The expression E = h × f is misleading because it implies the distribution of a photon quantum over 299 792 458 m, while the expression E = (h × c)/λ enables us to explain the particle-wave duality
The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.
The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.
This paper reviews humanity's understanding of photons, the evolution of quantum mechanics and quantum electrodynamics (QED), and analyzes their physical interpretations and philosophical implications. It attempts to uncover the true nature of photons by exploring possible hidden variables in the double-slit experiment. The wave-particle duality of photons, as posited by quantum mechanics, appears to me to lack verisimilitude. By designing a thought experiment involving a photon double-slit setup, I seek to falsify 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. This paper further explores the intrinsic relationship between electromagnetic waves and photons by examining the wavelength of electromagnetic radiation. It posits that electromagnetic waves are fundamentally pure particle-waves. An analysis of QED elucidates the potential influence of photon momentum on photon interactions, an effect that could have profound implications for quantum information transmission. This paper explores the non-wave-particle duality of photons through the double-slit experiment and the double-slit observer experiment. The essence of photons is purely particle-like. The thought experiment of the photon double-slit experiment is pivotal in demonstrating that photons and other particles—such as electrons, atoms, and macromolecules—are purely particulate in nature. Moreover, in space, photons can interfere with each other's paths based on their momentum. This can simultaneously alter the trajectory of photons and even modify their velocity. That is to say, a photon beam possessing greater momentum may carry along a portion of photon beams with lesser momentum, propagating them over considerable distances. The wavelength of a light wave fundamentally represents the distance between consecutive photons as they queue and advance through space. A longer wavelength corresponds to a greater distance between photons, causing them to diverge more widely in space, as seen with radio waves. Conversely, a shorter wavelength implies closer proximity between photons, resulting in denser emission and a highly directional nature, as seen in gamma rays. Photons within the visible spectrum may occasionally transmit information bearing specific content. This information, conveyed via photons, can propagate over distances ranging from several metres to thousands of kilometres.
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,
Dispersion dynamics applies wave-particle duality, together with Maxwell’s electromagnetism, and with quantization E = hν = ħω (symbol definitions in footnote) and p = h/λ = ħk, to special relativity E2 = p2c2 + m2c4. Calculations on a wave-packet, that is symmetric about the normal distribution, are partly conservative and partly responsive. The complex electron wave function is chiefly modelled on the real wave function of an electromagnetic photon; while the former concept of a “point particle” is downgraded to mathematical abstraction. The computations yield conclusions for phase and group velocities, vp⋅vg = c2 with vp ≥ c because vg ≤ c, as in relativity. The condition on the phase velocity is most noticeable when p≪mc. Further consequences in dispersion dynamics are: derivations for ν and λ that are consistently established by one hundred years of experience in electron microscopy and particle accelerators. Values for vp = νλ = ω/k are therefore systematically verified by the products of known multiplicands or divisions by known divisors, even if vp is not independently measured. These consequences are significant in reduction of the wave-packet by resonant response during interactions between photons and electrons, for example, or between particles and particles. Thus the logic of mathematical quantum mechanics is distinguished from experiential physics that is continuous in time, and consistent with uncertainty principles. [Footnote: symbol E = energy; h = Planck’s constant; ν = frequency; ω = angular momentum; p = momentum; λ = wavelength; k = wave vector; c = speed of light; m = particle rest mass; vp = phase velocity; vg = group velocity].
Based on the Maxwell theory and the principle of charges quantization, we prove that for any definite V , a symmetrical electromagnetic wave beam of minimum energy possesses the basic characters: ∈ = hv , p = h/λ , spin= and duality. They are the good reasons for us to treat the wave beam as a photon. A photon is consisted of ∈ -(energy) packet and ψ -(electromagnetic)wave. ∈ -packet is a circular polarized electromagnetic field wrapped by a cylindrical lateral membrane with ± charge e. They form an extremely stable structure like a “solid particle”. Under the protect of the membrane, no external electromagnetic field can break it or change its inner structure so as the photons can bring the information unchanged from the deep universe for over ten billion years. Photon ( ∈ -packet) of different frequencies V have different radius but same shape with same ratio L/R ≈ 0.04 like a circular coin. The ∈ -packet is floated on and carried by the ψ -(EM) wave to move together. ψ -wave decides and describes the probability behavior of the ∈ -packet (s). Such structure unifies the duality of photons. Analysis of the pair production shows that symmetry will make the particles produced possess spiral structure of mass. The mass density on particles’ cross section satisfy σ = σR (R/r)k.
Though it has been widely viewed that the light consists of quantum particles known as photons, the light is not made of quantum particles or photons, and the light is always a wave. What is quantized in the light is the frequency. The electromagnetic frequency is always quantized due to the quantized nature of the electromagnetic energy; the quantum energy results in quantum frequency. The light is made up of many discrete electromagnetic wave bursts of constant durations; each burst consists of an electromagnetic wave of a single frequency determined by an integer multiple of the indivisible quantum energy units. The quantum energy and frequency are synonymous; they are one and the same. The duration of a wave burst is a universal constant, and it is the same for all the wave bursts irrespective of the frequency of the electromagnetic wave they contain. Since the quantum energy is in the frequency of the electromagnetic wave in a wave burst, the light can be propagated unlimited distances with the quantum energy intact, without which, the evolution of life would not have occurred. The quantum energy is not affected by any gradual path degradation even after the propagation of light for billions of light years since the quantum energy is the frequency; this would have been an impossible task by any other means such as carrying the quantum energy in a particle or photon on a wave. The light is always a wave, and never a particle; there is no wave-particle duality. There is absolutely no need for an unrealistic, artificial quantum light particle, or photon hypothesis. The hypothetical mass-less particles only exist in human imagination; they do not exist in the nature.
This paper explores the nature of the photon through the double-slit thought experiment, demonstrating that it is not a wave-particle duality. The essence of the photon is that of a pure particle. The double-slit thought experiment concerning photons is pivotal in proving that photons, along with other particles such as electrons, atoms, and macromolecules, are purely particulate in nature. Between the double-slit partition and the screen, photons do not produce coherence or the superposition of probability wave functions. Instead, they generate alternating bright and dark fringes through repeated oscillations between the slits and the detection screen. Within space, photons can interfere with each other's paths based on their momentum, simultaneously altering their trajectories and even their velocities. Thus, a beam of photons possessing greater momentum may carry along a portion of lower-momentum photons, propagating them over considerable distances. By examining the wavelength of electromagnetic waves, the intrinsic relationship between electromagnetic waves and photons is revealed. This establishes that electromagnetic waves are fundamentally pure particle-wave phenomena of photons. The wavelength of an electromagnetic wave essentially represents the spatial distance between consecutive photons as they advance in formation through space. The longer the wavelength of an electromagnetic wave, the greater the distance between successive photons, causing them to diverge more widely in space, as seen with radio waves. Conversely, shorter wavelengths result in closer spacing between photons, leading to more concentrated emission and a pronounced directionality, exemplified by gamma rays. Within the visible spectrum of electromagnetic waves, humans can occasionally transmit information bearing specific content via photons. This information, conveyed through photons, can traverse distances ranging from metres to thousands of kilometres, where it is received and discerned by another individual.