The work relates to the fundamentals of quantum physics and photonics, in particular to the formation of processes of reflection, refraction and absorption of waves of ballistic photons. The study of these problems is an important and urgent task for understanding the foundations of the material world, which has not yet been fully resolved. An important property of ballistic photons is their motion in a straight line, which can be curved under the action of physical fields on the photons and the parameters of the medium of their motion. However, if external factors remain constant, their motion continues in a straight line, which allows us to apply the laws of geometric optics to them. The fundamentals of the geometric wave laws of reflection and refraction of light are laid down of the Young and Fresnel. However, they used sinusoidal waves similar to transverse waves in the of musical strings, which contradicts the motion of spherical waves of ballistic photons. Elimination of these shortcomings is the main goal of the work, and its scientific novelty is the substantiation and development of new geometric models of light motion. Research Methods: Since this work has the level of scientific discovery, for finding which strict methods have not yet been created, therefore, general principles of development of the theory of scientific knowledge were used, based on the laws of dialectics and consistency with the basic laws of physics. The author's research methodology was also used, based on the transition to the initial quantum level of the material world. New Results of the Work and their Discussion: It is shown that the first point of contact of photon waves lies on the unified normal to their spherical surface and the contact surface. This shifts the real normal of wave reflection relative to the traditional normal from the point of intersection of the axis of the tube of incident waves with the surface of reflection by the value of -Δ = λmax sin α. The real axis of reflection of spherical waves is associated with the crests most distant from the initial point of their reflection. When photon waves are refractional, their total deviation is formed from the last point of their incidence on the refraction surface. This shifts the real point of the normal of wave refraction relative to the traditional normal from the point of intersection of the axis of the tube of incident waves with the surface of reflection by the value of +Δ = λmax sin α. Geometric models of all these processes at different angles of incidence of photon waves are developed and their simplified schemes are given. Conclusions: The proposed models and schemes of reflection and refraction of spherical photon waves significantly clarify and change previously known schemes and do not contradict the real laws of physics and optics, therefore they have the level of scientific discoveries and should replace previously known processes and schemes.
The work relates to the fundamentals of quantum physics and photonics, in particular to the formation of processes of reflection, refraction and absorption of waves of ballistic photons. The study of these problems is an important and urgent task for understanding the foundations of the material world, which has not yet been fully resolved. An important property of ballistic photons is their motion in a straight line, which can be curved under the action of physical fields on the photons and the parameters of the medium of their motion. However, if external factors remain constant, their motion continues in a straight line, which allows us to apply the laws of geometric optics to them. The fundamentals of the geometric wave laws of reflection and refraction of light are laid down of the Young and Fresnel. However, they used sinusoidal waves similar to transverse waves in the of musical strings, which contradicts the motion of spherical waves of ballistic photons. Elimination of these shortcomings is the main goal of the work, and its scientific novelty is the substantiation and development of new geometric models of light motion. Research Methods: Since this work has the level of scientific discovery, for finding which strict methods have not yet been created, therefore, general principles of development of the theory of scientific knowledge were used, based on the laws of dialectics and consistency with the basic laws of physics. The author's research methodology was also used, based on the transition to the initial quantum level of the material world. New Results of the Work and their Discussion: It is shown that the first point of contact of photon waves lies on the unified normal to their spherical surface and the contact surface. This shifts the real normal of wave reflection relative to the traditional normal from the point of intersection of the axis of the tube of incident waves with the surface of reflection by the value of -Δ = λmax sin α. The real axis of reflection of spherical waves is associated with the crests most distant from the initial point of their reflection. When photon waves are refractional, their total deviation is formed from the last point of their incidence on the refraction surface. This shifts the real point of the normal of wave refraction relative to the traditional normal from the point of intersection of the axis of the tube of incident waves with the surface of reflection by the value of +Δ = λmax sin α. Geometric models of all these processes at different angles of incidence of photon waves are developed and their simplified schemes are given. Conclusions: The proposed models and schemes of reflection and refraction of spherical photon waves significantly clarify and change previously known schemes and do not contradict the real laws of physics and optics, therefore they have the level of scientific discoveries and should replace previously known processes and schemes.
