnetic waves are fundamentally pure particle-waves. 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For simplicity, we denote this approach as the "photon queue/longitudinal serialization (PQ/LS) model". PQ/LS denotes the theoretical framework of the photon queue model. A thought experiment on the conversion rate of quantum information into biological information reveals that, under identical light intensity (equivalent total energy input), the response of living systems is not solely determined by the 𝐼, but strongly depends on the spatial arrangement of the photon queue (where λ approximates the inter-photon distance).Bacterial-level matching of visible-light queues achieves the highest information-transmission efficiency (maximum mutual information and signal-to-noise ratio), thereby enabling dual optimization of energy utilization and rhythmic synchronization. This constitutes the core prediction of the model (PQ/LS): frequency (queue spacing), rather than total power (𝐼) alone, determines the conversion efficiency of quantum information into biological information. 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Conversely, shorter wavelengths result in closer distances between photons, leading to denser emission and highly directional propagation, exemplified by gamma rays. Photons within the visible-light spectrum may occasionally transmit information that carries specific content. This information, conveyed through light quanta, can propagate over distances ranging from several metres to thousands of kilometres. The essence of light quanta: particle queues (PQ/LS) and the profound meaning of frequency: light is fundamentally a sequence of light quanta (photons) advancing in spatial order. Regardless of whether the propagation path is straight or curved, the propagation maintains this queued formation, akin to a continuous jet of water. Within this model (PQ/LS), the wavelength λ of light observed macroscopically fundamentally represents the average distance between successive light quanta. The frequency f (or ν) is inversely proportional to this distance: the closer two light quanta are, the higher the frequency f; the greater the distance, the lower the frequency f. It can be expressed through the classical wave velocity formula: c=fλ. Within the visible spectrum, λ≈0.5×10⁻⁶ metres (500 nanometres). Remarkably, this distance corresponds precisely to the typical dimensions of bacteria (approximately 0.5–5 micrometres). The evolutionary tree of life takes bacteria as its root, while the wavelength of visible light—the fundamental scale for human vision and quantum information interaction—aligns exactly with this root-level dimension. As the product of billions of years of bacterial evolution, our human perception, communication, and even consciousness may possess an intrinsic connection to this "bacterial-scale" queue distance of light quanta. Philosophically, this unification reveals a grander picture: the frequency-distance relationship of the light quantum queue (PQ/LS) not only determines the magnitude of physical energy but also bridges the quantum realm with the origins of life. The evolution of human vision, which aligns precisely with this "bacterial-scale" dimension, suggests that our perceptual systems are rooted in life's most primordial mode of information exchange. As an information carrier, light transforms energy (E = hf) into biological signals, genetic expression, and even the emergence of consciousness—from photons stimulating retinal cells to potential quantum biological processes (such as quantum coherence in photosynthesis or brain microtubules), light weaves an information network between the microscopic and macroscopic realms. Bacterial circadian rhythms, particularly the KaiABC system in cyanobacteria, function as living fossils: they document how visible light quantum queues (PQ/LS) were transformed into ordered biological information programmes during life's earliest stages. This experimental finding not only validates the functional significance of scale consistency but illuminates the earliest step in the evolutionary path from light to meaning—within the unicellular world, light ceased to be mere energy, becoming instead the language of time and the rhythm of information. The relatively poor correlation between archaea and most bacteria in circadian rhythms and responses to visible light, from another perspective, suggests that archaea and bacteria did not originate on Earth but rather within protoplanetary discs or planetesimals. These archaea and bacteria can survive in the harshest natural environments, unaffected by Earth's 24-hour circadian rhythms or visible light. It further substantiates my published theory that life did not originate on Earth. From the bacterial scale to the scale of consciousness: information density remains operative. Within the Photon Quantum Queue Model (PQ/LS), the wavelength of visible light (~0.5 μm interphoton spacing) aligns remarkably with the bacterial scale, suggesting that the informational "foundation" of life's origin is set by the interphoton spacing. As we ascend from single-celled bacteria (scale 0.5–5 μm) to multicellular organisms, nervous systems, and ultimately human consciousness (neuronal scale ~10–100 μm, brain as a whole ~0.1 m), a central question emerges: does this information density, originating from the photon quantum distance, continue to operate at higher scales, bridging microscopic origins with macroscopic awareness? From bacteria to conscious scales: Implications of information density for SETI and the search for extraterrestrial life. An intuitive interpretation of light's nature: Mainstream quantum electrodynamics (QED) views photons as quantum field excitations, where wavelength λ represents the phase oscillation scale associated with a single photon, not the physical distance between multiple photons. This theory deliberately adopts a semi-classical "particle queue" image, directly correlating λ with the average distance between adjacent photons. While not strictly valid in weak-light or single-photon experiments, the theory challenges the orthodoxy that "wavelength is solely a property of individual photons." The theory's stance can be summarized as one of maximizing continuity and wholeness within strict scientific boundaries. Our challenge lies in rejecting the compartmentalization of the quantum realm, the origins of life,

•Feb 11, 2026•0 citations
Based on the model of a photon as a 'radiation oscillator' of a field moving in space with the speed of light and having a zero rest mass, we have constructed a wave function that describes the photon states of the electromagnetic field. It has been suggested that the entire space where the field is present splits into separate regions of the order of the radiation wavelength, within which the field is coherent and the total field energy is equal to the photon energy.
