Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700164
A. P. Davydov, D. M. Dolgushin, T. P. Zlydneva, N. R. Faizrakhmanov
Abstract
The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.
{"title":"Young’s Single- and Double-Slit Experiments in Terms of the Feynman Amplitudes, Green’s Functions, and Photon Coordinate Wave Functions","authors":"A. P. Davydov, D. M. Dolgushin, T. P. Zlydneva, N. R. Faizrakhmanov","doi":"10.1134/s0030400x24700164","DOIUrl":"https://doi.org/10.1134/s0030400x24700164","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The Young’s single- and double-slit experiments are explained using six-component quantum and one-component quasi-classical photon wave functions in the coordinate representation, which are modeled by different mechanisms of photon diffraction on slits or simultaneous emission of two photons by (two) independent sources. This explanation is compared with the well-known statement about the interference of a particle with itself when passing through both slits simultaneously in the Young’s experiment on the basis of the postulated Feynman amplitudes. It is argued that these amplitudes cannot be wave functions, in the literal sense, describing some states of quantum particles. In all cases, under the assumption of the linear polarization of photons, a pronounced interference pattern has been obtained, which suggests that the coordinate wave function of a photon can explain the phenomena of the one- and two-photon interference. This conclusion, in turn, makes it possible to associate the coordinate wave function of a photon (two photons, in the entangled state) measured in some recent experiments with the quasi-classical wave function of a photon (two photons), although it does not take into account its (their) polarization properties.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700292
A. B. Petrin
Abstract
The problem about heat propagation from a transient point heat source located inside or outside a plane layered heat-conducting medium is studied. The transient problem is reduced to the harmonic point heat source problem for which the reflection method is generalized. The developed reflection method for a point harmonic source is generalized to the case of an arbitrary system of sources and applied to solving problems of transient heat conduction of plane layered media with axially symmetric heat sources with a complex shape.
{"title":"Development of Methods for Solving Problems of Transient Heat Conduction of Plane Layered Media","authors":"A. B. Petrin","doi":"10.1134/s0030400x24700292","DOIUrl":"https://doi.org/10.1134/s0030400x24700292","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The problem about heat propagation from a transient point heat source located inside or outside a plane layered heat-conducting medium is studied. The transient problem is reduced to the harmonic point heat source problem for which the reflection method is generalized. The developed reflection method for a point harmonic source is generalized to the case of an arbitrary system of sources and applied to solving problems of transient heat conduction of plane layered media with axially symmetric heat sources with a complex shape.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700139
E. S. Kozlova, A. A. Savel’eva, V. V. Kotlyar
Abstract
Using simulation by means of the finite difference method in the time domain (FDTD), we demonstrated that focal spots of different shape with respect to both intensity and energy flux form upon tight focusing of a Gaussian linearly polarized beam containing an optical vortex by a Fresnel zone plate and upon focusing of a Gaussian beam by a spiral zone plate. The most significant differences are observed for the topological charge equal three. The energy flux upon focusing of a Gaussian beam by a Fresnel zone plate has a ring distribution, while the distribution of intensity and energy flux upon beam focusing by a spiral zone plate has three local maxima, which corresponds to the spiral-zone-plate order. The petal structure of intensity (and the energy flux) changes to a ring distribution at a certain distance from the focus.