The work relates to the fundamentals of quantum physics and photonics, in particular to the formation of ballistic photons, as well as to the parameters of their structure and processes of their motion. The study of these problems is an important and urgent task for understanding the foundations of the material world, which has not yet been fully resolved. At present, a wide range of electromagnetic waves is referred to as photons or quanta of wave radiation. But it is necessary to highlight the waves of the optical range of 380 – 760 nm, associated with photons – the only massless physical particles in the material world. This led to an attempt to abandon photons as physical particles and replace them with wave radiation. In addition to the problem of mass, the problem of ballistic photons and the motion pattern is acute. Its solution is the main goal of the work performed, and new confirmations of the ballistic motion of photons as an electromagnetic wave and as a physical particle within the duality of its existence is its scientific novelty. Research Methods: Since this work has the level of scientific discovery, for finding which strict methods have not yet been created, therefore, general principles of development of the theory of scientific knowledge were used, based on the laws of dialectics and consistency with the basic laws of physics. The author's research methodology was also used, based on the transition to the initial quantum level of the material world and the processes occurring at the same time. New Results of the Work and their Discussion: It is shown that photons are dual matter-wave physical objects, in which the properties of an electromagnetic wave prevail when they move at the speed of light, and the properties of a material particle are manifested when they slow down or meet an obstacle. The rectilinearity of their movement reduces them to ballistic ones. In this case, photons are transformed into spherical waves of Planck thickness 4.05×10-35 m, with a transverse surface of the sphere of 1 steradian, the radius of which and half the length of its arc are equal to the wavelength of radiation λmax, and spherical waves rotate perpendicular to the vector of their motion. When reflected from a mirror surface, they turn inside out, preserving the previous direction of rotation, and a change in the vector of the direction of motion makes them antiphotons, in which the spin and direction of the right and left mapping change. Conclusions: All photons are ballistic, from their emission to absorption or re-emission. Other types of photons and their motion by re-emission of energy make up an insignificant part of their total number. There are possibilities for experimental confirmation of the obtained results, to which all laboratories and researchers with such capabilities are invited.
This chapter introduces quantum optics, focusing on wave-particle duality, superposition, entanglement, and quantum teleportation, while employing algebra, trigonometry, and physical reasoning to make quantum mechanics accessible without calculus. It systematically builds from classical optics to historical experiments revealing quantum behavior, using examples and practice problems designed for technician-level education, and prepares students for further study in quantum information science. The chapter explores fundamental properties of light waves, including coherence, polarization, and reflection, with coherent light exhibiting organized interference patterns and incoherent light lacking phase consistency. Polarization is discussed, distinguishing between unpolarized and polarized light, and polarizers are introduced as tools to filter light based on its polarization state. The law of reflection is explained, detailing how light bounces off surfaces based on the angle of incidence and media properties. The chapter also discusses reflection and refraction at media interfaces, introducing Fresnel equations for calculating reflectance for perpendicular and parallel polarized light, simplifying these for normal incidence, and presenting an example calculation for an air–glass interface.
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.
It is known that if a photon hits a surface with a different index of refraction (at an angle within a certain range), it has a specific probability “a” to reflect and 1-a to refract. In this note we ask: Where does this statistical nature come from? In previous notes, we have considered Fermat’s principle applied separately to explain two dimensional reflection and refraction. We have also used the idea of a difference of squares and energy conservation in one dimensional reflection/refraction to find values of the probabilities. The question we ask is: Why are there probabilities in the first place? Is there some general idea at work despite the complicated details of the photon interacting with the atoms of the new medium.We argue the general notion is due to the idea of spatial invariance which is linked to the translation operator d/dx which in turn in linked to a p impulse occurring at a given x .Thus the variables p and x are linked through the notion of an impulse existing at some x. The idea that d/dx may operate on a function of constant p and x to yield p, implies the function of p,x should have physical meaning. This is a problem as classically a particle moving with constant p should not be associated with any function of x except a constant. (All x points are the “same”.) Thus we argue that a “probability” in x is established with a constantly moving particle (or even photon). The eigenfunction of d/dx (or rather -id/dx) which exhibits some kind of spatial invariance is exp(ipx). This contains two different x probability distributions cos(px) and sin(px). We noted that d/dx is associated with p due to an impulse hit at say an x point. Thus various exp(ipx)s with different weights should appear together in a physical problem with impulses such as reflection/refraction. The weights of the various exp(ip1 x), exp(ip2 x) etc become linked to probabilities associated with the state 1, 2 etc. Thus the origin of these probabilities (i.e. their specific values) follow from the probabilistic form exp(ipx) which follows from d/dx. (In (1) we have argued that the x distributions in exp(ipx) may be further linked to the force which “created” the p in the first place, with different p values having different distributions cos(px), sin(px)).
