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.
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.
This paper investigates the relationship between subsystems and time in a closed nonrelativistic system of interacting bosons and fermions. It is possible to write any state vector in such a system as an unentangled tensor product of subsystem vectors, and to do so in infinitely many ways. This requires the superposition of different numbers of particles, but the theory can describe in full the equivalence relation that leads to a particle-number superselection rule in conventionally defined subsystems. Time is defined as a functional of subsystem changes, thus eliminating the need for any reference to an external time variable. The dynamics of the unentangled subsystem decomposition is derived from a variational principle of dynamical stability, which requires the decomposition to change as little as possible in any given infinitesimal time interval, subject to the constraint that the state of the total system satisfy the Schroedinger equation. The resulting subsystem dynamics is deterministic. This determinism is regarded as a conceptual tool that observers can use to make inferences about the outside world, not as a law of nature. The experiences of each observer define some properties of that observer's subsystem during an infinitesimal interval of time (i.e., the present moment); everything else must be inferred from this information. The overall structure of the theory has some features in common with quantum Bayesianism, the Everett interpretation, and dynamical reduction models, but it differs significantly from all of these. The theory of information described here is largely qualitative, as the most important equations have not yet been solved. The quantitative level of agreement between theory and experiment thus remains an open question.
Continuous degrees of freedom The quantum systems we have discussed so far have been described by finite-dimensional Hilbert spaces. Basic measurements on such systems have a finite number of possible outcomes, and a quantum state predicts a discrete probability distribution over these. Now we wish to extend our theory to handle systems with one or more continuous degrees of freedom, such as the position of a particle that can move in one dimension. This will require an extension of our theory to Hilbert spaces of infinite dimension, and to systems with continuous observables. There is a philosophical issue here. How do we know that there really are infinitely many distinct locations for a particle? The short answer is, we don't. It might be that space itself is both discrete (at the tiniest scales) and bounded (at the largest), so that the number of possible locations of a particle is some very large but finite number. If this is the case, then the continuum model for space is nothing more than a convenient approximation. Infinity is just a simplified way of describing a quantity that is immense, but still finite. In this section, we will adopt this view of infinity. We will imagine that any continuous variable is really an approximation of a “true” discrete variable. This idea will motivate the continuous quantities and operations that we need.
Quantum systems with infinite degrees of freedom exhibit properties, like relaxation to equilibrium, phase-transitions and the existence of inequivalent representations of the CAR and CCR , that can satisfactorily be dealt with by means of the methods and techniques of algebraic quantum statistical mechanics [80, 81, 130]. The point of departure from standard quantum mechanics, is that in an infinite dimensional context one is usually provided with the algebraic properties of the relevant observables, but, in general, not with an a priori given representation on a Hilbert space; the latter rather depends on to the physical properties of the systems under consideration [324, 342, 343].
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.
The model of the physical system with discrete interactions is based on the postulates that (i) parameters of the physical system are defined in process of its interaction; (ii) the process of interaction is discrete. Consequently ordering of the events in the system is not automatically implied based on the values of time, but must be specified explicitly. This suggests the specific logic of events as well as complex character of the function, which describes stochastic behavior of the system, hence the parameters of the system are defined by Hermitian operators in the Hilbert space of functions. The model gives an essential way to introduce the basic notions and obtain the results of the quantum theory, to derive the meaning of the main physical parameters, such as momentum or electric charge. Based on the proposed postulates, Schrodinger equation for the particle is deduced in a way similar to inferring of Smoluchowski equation in the classical statistical mechanics. Similarly, the equations of motion of linear fields are established by considering Smoluchowski-type equations for amplitudes of harmonics. The concept of discrete interaction gives a way to de-couple the object of experiment and a testing device (the traditional source of controversy in quantum theory), though at expense of limitation of the principle of locality.
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.