{"title":"A Comparative Analysis of Intensity and Energy Flux in the Focus of the High-Numeric-Aperture Conventional and Spiral Zone Plates","authors":"E. S. Kozlova, A. A. Savel’eva, V. V. Kotlyar","doi":"10.1134/s0030400x24700139","DOIUrl":"https://doi.org/10.1134/s0030400x24700139","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Using simulation by means of the finite difference method in the time domain (FDTD), we demonstrated that focal spots of different shape with respect to both intensity and energy flux form upon tight focusing of a Gaussian linearly polarized beam containing an optical vortex by a Fresnel zone plate and upon focusing of a Gaussian beam by a spiral zone plate. The most significant differences are observed for the topological charge equal three. The energy flux upon focusing of a Gaussian beam by a Fresnel zone plate has a ring distribution, while the distribution of intensity and energy flux upon beam focusing by a spiral zone plate has three local maxima, which corresponds to the spiral-zone-plate order. The petal structure of intensity (and the energy flux) changes to a ring distribution at a certain distance from the focus.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700280
A. A. Pan’kov
Abstract
The object of the study is flexible piezoelectric bimorphs of rod and membrane types, consisting of two or more homogeneous piezoelectric layers (films) of equal thickness with the same or opposite-directional polarization, interlayer, and external electrodes (are electrode coatings). The solution of the actual problem has been considered: increasing the operating characteristics of flexible piezoelectric bimorphs for more efficient use as generators of electric energy, sensors, and actuators—converters of control electrical signals into movement of working surfaces for manipulating or assembling microscale objects. The regularities of the influence of the magnitude of the initial longitudinal load applied to the ends of a bimorphic rod or uniformly distributed along the outer circular contour (perimeter) of the bimorphic round membrane on the resulting performance values for flexible piezoelectric bimorphs of the rod and membrane types, respectively, have been investigated. We believe that the magnitude of the longitudinal force applied to the movable end of the rod bimorph or to the outer perimeter of the membrane does not change over time and does not exceed the corresponding value of the strength of instability considering the cantilever or hinge fastening of the bimorph. Therefore, we have variable multidirectional bending directions of the bimorph (actuator) when an alternating control electric voltage is applied to the electrodes, i.e., when the sign of the control electric voltage is changed, the direction of bending (blocking force) also changes to the opposite one and after “switching off” the control electric voltage, the bimorph returns from the curved state to the original rectilinear one. Analytical solutions have been obtained for the deformation fields: deflections and angles of rotation of working cross sections of flexible piezoelectric bimorphs using the well-known “hypothesis of flat sections” and the method of Mor’s integrals in Mechanics of Materials. The effect of increasing the resulting deflections and blocking forces of flexible piezoelectric bimorphs because of the action of the initial compressive load has been identified and studied. The results of numerical modeling have been obtained for a flexible rod bimorph made of PZT piezoceramic layers, the effective deformation characteristics of which were determined by solving the reverse problem on the basis of the results of other authors. The cases of cantilever and hinge fastening of the ends of the rod bimorph have been considered. It has been found that the magnitude of the blocking force for the bimorph in the form of a hinged rod significantly exceeds that for the bimorph in the form of a cantilever, while the action of the longitudinal compressive force linearly increases the magnitude of the deflection and blocking force of the bimorph.
{"title":"Effect of Increasing Piezomodules of the Initially Compressed Flexible Bimorph","authors":"A. A. Pan’kov","doi":"10.1134/s0030400x24700280","DOIUrl":"https://doi.org/10.1134/s0030400x24700280","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The object of the study is flexible piezoelectric bimorphs of rod and membrane types, consisting of two or more homogeneous piezoelectric layers (films) of equal thickness with the same or opposite-directional polarization, interlayer, and external electrodes (are electrode coatings). The solution of the actual problem has been considered: increasing the operating characteristics of flexible piezoelectric bimorphs for more efficient use as generators of electric energy, sensors, and actuators—converters of control electrical signals into movement of working surfaces for manipulating or assembling microscale objects. The regularities of the influence of the magnitude of the initial longitudinal load applied to the ends of a bimorphic rod or uniformly distributed along the outer circular contour (perimeter) of the bimorphic round membrane on the resulting performance values for flexible piezoelectric bimorphs of the rod and membrane types, respectively, have been investigated. We believe that the magnitude of the longitudinal force applied to the movable end of the rod bimorph or to the outer perimeter of the membrane does not change over time and does not exceed the corresponding value of the strength of instability considering the cantilever or hinge fastening of the bimorph. Therefore, we have variable multidirectional bending directions of the bimorph (actuator) when an alternating control electric voltage is applied to the electrodes, i.e., when the sign of the control electric voltage is changed, the direction of bending (blocking force) also changes to the opposite one and after “switching off” the control electric voltage, the bimorph returns from the curved state to the original rectilinear one. Analytical solutions have been obtained for the deformation fields: deflections and angles of rotation of working cross sections of flexible piezoelectric bimorphs using the well-known “hypothesis of flat sections” and the method of Mor’s integrals in Mechanics of Materials. The effect of increasing the resulting deflections and blocking forces of flexible piezoelectric bimorphs because of the action of the initial compressive load has been identified and studied. The results of numerical modeling have been obtained for a flexible rod bimorph made of PZT piezoceramic layers, the effective deformation characteristics of which were determined by solving the reverse problem on the basis of the results of other authors. The cases of cantilever and hinge fastening of the ends of the rod bimorph have been considered. It has been found that the magnitude of the blocking force for the bimorph in the form of a hinged rod significantly exceeds that for the bimorph in the form of a cantilever, while the action of the longitudinal compressive force linearly increases the magnitude of the deflection and blocking force of the bimorph.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700309
S. V. Yakovlev, S. A. Sadovnikov, N. S. Kravtsova
Abstract
The results of calculating the atmospheric transmission spectrum and modeling lidar signals in the informative range of greenhouse gas sounding (CO2 and H2O) on horizontal tropospheric paths using the two-channel infrared lidar system under development are presented. It is shown that the lidar system operation spectral range of 4878–4894 cm–1 (2043–2050 nm) is preferable for simultaneous probing of CO2 and H2O. In this range, the level of lidar signals lies in the range of 10–6–10–10 W and exceeds the equivalent power photodetector noise. Based on the results of the calculations, the technical appearance of the developed two-channel infrared lidar system is determined.
