In modern physical theories, when modeling fundamental structures of reality, the relational concept of space and time is not sufficiently taken into account. In modern physical theories, the relational concept of space and time is not sufficiently taken into account when modeling fundamental structures of reality. A priori, the concepts of space and time are introduced, which leads to contradiction. The purpose of the present work is to simulate the localization and motion of a free particle taking into account the relational concept of space and time. When modeling the localization and motion of a free particle, it is shown that the use of the superposition principle, namely, the overlay of subsystems, allows you to take into account the relational concept of space and time. For this, Minkowski space is generalized. State space is introduced - homogeneous space of possible subsystems. From the overlay of these subsystems, Minkowsky space is manifested, taking into account the presence of particles. It is shown that homogeneity and isotropy of space and homogeneity of time follow from homogeneity of space of possible subsystems. For the particle, a non-swinging de Broglie wave packet is obtained.
In modern physical theories, when modeling fundamental structures of reality, the relational concept of space and time is not sufficiently taken into account. In modern physical theories, the relational concept of space and time is not sufficiently taken into account when modeling fundamental structures of reality. A priori, the concepts of space and time are introduced, which leads to contradiction. The purpose of the present work is to simulate the localization and motion of a free particle taking into account the relational concept of space and time. When modeling the localization and motion of a free particle, it is shown that the use of the superposition principle, namely, the overlay of subsystems, allows you to take into account the relational concept of space and time. For this, Minkowski space is generalized. State space is introduced - homogeneous space of possible subsystems. From the overlay of these subsystems, Minkowsky space is manifested, taking into account the presence of particles. It is shown that homogeneity and isotropy of space and homogeneity of time follow from homogeneity of space of possible subsystems. For the particle, a non-swinging de Broglie wave packet is obtained.
On an example of modeling of motion of a free particle, possible positions of the particle in Minkowski space are determined, which are approximated by a periodic function. A concept of a subsystem corresponding to the possible position of the particle is introduced. A family of these subsystems is considered as independent elements of a large infinite composite system. The homogeneous space of possible states is introduced, from which basic properties of the Minkowski space follow. Superimposition of the subsystems is quantum superposition of the states. Justifications of the Heisenberg uncertainty principle are given. In the modeling, an idea of manifestation of reality as a result of the superimposition of the systems was used. A condition of closedness of the system is determined. The law of increase of entropy of the closed system is justified.
The concept of position and its measurement are fundamental to modern navigation technology as well as to theoretical physics. Nevertheless, a consistent notion of position has not been found in modern physics because of apparent inconsistencies between quantum mechanics and relativity. In quantum mechanics the probability distribution for a particle's position is determined by its wave function. A wave function strictly localized in space describes a particle within that locality, and nowhere else. But the quantum equations of motion predict the function will disperse, after any length of time at all, to occupy all space. Therefore the theoretical prediction is that, shortly after detection in a laboratory, a particle may be found anywhere in the universe, including regions requiring faster-than-light travel to reach. This contradicts the theory of relativity, which precludes a body traveling faster than the speed of light. The conflict arises from unexamined assumptions regarding the time of the measurement event and the time of the system under measurement. The prevailing view in physics is that time is only a parameter, having a definite value, describing dynamic changes in physical systems. This view endures even though quantum mechanics recognizes position as a quantum variable with inherent uncertainty, and relativity indicates that time should be placed on the same footing as position. But if time is recognized as a quantum variable with inherent uncertainty, the conceptual problems with position are resolved. The particle has finite probability of being in the past (or future) of the observer, while the quantum mechanical operator describing the position measurement contains a term which extrapolates from the intrinsic time of the particle to the time of the observer. Being potentially well in the past of the measurement event, the particle has time to travel to remote regions without exceeding the speed of light, and the conflict with relativity is resolved. A relativistic quantum theory can therefore be constructed incorporating a well-defined concept of position.
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has insoluble semantic interpretations like reduction of wave packet on observations of physical values. Especially, it is not clear that the wave function which is described by complex function, is whether formality or reality to express the state of particle motion. On this paper, we interpret the wave nature of particle as not the inherency of particle itself, but the motional property of particle in fluctuated space-time due to the kinetic energy and momentum the belief that the kinetic energy and momentum fluctuates the microscopic space-time, and the particle move through the fluctuated space-time adversely. Then, through the particle motion in the Euclidean space-time, the particle will be recognized as if it has the wave nature. We estimate the governing equation of fluctuations of microscopic space-time based on the macroscopic law of motion. On this paper, the equivalence between the governing equation and the Schrodinger equation is indicated.
Abstract This chapter continues with a study of the time independent Schrödinger equation and seeks to contrast the quantum behavior of a free particle with that of a particle localized in a potential quantum well. A free particle can exist over all space or can be localized in a wave package. The wave packet is a coherent superposition of the plane waves that make up the wave function that localizes the particle because of constructive and destructive interference. The wave packet spreads out in time because the waves leading to constructive interference get out of phase. In Chapter 2, the particle was localized by a quadratic potential energy. Here, the potentials are described as piecewise constant. The approach is based on assuming a one-dimensional space, x, which is relevant to many problems in the laboratory. The solution is easily generalized to higher dimensions (x-y or x-y-z), but the physics remains the same. The objective is to understand the shape of the eigenfunctions in space and to be able to relate this to the probability density of locating the particle, as well as understanding the relevance of these systems to today’s technology.