I will discuss a real imaginary photon model that has a constant energy content with its rotating elementary charges e + and e - around a common center and moving with a constant speed as a particle, wavelike through empty space. This leads to an indication that there is a difference between the electromagnetic oscillation of dipoles radiating in all direction and the single-direction rotation of the forward moving electrical potential difference of the photon, as photovoltaic and photoconductive detetcters indicate, since they can detect no wavelengths larger then 42 µm (GeZn detector). Furthermore, this photon model explains why gravitational waves, accelerating galaxies as the source of red shifts, and the universal equation E = mc2 are not possible if this model is found to be true. Here it is also explained why the rotating and forward moving charges have no magnetic field. Finally, it is shown that at a beam splitter a photon is either reflected or transmitted and why interference still occurs in an inteferometer in so-called single-photon experiments.
The quantum mechanical model of electromagnetic waves is considered. The photon as a particle moves with thespeed of light with respect to the CMB frame. The spatial wave function of the photon is introduced as a waveaccompanying the photon, with an infinite speed of spreading throughout the whole space at some moment oftime. The temporal wave function of the photon emitted (absorbed) by the electron is defined through thetemporal wave function of the electron (virtual photon associated with the electron) at some point of space. TheMichelson-Morley experiment is studied with use of both the spatial and temporal wave functions of photon, andthe null result being obtained in both the cases.
The present work is concerned with de Broglie's quantum theory of light. It is assumed that the photon is described by a Hermitian wave function with 16 components. Using this wave function it is shown that the 32 of de Broglie's equations are reduced to one set of 16 equations in the form: [equation] where the [alpha]'[rho] are Dirac matrices and [psi] is a matrix with 16 components. The electromagnetic quantities associated with the photon are described by means of the Dirac matrices operating on [psi] in a specified way. It is shown also that these electromagnetic quantities satisfy Maxwell's equations as a result of the equation the interaction between an electron and a photon is developed and the matrix elements for the radiation transitions are calculated. It is further shown that the above wave equation can be considered as the superposition of two similar wave equations, one for the positive energy photons and the other for the negative energy photons. To each of these states there corresponds electromagnetic quantities defined by the above method. It is the superposition of these fields which gives rise to the reality of the electromagnetic field, found in experience. The wave mechanics of the positive energy photon is discussed and the method of second quantization is applied to its wave function, from which we deduce the commutation relations for the complex fields.
Light has the dual characteristics of particles (photons) and electromagnetic waves. The photon has an energy of 𝐸 = ℎ𝜈 (𝜈: frequency, h: Planck constant) and the momentum of 𝑝⃗ = ℎ𝑘⃗⃗ (𝑘⃗⃗: wavenumber and 1|𝑘⃗⃗| is the wavelength). The photon density is proportional to the square of the amplitude of the electromagnetic waves. The fundamental aspect of quantum mechanics is that these characteristics apply to all matters. The properties of matters are described by wave functions. The probability of the existence of the matter is proportional to the square of the associated wave function. When a matter is localized in a limited region, it can only assume discrete values of energy because the wavelength of the matter wave must be an integral division of the region. The phase of the wavefunction has uncertainty on order 1/2 radians; therefore, position and momentum (time and energy) cannot be simultaneously determined. As the size of the localization area of the wavefunction becomes smaller, the minimum kinetic energy becomes larger because of the smaller wavelength (larger momentum uncertainty). The Schroedinger equation was derived based on the idea that the relationship between the frequency and the wavenumber corresponds to that between energy and momentum given by classical mechanics, which makes it possible to obtain the wave functions of matters in the energy eigenstates. Several examples of solutions to the Schroedinger equation are introduced. The mixture between different energy eigenstates and the shift in the energy eigenvalues are induced by electromagnetic fields. The temporal change of the wave function (transition between different energy states) is also obtained using the Schroedinger equation.
