The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical model of physical objects is proposed. This model gives a possibility to unite a description of corpuscular and wave properties of real physical objects, i.e. fields and particles. There are substantiated an approach and a mathematical pattern which give a possibility to describe physical object not only in causal, but also in absolute remote fields of the Minkowski space. Applying the proposed approach to the microcosm description, one can get the equations that in passage to the limit transfer to such quantum mechanics equations as Schrodinger, Klein-Gordon-Fock and in particular case - the wave equation. The event nature of the received equations is discussed. It is shown that all mentioned equations reflect the space-time relativistic properties during the description of the invariant and non-invariant physics object characteristics.
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical model of physical objects is proposed. This model gives a possibility to unite a description of corpuscular and wave properties of real physical objects, i.e. fields and particles. There are substantiated an approach and a mathematical pattern which give a possibility to describe physical object not only in causal, but also in absolute remote fields of the Minkowski space. Applying the proposed approach to the microcosm description, one can get the equations that in passage to the limit transfer to such quantum mechanics equations as Schrodinger, Klein-Gordon-Fock and in particular case - the wave equation. The event nature of the received equations is discussed. It is shown that all mentioned equations reflect the space-time relativistic properties during the description of the invariant and non-invariant physics object characteristics.
A hypothesis is put forward according to which the formulas of Relativity are a consequence of the laws of quantum physics and may be applied only to quantum objects. According to the wave - particle duality quantum bodies are simultaneously the waves and considered in the present research with a use of the wave equation and requirement of its Lorentz‘s invariance. The property of invariance with respect to the Lorentz’s transform is analysed in hyperbolic coordinates in an area of complex numbers. An examination showed that formulas of relativistic kinematics can be obtained based on the condition of equality of the amplitudes and phases of the wave, observed from different inertial frames. There is no need to introduce the concept of a unified entity of space-time, but the return to the idea of aether and matter waves de Broglie occurs. The physical model becomes borrowed partly from quantum field theory. It is assumed that the moving particle binds to a wave of the aether disturbance, and only this wave acts on the other particle like an electromagnetic field pushes an electrical charge. The model of colliding elastic balls becomes inapplicable, but equations of relativity mechanics remain the same, however, with a new interpretation. The mass of a particle in all coordinate systems is constant, in exchange the expressions of energy and momentum alter relative the classical case, include the property of aether – coefficient c of the wave equation, and acquire relativistic forms.
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.
The implications of the relativistic space-time structure for a physical description by quantum mechanical wave-functions are investigated. On the basis of a detailed analysis of Bell's concept of local causality, which is violated in quantum theory, we argue that this is a subtle, as well as an important effort. A central requirement appearing in relativistic quantum mechanics, namely local commutativity, is analyzed in detail and possible justifications are given and discussed. The complexity of the implications of wave function reduction in connection with Minkowski space-time are illustrated by a quantum mechanical measurement procedure which was proposed by Aharonov and Albert. This procedure and its relativistic implications are explicitly analyzed and discussed in terms of state evolution. This analysis shows that the usual notion of state evolution fails in relativistic quantum theory. Two possible solutions of this problem are given. In particular, it is shown that also a theory with a distinguished foliation of space-time into space-like leafs - accounting for nonlocality - makes the right predictions for the Aharonov-Albert experiment. We will repeatedly encounter that an analysis of the wave-function alone does not suffice to answer the question of relativistic compatibility of the theory, but that the actual events in space time, which are predicted and described by the theory, are crucial. Relativistic versions of quantum mechanical theories which precisely describe actual processes in space-time are briefly described and discussed in the appendix.
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, commutation and uncertainty relations, probability density current, momentum operator, rules for including the scalar and vector potentials and antiparticles can be obtained from the probabilistic description of results of measurement of the space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrodinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the space-time Fisher information. The limit case of the delta-like probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many particle systems and the postulates of quantum mechanics are also discussed.
The present study explores a theoretical extension of relativistic quantum wave equations through the introduction of complex space-time coordinates. The motivation for this approach arises from persistent conceptual challenges in relativistic quantum mechanics, particularly those related to probability interpretation and particle localization. By reformulating the Klein?Gordon and Dirac equations within a complex coordinate framework, the paper examines how the mathematical structure of these equations can be broadened without compromising fundamental physical principles. The analysis shows that treating the wave function as an analytic entity in complex space-time provides additional flexibility in handling boundary conditions and singularities. It also offers a refined perspective on the interpretation of solutions, especially in cases where traditional real-valued formulations lead to ambiguities. The study further demonstrates that Lorentz invariance can be preserved through analytic continuation, ensuring consistency with relativistic requirements. Although the framework remains theoretical, it suggests that complexification of space-time may serve as a useful tool in addressing certain limitations of relativistic quantum theory. The findings indicate that this approach has the potential to contribute to ongoing developments in quantum field theory and may provide a conceptual bridge toward more generalized formulations of quantum physics.
Aiming at the quantum mechanics wave function description probability feature, statistical interpretation, randomicity, uncertainty, nonlocality and agnosticism etc fundamental principles and concepts, based on the mass-space interaction, mass-space space-time view, microscopic mass-energy systems correlating with space-time model etc principles and theories, and the quantum entanglement particle experiments etc facts, present the matter-ordering-energy conservation laws and the Dong Pei innovating group interpretation of quantum mechanics. Simultaneously indicate: In the universe there exists the ordering- and disordering-energy matter, together known as matter. Existing the absolute space and absolute time. The absolute space-time is continuous. Matter and the absolute space-time together create and compose the objective world. The objective world is a harmonious and unified whole. Physical laws are completely unified. The objective world and matter are all finite. Matter exists, evolves and moves in the absolute space-time. Interactions are the most essential and most root basic attribute of matter. The interaction among matter is the mass-space interaction. The mass-space interaction is continuous and stable, is not random and intermittent. Macroscopic and microscopic regions all observe the identical physical laws. Elementary particles and they compose the microscopic mass-energy systems are all the ordering-energy matter, their mass-energy space-time is a interdependent whole, their feature, state, structure and motion laws are all entirely determined by the mass-space interaction, correspond with the determinism and causality, the motion state and feature, motion orbitals, position and speed of particles in the absolute space-time are all absolutely determined and could be measured exactly, their quantum states could be approximately described by the wave function of quantum mechanics. The wave functions are the simplified mathematical function approximate expression of quantum system states of adopted interaction, can be used to calculate the correlative physical quantities. The wave functions could approximately describe the state of the mass-energy space-time whole of a microscopic mass-energy system with the mass-space interaction acting and continuously moving. An eigenstate just is the state making the system energy minimum and in rather stable existence. Scientific theories are the abstract simplified approximate expression for the essential of natural phenomena. Physical theory is the abstract simplified approximate representation for the matter structure and its motion laws. Whereas the mathematical formulation then is the further simplified approximate representation for physical contents. All of theories, include quantum mechanics and relativity, only when the assumed approximate condition is satisfied, just are the applied correct scientific theory, could describe the objective world good enough but not exactly. Develop scientific theory, correctly cognize and reasonably interpret the objective world, without the end.