摘要 介绍了利用正在开发的双通道红外激光雷达系统计算对流层水平路径上温室气体（CO2 和 H2O）探测信息范围内的大气传输谱和激光雷达信号建模的结果。结果表明，激光雷达系统的工作光谱范围为 4878-4894 cm-1（2043-2050 nm），是同时探测 CO2 和 H2O 的理想选择。在这一范围内，激光雷达信号水平在 10-6-10-10 W 之间，超过了等效功率光电探测器噪声。根据计算结果，确定了所开发的双通道红外激光雷达系统的技术外观。
{"title":"The Concept of a Two-Channel Infrared Lidar for Monitoring Greenhouse Gases in the Surface Layer of the Atmosphere","authors":"S. V. Yakovlev, S. A. Sadovnikov, N. S. Kravtsova","doi":"10.1134/s0030400x24700309","DOIUrl":"https://doi.org/10.1134/s0030400x24700309","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The results of calculating the atmospheric transmission spectrum and modeling lidar signals in the informative range of greenhouse gas sounding (CO<sub>2</sub> and H<sub>2</sub>O) on horizontal tropospheric paths using the two-channel infrared lidar system under development are presented. It is shown that the lidar system operation spectral range of 4878–4894 cm<sup>–1</sup> (2043–2050 nm) is preferable for simultaneous probing of CO<sub>2</sub> and H<sub>2</sub>O. In this range, the level of lidar signals lies in the range of 10<sup>–6</sup>–10<sup>–10</sup> W and exceeds the equivalent power photodetector noise. Based on the results of the calculations, the technical appearance of the developed two-channel infrared lidar system is determined.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x2470022x
S. B. Bogdanova, S. O. Gladkov
Abstract
A system of differential equations describing the motion of a freely falling body from the point of view of an observer fixed in the center of the standard basis of a specified plane curve and moving together with it has been obtained. Using computer simulation, respective trajectories have been built for two cases: with the observer moving along the circumference either with a constant angular velocity or with an angular velocity varying in accordance with specified laws in the form of a cosine and in the form of a Bessel function.
{"title":"On the Issue of the Trajectory of a Freely Falling Body in Noninertial Frames of Reference","authors":"S. B. Bogdanova, S. O. Gladkov","doi":"10.1134/s0030400x2470022x","DOIUrl":"https://doi.org/10.1134/s0030400x2470022x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A system of differential equations describing the motion of a freely falling body from the point of view of an observer fixed in the center of the standard basis of a specified plane curve and moving together with it has been obtained. Using computer simulation, respective trajectories have been built for two cases: with the observer moving along the circumference either with a constant angular velocity or with an angular velocity varying in accordance with specified laws in the form of a cosine and in the form of a Bessel function.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887173","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700231
V. F. Tarasenko, D. V. Beloplotov, M. I. Lomaev, A. N. Panchenko, D. A. Sorokin
Abstract
The glow of a nanosecond diffuse discharge between two tips with high spatial resolution has been studied. At atmospheric air pressure, as well as at pressures of 300, 100, and 30 Torr, a large number of thin luminous tracks, starting from the region of bright spots on the electrodes, have been discovered. It is shown that the shape of the tracks changes from straight lines to winding ones, and the direction of their movement in some cases changes to the opposite. It is shown that, under conditions of the formation of thin luminous tracks, the bands of the second positive nitrogen system dominate in the emission spectrum of diffuse plasma with a sharply inhomogeneous electric field and nanosecond duration of the voltage pulse. Using an ICCD camera, it has been shown that no emission of the tracks is detected during the first tens of nanoseconds against the background of wide streamers and a diffuse discharge. A hypothesis has been put forward to explain the appearance of numerous tracks during air breakdown in a nonuniform electric field.