The nature of light is studied by comparison between the real and digital worlds. Combining the theoretical results obtained from a relative quantum mechanical equation which is suited for a particle with zero rest mass, spin quantum number 1/2 with experiments analysis results, we discuss the possibility that a photon could have structure. A possible photon model with internal structure is proposed and discussed. A photon could consist of a pair particles named particle x+ and antiparticle x-. x+ and x- both have zero rest masses, and spin quantum number 1/2. x+ and x- oscillate in opposite directions but spin in the same direction, which means there is an internal oscillation. The frequency of light is the frequency of the oscillation. The model can be used to explain not only all of the experiment phenomena, but also the wave particle dualism of light. It can provide clear pictures of both polarization and coherency of light. It can also explain that there are two spin states of 1 and -1. The possible experiments that could be used to prove the model are addressed too.
This paper reviews humanity's understanding of the photon, the evolution of quantum mechanics and quantum electrodynamics (QED), and analyzes their physical interpretations and philosophical implications. It seeks to elucidate the true nature of the photon by examining the possibility of hidden variables in the double-slit experiment. The wave-particle duality of the photon, as posited by quantum mechanics, appears to me to be less than entirely convincing. By designing a thought experiment involving a photon double-slit setup, I aim to refute the notion that photons generate Coherence, or so-called wave-function superposition, within the light field between the slits and the screen. This endeavour aims to demonstrate the pure particle nature of photons. Furthermore, by examining the wavelength of electromagnetic waves, this paper explores the intrinsic relationship between electromagnetic waves and photons, positing that electromagnetic waves are fundamentally pure particle-waves. Analysis of QED elucidates the potential influence of photon momentum on photon interactions, an effect that may profoundly impact quantum information transmission. To comprehensively describe the mathematical model of photon queues, this paper introduces the concept of a photon train. This metaphor likens photons travelling through space to a train in motion. The distance between carriages is denoted by (d), representing the wavelength of the photon。 Within the "particle train" model of the photon queue, the wavelength λ is defined as the distance d between adjacent photons. This yields a structural equivalence between wavelength and photon spacing: ; . The longer the wavelength (smaller f), the greater the distance d between photons (corresponding to radio waves, where photons are "sparsely" dispersed). The shorter the wavelength (larger f), the closer the distance d between photons (corresponding to X-rays or γ-rays, where photons are "focused"). f represents the frequency of light. In standard physics, frequency is typically defined as the number of oscillations of an electromagnetic field per unit time, expressed by the relationship: . This is directly linked to the energy of a photon. However, although mathematically and experimentally complete, this definition obscures the intuitive informational structure of frequency. In this paper, we introduce a longitudinally structured interpretation: viewing frequency as the manifestation of "front-to-back density" or "longitudinal spacing" of light quanta along their propagation direction. This understanding does not replace the standard physical definition but operates in parallel to reveal frequency's deeper significance in energy transmission and information organization. For simplicity, we denote this approach as the "photon queue/longitudinal serialization (PQ/LS) model". PQ/LS denotes the theoretical framework of the photon queue model. A thought experiment on the conversion rate of quantum information into biological information reveals that, under identical light intensity (equivalent total energy input), the response of living systems is not solely determined by the 𝐼, but strongly depends on the spatial arrangement of the photon queue (where λ approximates the inter-photon distance).Bacterial-level matching of visible-light queues achieves the highest information-transmission efficiency (maximum mutual information and signal-to-noise ratio), thereby enabling dual optimization of energy utilization and rhythmic synchronization. This constitutes the core prediction of the model (PQ/LS): frequency (queue spacing), rather than total power (𝐼) alone, determines the conversion efficiency of quantum information into biological information. The paper explores the non-wave-particle duality of photons through double-slit experiments and double-slit observer experiments. The essence of photons is purely particle-like. The thought experiment of the photon double-slit is pivotal in demonstrating that photons, like other particles such as electrons, atoms, and macromolecules, are purely particle-like. In space, photons can interfere with each other's paths based on their momentum. This can simultaneously alter the trajectory and even the velocity of photons. That is, a photon beam with higher momentum may carry a portion with lower momentum, allowing it to propagate over vast distances. The wavelength of a light wave is fundamentally the distance