A unified wave-phase description of the photon and of the motion of a material body is developed. The construction is based on the description of wave processes and on the preservation of their phase state as a fundamental principle, leading to Lorentz transformations and the structure of Minkowski spacetime without introducing them a priori. It is shown that the physically significant characteristic of a wave process is its phase state, which is preserved during evolution and acquires physical meaning only through the comparison of different processes. The wave invariant associated with the motion of a material body is factorized into two oppositely directed light-like components Q± = Ω ± cK = 2Ω_{l,±}, whose product, after a natural rescaling, takes the normalized form Q₊Q₋ = 1. In this representation, the parameters (Ω, K) are not independent quantities but are determined by the two light-like components: Ω characterizes their combined frequency content, whereas cK characterizes the asymmetry between them. Within the proposed framework, the Doppler shift is interpreted as a phase relation between wave processes, while relative velocity in special relativity corresponds to a Doppler asymmetry between the two light-like components of the wave process associated with motion. The resulting construction reproduces the kinematic structure of special relativity and provides a unified wave-phase description of the photon and of the motion of a material body.
Since the establishment of modern optics, the physical nature of light has been debated for centuries, which finally led to the mainstream theory of waveparticle duality. This theory holds that photons intrinsically possess both particle and wave properties, and it is adopted to interpret diverse optical phenomena including rectilinear propagation, polarization, interference and diffraction, forming the fundamental framework of modern quantum optics. Nevertheless, the theory of waveparticle duality contains inherent logical defects. Its essential flaw lies in confusing two completely distinct physical concepts: the intrinsic properties of a substance itself and the morphological features of its motion trajectory. Conventional theories mistake the apparent waveshaped trajectory produced by particle motion for the intrinsic wave property of microparticles, resulting in persistent conceptual ambiguity, missing physical mechanisms and logical inconsistencies within microoptics. This paper constructs an optical underlying model from a purely particle perspective to clarify the real mechanism behind waveparticle phenomena of light. A photon is an indivisible, nonspreading, nontrailing pointlike physical particle with no intrinsic wave property. While propagating, a photon travels along a fixed straightline direction and undergoes inherent transverse oscillation within the plane perpendicular to its propagation direction. At the moment of its generation, a photon uniquely fixes its transverse oscillation angle, amplitude and frequency within the 360degree plane perpendicular to its travelling direction. Once determined, these parameters remain constant throughout propagation without random shifts or arbitrary changes. Superposition of the photon’s longitudinal rectilinear motion and fixedangle transverse oscillation generates a standard sinusoidal trajectory. Consequently, all wavelike features observed in optics are geometric apparent effects originating from particle motion trajectories, rather than material properties intrinsic to photons. Based on this model, this paper reinterprets the core physical mechanism behind doubleslit interference. Contrary to the traditional explanation of photon selfinterference or wavefield superposition, interference fringes arise from microscopic mechanical interactions between transverselyoscillating photons and slit walls when photons pass through the slits. Such interactions regularly deflect photon flight angles. After being deflected and filtered by slits, large numbers of photons form uneven statistical distributions on the receiving plane and produce macroscopically observable lightanddark fringes. This paper also defines the threshold for photonphoton interactions. Ordinaryenergy photons such as visiblelight, infrared and ultraviolet photons do not interact, collide or exchange energy with one another in free space. Only gammaraylevel highenergy photons may collide, undergo energy annihilation, and convert into material particles such as electronpositron pairs. Relying entirely on classical mechanical superposition principles and discarding the contradictory hypothesis of waveparticle duality, the proposed purelyparticle model provides selfconsistent explanations for core classical optical phenomena and achieves analytical revision for the underlying logic of optical waveparticle phenomena.