A presentation showing how the statements which relate to microphysical objects as they are different from the statements of classical mechanics is made. The determinism of classical and of quantum-mechanical theories is qualified. A (crucial) distinction between causality and determinism is given. Detailed analyses of diffraction as a result of single and double-slit demonstrations point to paradoxes arising from the use of particle or wave models, respectively, for photons and electrons. The compromising wave-packet model is underscored. The meanings for the Psi-function and for |ψ|2 are presented, with an explanation of the limitations that arise from giving an interpretation of |ψ|2 as a probability. The meaning of ψ-waves is analyzed. A case is made for the ψ-function's describing a well-ordered list of betting odds, based on previous statistical experiences, for the different results of specific experiments of a microscopic object of study with macroscopic apparatus. The Schrödinger wave equation is evaluated for meaning and judged as a deterministic expression.
A presentation showing how the statements which relate to microphysical objects as they are different from the statements of classical mechanics is made. The determinism of classical and of quantum-mechanical theories is qualified. A (crucial) distinction between causality and determinism is given. Detailed analyses of diffraction as a result of single and double-slit demonstrations point to paradoxes arising from the use of particle or wave models, respectively, for photons and electrons. The compromising wave-packet model is underscored. The meanings for the Psi-function and for |ψ|2 are presented, with an explanation of the limitations that arise from giving an interpretation of |ψ|2 as a probability. The meaning of ψ-waves is analyzed. A case is made for the ψ-function's describing a well-ordered list of betting odds, based on previous statistical experiences, for the different results of specific experiments of a microscopic object of study with macroscopic apparatus. The Schrödinger wave equation is evaluated for meaning and judged as a deterministic expression.
Microscopic particles, like electrons, do not move following the classical laws of motion, given by Newtonian Mechanics. These particles, however, follow other laws that are associated to the propagation of waves. This becomes qualitatively clear when we observe an interference pattern arise in an experiment in which an electron beam passes through a double slit. In this brief study, we will deal with the quantum analysis of the dynamics of particles, by means of its postulates and its precise mathematical formulation. That is, we intend to introduce the wave function and the Schrodinger equation, as well as to interpret physically such a function. The scientific bases of this essay (1),(2),(3),(4),(5) can be found in the books listed in the bibliographic references.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.
The wave-particle duality is a fundamental property of the nature. At the same time, it is one of the greatest mysteries of modern physics. This gave rise to a whole direction in quantum physics - the interpretation of quantum mechanics. The Wiener experiments demonstrating the wave-particle duality of light are discussed. It is shown that almost all interpretations of quantum mechanics allow explaining the double-slit experiments, but are powerless to explain the Wiener experiments. The reason of the paradox, associated with the wave-particle duality is analyzed. The quantum theory consists of two independent parts: (i) the dynamic equations describing the behavior of a quantum object (for example, the Schrodinger or Maxwell equations), and (ii) the Born’s rule, the relation between the wave function and the probability of finding the particle at a given point. It is shown that precisely the Born’s rule results in paradox in explaining the wave-particle duality. In order to eliminate this paradox, we propose a new rational interpretation of the wave-particle duality and associated new rule, connecting the corpuscular and wave properties of quantum objects. It is shown that this new rational interpretation of the wave-particle duality allows using the classic images of particle and wave in explaining the quantum mechanical and optical phenomena, does not result in paradox in explaining the doubleslit experiments and Wiener experiments, and does not contradict to the modern quantum mechanical concepts. It is shown that the Born’s rule follows immediately from proposed new rules as an approximation.
An outline is given of the interpretation of quantum mechanical expressions if one assumes that what is called Quantum Mechanics today, refers to an underlying reality as in Chap. 2 , even if many authors claim to have evidence to the contrary, as is usually brought forward. If there exists a sub-microscopic classical world of real things, is that the same classical world as the world of large things such as planets, rocks and people? How does the notion of probability enter into quantum mechanics? These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
From the fact that many people are dedicated to the quantization of gravity, it can be seen that people crave the integration of quantum theory and macroscopic theory. Let's first combine quantum mechanics with classical mechanics to gain insightful experiences. The citation introduces the Schrödinger-Tu equation, which has gravitational potential energy and can describe macroscopic objects. Several successful computational examples related to atoms and molecules using the combination of quantum and classical methods for use were listed. The wave mechanics representation method of classical mechanics laws has been derived. This indicates that quantum mechanics and classical mechanics can be compatible and coexist. There is still much evidence to suggest that the Schrödinger equation (SE) cannot exclude classical mechanical laws: The mass m in the SE can be large enough to bring the described object into the macroscopic range; Steady state SE is the Tψ+Vψ=Eψ, a combination of the wave function ψ and the expression T+V=E in classical mechanics; The potential energy function in the SE can originate from macroscopic force fields; F=ma and the SE can be converted to each other; Completed electron diffraction experiments that exhibit both wave and particle characteristics simultaneously. Important conceptual changes can drive the renewal of physics. The shift from quantum and classical incompatibility to compatibility is an important conceptual change that can lead to the birth of general wave mechanics.
Quantum mechanics based on the probabilistic approach provides a powerful tool for accurate prediction and interpretation of quantum phenomena, allowing statistically sound predictions about the behavior of microparticles and quantum systems. This statement emphasizes the probabilistic nature of quantum mechanics, its applicability to quantum phenomena and microparticles, as well as the statistical nature of its predictions when applied to the macro effects of classical physics. In addition, the role of statistics and probability in various fields of science, such as particle physics, thermodynamics, biology, sociology, psychology, economics and finance, is discussed. The philosophical implications of the probabilistic approach and the associated limitations and challenges are also considered.