between consecutive photons as they propagate through space. The longer the wavelength of a light wave, the greater the distance between successive photons, causing them to diverge more widely in space, as observed with radio waves. Conversely, shorter wavelengths result in closer distances between photons, leading to denser emission and highly directional propagation, exemplified by gamma rays. Photons within the visible-light spectrum may occasionally transmit information that carries specific content. This information, conveyed through light quanta, can propagate over distances ranging from several metres to thousands of kilometres. The essence of light quanta: particle queues (PQ/LS) and the profound meaning of frequency: light is fundamentally a sequence of light quanta (photons) advancing in spatial order. Regardless of whether the propagation path is straight or curved, the propagation maintains this queued formation, akin to a continuous jet of water. Within this model (PQ/LS), the wavelength λ of light observed macroscopically fundamentally represents the average distance between successive light quanta. The frequency f (or ν) is inversely proportional to this distance: the closer two light quanta are, the higher the frequency f; the greater the distance, the lower the frequency f. It can be expressed through the classical wave velocity formula: c=fλ. Within the visible spectrum, λ≈0.5×10⁻⁶ metres (500 nanometres). Remarkably, this distance corresponds precisely to the typical dimensions of bacteria (approximately 0.5–5 micrometres). The evolutionary tree of life takes bacteria as its root, while the wavelength of visible light—the fundamental scale for human vision and quantum information interaction—aligns exactly with this root-level dimension. As the product of billions of years of bacterial evolution, our human perception, communication, and even consciousness may possess an intrinsic connection to this "bacterial-scale" queue distance of light quanta. Philosophically, this unification reveals a grander picture: the frequency-distance relationship of the light quantum queue (PQ/LS) not only determines the magnitude of physical energy but also bridges the quantum realm with the origins of life. The evolution of human vision, which aligns precisely with this "bacterial-scale" dimension, suggests that our perceptual systems are rooted in life's most primordial mode of information exchange. As an information carrier, light transforms energy (E = hf) into biological signals, genetic expression, and even the emergence of consciousness—from photons stimulating retinal cells to potential quantum biological processes (such as quantum coherence in photosynthesis or brain microtubules), light weaves an information network between the microscopic and macroscopic realms. Bacterial circadian rhythms, particularly the KaiABC system in cyanobacteria, function as living fossils: they document how visible light quantum queues (PQ/LS) were transformed into ordered biological information programmes during life's earliest stages. This experimental finding not only validates the functional significance of scale consistency but illuminates the earliest step in the evolutionary path from light to meaning—within the unicellular world, light ceased to be mere energy, becoming instead the language of time and the rhythm of information. The relatively poor correlation between archaea and most bacteria in circadian rhythms and responses to visible light, from another perspective, suggests that archaea and bacteria did not originate on Earth but rather within protoplanetary discs or planetesimals. These archaea and bacteria can survive in the harshest natural environments, unaffected by Earth's 24-hour circadian rhythms or visible light. It further substantiates my published theory that life did not originate on Earth. From the bacterial scale to the scale of consciousness: information density remains operative. Within the Photon Quantum Queue Model (PQ/LS), the wavelength of visible light (~0.5 μm interphoton spacing) aligns remarkably with the bacterial scale, suggesting that the informational "foundation" of life's origin is set by the interphoton spacing. As we ascend from single-celled bacteria (scale 0.5–5 μm) to multicellular organisms, nervous systems, and ultimately human consciousness (neuronal scale ~10–100 μm, brain as a whole ~0.1 m), a central question emerges: does this information density, originating from the photon quantum distance, continue to operate at higher scales, bridging microscopic origins with macroscopic awareness? From bacteria to conscious scales: Implications of information density for SETI and the search for extraterrestrial life. An intuitive interpretation of light's nature: Mainstream quantum electrodynamics (QED) views photons as quantum field excitations, where wavelength λ represents the phase oscillation scale associated with a single photon, not the physical distance between multiple photons. This theory deliberately adopts a semi-classical "particle queue" image, directly correlating λ with the average distance between adjacent photons. While not strictly valid in weak-light or single-photon experiments, the theory challenges the orthodoxy that "wavelength is solely a property of individual photons." The theory's stance can be summarized as one of maximizing continuity and wholeness within strict scientific boundaries. Our challenge lies in rejecting the compartmentalization of the quantum realm, the origins of life,