{"title":"Thin Luminous Tracks during a Nanosecond Discharge in a Nonuniform Electric Field","authors":"V. F. Tarasenko, D. V. Beloplotov, M. I. Lomaev, A. N. Panchenko, D. A. Sorokin","doi":"10.1134/s0030400x24700231","DOIUrl":"https://doi.org/10.1134/s0030400x24700231","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The glow of a nanosecond diffuse discharge between two tips with high spatial resolution has been studied. At atmospheric air pressure, as well as at pressures of 300, 100, and 30 Torr, a large number of thin luminous tracks, starting from the region of bright spots on the electrodes, have been discovered. It is shown that the shape of the tracks changes from straight lines to winding ones, and the direction of their movement in some cases changes to the opposite. It is shown that, under conditions of the formation of thin luminous tracks, the bands of the second positive nitrogen system dominate in the emission spectrum of diffuse plasma with a sharply inhomogeneous electric field and nanosecond duration of the voltage pulse. Using an ICCD camera, it has been shown that no emission of the tracks is detected during the first tens of nanoseconds against the background of wide streamers and a diffuse discharge. A hypothesis has been put forward to explain the appearance of numerous tracks during air breakdown in a nonuniform electric field.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700206
A. Yu. Karavayskiy, Yu. I. Lukin
Abstract
Using a generalized refractive mixture dielectric model, the influence of the relative permittivity spectra of bound and unbound water in mineral soil on the nature of the temperature dependence of the relative permittivity of natural mineral soil, with a clay fraction content of 41.3%, was studied in the electromagnetic field frequency range from 50 MHz to 15 GHz. The causes of the emergence of intersections in the relative permittivity spectra of mineral soil, obtained at different temperatures but for a sample of the same moisture content, have been studied. It has been proved that the emergence of such an intersection point in the frequency range up to 1.5 GHz is due to the Maxwell–Wagner effect in bound water. The dependences of the frequency of the intersection point of the relative permittivity spectra of mineral soil on the temperature and volumetric content of bound and unbound water have been studied.
{"title":"Influence of Dielectric Relaxations of Soil Water on the Temperature Dependence of Soil Permittivity","authors":"A. Yu. Karavayskiy, Yu. I. Lukin","doi":"10.1134/s0030400x24700206","DOIUrl":"https://doi.org/10.1134/s0030400x24700206","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Using a generalized refractive mixture dielectric model, the influence of the relative permittivity spectra of bound and unbound water in mineral soil on the nature of the temperature dependence of the relative permittivity of natural mineral soil, with a clay fraction content of 41.3%, was studied in the electromagnetic field frequency range from 50 MHz to 15 GHz. The causes of the emergence of intersections in the relative permittivity spectra of mineral soil, obtained at different temperatures but for a sample of the same moisture content, have been studied. It has been proved that the emergence of such an intersection point in the frequency range up to 1.5 GHz is due to the Maxwell–Wagner effect in bound water. The dependences of the frequency of the intersection point of the relative permittivity spectra of mineral soil on the temperature and volumetric content of bound and unbound water have been studied.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x2470019x
I. P. Popov
Abstract
Relevance and formulation of the problem. The number of areas of scientific and practical activity in which it is necessary to consider relativistic corrections is steadily growing. In many cases, two objects under study move towards one another. This takes place both in relation to astronomical objects and in relation to quantum particles, including in colliders—accelerators of charged particles in colliding beams. With counter relativistic motions, the relative velocity does not coincide with the approach velocity. However, considering relative velocity alone limits the arsenal of research tools and methods. As opposed to relative velocity, which is determined in accordance with the relativistic formula for velocity addition, the approach velocity of unaccelerated objects is defined as the ratio of the distance between them to the time it takes to cover it. The purpose of this work is to analyze the variety of the relativistic approach velocity of objects depending on the choice of inertial reference frames based on the data of the Large Hadron Collider. Results. At the Large Hadron Collider, the approach velocity of protons is almost twice as high as the speed of light in the laboratory reference frame. In frames of reference associated with moving protons, depending on the options of relativistic transformation of segments of lengths and time intervals, the maximum approach velocity of protons is 1.1 × 108с, and the minimum is 1.2 m/s. In accordance with the technique based on the relativistic velocity addition formula, the approach velocity in reference systems associated with moving protons is almost equal to the speed of light. In this case, the approach velocity becomes equal to the relative velocity, which should not be considered as a generalization of the classical mechanics rule on the indistinguishability of these velocities to relativistic mechanics. Practical significance. The results obtained may be of interest in assessing the approach velocities of astronomical objects, including the Earth and asteroids, as well as significantly expand the variability of hypotheses when processing experimental data arrays obtained at elementary particle accelerators, including the Large Hadron Collider.