Аннотация. При моделировании физических объектов в качестве основного элементавыбирают модель материальной точки. Однако при исследовании фундаментальных структур реальности применение классической модели материальной точки нецелесообразно. Потому что в классической модели материальной точки априори вводится понятие пространства, независящее от нее, что приводит к противоречию с реляционной концепцией пространства и времени.Следует отметить также противоречие, которое возникает при попытке определения«кирпичика» мироздания в виде крохотной частицы с понятием квантовой нелокальности. Экспериментальные исследования, проведенные с целью проверки неравенства Белла доказали, что в фундаментальной структуре реальности имеет место квантовая нелокальность. Этоозначает, что каждая частица имеет некоторую таинственную связь с окружением. Поэтому пространству Минковского требуется обобщение, учитывающее наличие материи. В настоящей работе обобщается пространство Минковского. Вводится пространство состояний – однородное пространство возможных подсистем. Из наложения этих подсистем проявляется пространство Минковского, учитывающее наличие частиц. На примере моделирования локализации и движения свободной частицы показано, что из однородности пространства возможных подсистем следуют однородность и изотропность пространства, однородность времени. При этом однородное пространство проявляется при наложении подсистем однородного пространства состояний. Изотропное пространство проявляется при наложении подсистем под определенными углами. При последовательных переходах из одной подсистемы в другую внутри подсистемы индуцируется однородное время. В результате наложений подсистем и вышеуказанных переходов происходит и локализация частицы в пространстве Минковского. Дано объяснение принципу неопределенности Гейзенберга. Предложено оригинальное определение понятия спина частицы. Симметрии пространства и времени непосредственно связаны с параметрами частицы, а именно с импульсом, спином и энергией. Сохранение этих величин обуславливает свойства симметрии пространства Минковского. Если рассматривается более сложная система, например, из многих частиц,то она находится в запутанном состоянии. В этом случае задача намного усложняется, но идля этой системы также можно ввести волновую функцию. Поэтому предложенный подходпозволяет сказать, что наложение возможных подсистем и самосогласованные переходы из одной возможной подсистемы в другую могут локализовать объекты нашего пространства подобно явлению декогеренции. Abstract. When modeling physical objects, the material point model is chosen as the main element. However, in the study of the fundamental structures of reality, the application of the classicalmodel of the material point is inappropriate. Because, in the classical model of a material point,the concept of space independent of it is introduced a priori, which leads to a contradiction with therelational concept of space and time. It should be noted also the contradiction that occurs when trying to determine the "brick" of the universe in the form of a tiny particle with the concept of quantumnon-locality. Experimental studies to verify Bell's inequality proved that quantum nonlocality takesplace in the fundamental structure of reality. This means that each particle has some mysteriousconnection with the environment. Therefore, Minkowski space requires a generalization taking intoaccount the presence of matter. This paper generalizes the Minkowski space. The state space isintroduced – a homogeneous space of possible subsystems. From the superposition of these subsystems, the Minkowski space appears, taking into account the presence of particles. Using the modeling oflocalization and motion of a free particle as an example, it is shown that the uniformity and isotropyof space, the uniformity of time, follow from the homogeneity of the space of possible subsystems.In this case, a homogeneous space appears when superimposing subsystems of a homogeneousstate space. Isotropic space appears when superimposing subsystems at certain angles. During successive transitions from one subsystem to another, homogeneous time is induced inside the subsystem. As a result of overlapping subsystems and the above transitions, the particle is also localized in Minkowski space. Heisenberg's uncertainty principle is explained. An original definition of the particle spin concept is proposed. The symmetries of space and time are directly related to the parameters of the particle, namely, with momentum, spin and energy. The conservation of these quantities determines the symmetryproperties of Minkowski space. If we consider a more complex system, for example, of many particles,then it is in an entangled state. In this case, the task is much more complicated, but for this system youcan also introduce the wave function. Therefore, the proposed approach allows us to say that theimposition of possible subsystems and self-consistent transitions from one possible subsystem to anothercan localize objects of our space, similar to decoherence.
Abstract Relative motion of particles is examined in the context of relational space-time. It is shown that de Broglie waves may be derived as a representation of the coordinate maps between the rest-frames of these particles. Energy and momentum are not absolute characteristics of these particles, they are understood as parameters of the coordinate maps between their rest-frames. It is also demonstrated the position of a particle is not an absolute, it is contingent on the frame of reference used to observe the particle. Version of Record This preprint has not undergone peer review or any post-submission improvements or corrections. The Version of Record of this article is published in Foundations of Physics, and is available online at https://doi.org/10.1007/s10701-023-00715-9