{"title":"Analysis of the Variety of the Relativistic Approach Velocity of Objects Based on the Data of the Large Hadron Collider","authors":"I. P. Popov","doi":"10.1134/s0030400x2470019x","DOIUrl":"https://doi.org/10.1134/s0030400x2470019x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Relevance and formulation of the problem. The number of areas of scientific and practical activity in which it is necessary to consider relativistic corrections is steadily growing. In many cases, two objects under study move towards one another. This takes place both in relation to astronomical objects and in relation to quantum particles, including in colliders—accelerators of charged particles in colliding beams. With counter relativistic motions, the relative velocity does not coincide with the approach velocity. However, considering relative velocity alone limits the arsenal of research tools and methods. As opposed to relative velocity, which is determined in accordance with the relativistic formula for velocity addition, the approach velocity of unaccelerated objects is defined as the ratio of the distance between them to the time it takes to cover it. The purpose of this work is to analyze the variety of the relativistic approach velocity of objects depending on the choice of inertial reference frames based on the data of the Large Hadron Collider. Results. At the Large Hadron Collider, the approach velocity of protons is almost twice as high as the speed of light in the laboratory reference frame. In frames of reference associated with moving protons, depending on the options of relativistic transformation of segments of lengths and time intervals, the maximum approach velocity of protons is 1.1 × 10<sup>8</sup><i>с</i>, and the minimum is 1.2 m/s. In accordance with the technique based on the relativistic velocity addition formula, the approach velocity in reference systems associated with moving protons is almost equal to the speed of light. In this case, the approach velocity becomes equal to the relative velocity, which should not be considered as a generalization of the classical mechanics rule on the indistinguishability of these velocities to relativistic mechanics. Practical significance. The results obtained may be of interest in assessing the approach velocities of astronomical objects, including the Earth and asteroids, as well as significantly expand the variability of hypotheses when processing experimental data arrays obtained at elementary particle accelerators, including the Large Hadron Collider.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-02DOI: 10.1134/s0030400x24700140
A. P. Davydov, T. P. Zlydneva
Abstract
The description of photon-matter interaction upon control, transmission, and detection of single-photon, two-photon, and multiphoton states, including the entangled ones, will play an ever-increasing role in many areas of photonics. An appropriate description requires taking into consideration various types of interference effects associated with these states. However, the relatively complex apparatus of second quantization of the electromagnetic field is used even in the simplest single-photon experiments equivalent to the Young’s one, e.g., the experiments with the Mach–Zehnder interferometer. In the present work, the Young’s single-photon mental experiment is explained using the coordinate photon wave function (PWF). The explanation is illustrated by specific examples of the single-photon states at certain wavelengths and different duration of radiation within the framework of two approaches: the quantum mechanical and the “quasi-classical.” In the first approach, a 6-component coordinate PWF is constructed based on the spherically symmetric momentum distribution in a wave packet, followed by approximate analytical calculations. In the second approach, a one-component quasi-classical PWF corresponding to the electric-dipole radiation is constructed. The same pronounced interference pattern was obtained in both cases, which makes is possible to draw the conclusion that the coordinate PWF allows explaining the one- and two-photon interference phenomena. This conclusion sheds the light on theoretical interpretation of the measurement of the coordinate PWF carried out in some of the recent experiments.
{"title":"Analytical Modeling of the Young’s Single-Photon Experiment Using the Quasi-Classical and Approximate Quantum-Mechanical Coordinate Photon Wave Functions","authors":"A. P. Davydov, T. P. Zlydneva","doi":"10.1134/s0030400x24700140","DOIUrl":"https://doi.org/10.1134/s0030400x24700140","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The description of photon-matter interaction upon control, transmission, and detection of single-photon, two-photon, and multiphoton states, including the entangled ones, will play an ever-increasing role in many areas of photonics. An appropriate description requires taking into consideration various types of interference effects associated with these states. However, the relatively complex apparatus of second quantization of the electromagnetic field is used even in the simplest single-photon experiments equivalent to the Young’s one, e.g., the experiments with the Mach–Zehnder interferometer. In the present work, the Young’s single-photon mental experiment is explained using the coordinate photon wave function (PWF). The explanation is illustrated by specific examples of the single-photon states at certain wavelengths and different duration of radiation within the framework of two approaches: the quantum mechanical and the “quasi-classical.” In the first approach, a 6-component coordinate PWF is constructed based on the spherically symmetric momentum distribution in a wave packet, followed by approximate analytical calculations. In the second approach, a one-component quasi-classical PWF corresponding to the electric-dipole radiation is constructed. The same pronounced interference pattern was obtained in both cases, which makes is possible to draw the conclusion that the coordinate PWF allows explaining the one- and two-photon interference phenomena. This conclusion sheds the light on theoretical interpretation of the measurement of the coordinate PWF carried out in some of the recent experiments.</p>","PeriodicalId":723,"journal":{"name":"Optics and Spectroscopy","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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