A memory is attributed to quantum systems. The time range of this memory is found to be inversely proportional to the energy of a system. The value of the wave function at any moment of time is the time average of its past values during the memory range. The formalism of quantum mechanics is reproduced in terms of integral operators and the time span of the memory of a system. The representation of the state of a quantum system at any moment of time is found to include an explicit representation of its past states as well. Measurement processes are explained from this point of view. Some experiments are analyzed using the present new interpretation.
A memory is attributed to quantum systems. The time range of this memory is found to be inversely proportional to the energy of a system. The value of the wave function at any moment of time is the time average of its past values during the memory range. The formalism of quantum mechanics is reproduced in terms of integral operators and the time span of the memory of a system. The representation of the state of a quantum system at any moment of time is found to include an explicit representation of its past states as well. Measurement processes are explained from this point of view. Some experiments are analyzed using the present new interpretation.
We present a new interpretation of the terms superposition, entanglement, and measurement that appear in quantum mechanics. We hypothesize that the structure of the wave function for a quantum system at the sub-Planck scale has a deterministic cyclic structure. Each cycle comprises a sequential succession of the eigenstates that comprise a given wave function. Between unitary operations or measurements on the wave function, the sequential arrangement of the current eigenstates chosen by the system is immaterial, but once chosen it remains fixed until another unitary operation or measurement changes the wave function. The probabilistic aspect of quantum mechanics is interpreted by hypothesizing a measurement mechanism which acts instantaneously but the instant of measurement is chosen randomly by the classical measuring apparatus over a small but finite interval from the time the measurement apparatus is activated. At the instant the measurement is made, the wave function irrevocably collapses to a new state (erasing some of the past quantum information) and continues from thereon in that state till changed by a unitary operation or a new measurement.
A new type of representation of the wave function of quantum mechanics, and a new form of the statistical interpretation of the wave function, are presented. The variable in the new representation is a mapping of points of differential space, closely related to Hilbert space, but having an associated measure for suitably defined sets of points in it. In the new statistical interpretation, an eigenvalue of every observable defined in the system is associated with each point in differential space. This can be done in such a way that, for each observable, the measure (=probability) of the set of all differential-space points belonging to a given set of eigenvalues is equal to the quantum-mechanical probability, calculated in the usual way (Born statistical postulate), that an experiment will yield an eigenvalue in this set. Thus we obtain an interpretation of quantum mechanics in terms of probability densities or probabilities instead of probability amplitudes.
In the well known Copenhagen interpretation of Quantum mechanics, advocated by N. Bohr, the physical objects and the experimental results can be described only in a macroscopic language, leaving any possible microscopic description as unspeakable. This point of view has been deepened by C. Rovelli in the relational interpretation of Quantum mechanics. Most of the alternative interpretations, which try a detailed microscopic description of physical phenomena and of their evolution, have in common the explicit introduction of the wave function as the basic element of the theory. These interpretations require the notion of quantum state as the fundamental concept of the theory, which is the typical unspeakable physical element according to the Copenhagen interpretation. The two basic physical entities are intimately bound together by the integrity of the wave function. These interpretations are usually indicated as realistic. It is well known that the use of the wave function and its time evolution in the description of the physical processes leads unavoidably to some difficulties or so-called paradoxes. The measurement problem is at the center of these difficulties, mainly because it requires the introduction of the reduction process of the wave function, which is not included explicitly within the mathematical formalism of Quantum Mechanics. In this paper we build up and propose a model which goes beyond the standard formalism and which is able to solve the measurement problem and all the other difficulties which, in a way or in another, are related to it.
Quantum mechanics has been enormously successful in explaining the behavior of microsystems such as molecules, atoms, and nuclei. We have seen that quantum mechanics describes a quantum system by the wave function ψ, which is the solution of the Schro¨dinger equation. The wave function determines the probability amplitudes (whose modulus squared gives the probability) for all possible outcomes of a measurement corresponding to an observable on the system. In general, the wave function does not uniquely predict the result of a measurement; it only provides a probability distribution for all possible results of the measurement on a quantum system. Only if the system happens to be in an eigenstate corresponding to the observable being measured, is the result of a measurement of this observable completely predictable. On the other hand, the results of measurements corresponding to a conjugate or non-commuting observable, on the same system in the same state, are indeterminate. Quantum mechanical description of physical systems raises profound questions: How are the wave function and the probabilities for different outcomes of a measurement to be interpreted? Does the wave function represent a single system or an ensemble of systems? Does the physical system actually have the attribute corresponding to the measurement in question or does the measurement itself create the attribute? These questions led to different interpretations of quantum mechanics, which were vigorously debated during the years of its discovery as also in the following decades. The new idea of indeterminacy was especially difficult to reconcile with the long-held view that a physical theory should aim at predicting accurately, and without ambiguity, the result of any measurement on any system, big or small. These debates not only gave us a deeper understanding of quantum mechanics but also changed profoundly the way we view the micro-world.
The meaning of the wave function has been a hot topic of debate since the early days of quantum mechanics. Recent years have witnessed a growing interest in this long-standing question. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? In this book, I aim to make sense of the wave function in quantum mechanics and find the ontological content of the theory. The book can be divided into three parts. The first part addresses the question of the nature of the wave function (Chapters 1-5). After giving a comprehensive and critical review of the competing views of the wave function, I present a new argument for the ontic view in terms of protective measurements. In addition, I also analyze the origin of the wave function by deriving the free Schroedinger equation. The second part analyzes the ontological meaning of the wave function (Chapters 6, 7). I propose a new ontological interpretation of the wave function in terms of random discontinuous motion of particles, and give two main arguments supporting this interpretation. The third part investigates whether the suggested quantum ontology is complete in accounting for our definite experience and whether it needs to be revised in the relativistic domain (Chapters 8, 9).
Through studying we investigate the sense of the wave function of the mass and charge the density distributions of the quantum system. According to the protective calculation, a charged quantum system has effective distribution of mass and charging density in space, proportional to the square of the absolute value of its wave function. In a practical interpretation a wave function of the quantum system can be taken as a definition of either a physical field or the ergodic motion of a particle. The main distinction among the ergodic movement of a sphere and a cell lies in the concurrent property a sphere occurs simultaneously in space, while the agosic movement of a cell is spatially separated in time. If the wave function is a physical force, then the mass and charging density are simultaneously distributed in space to the charged quantum system and thus to the gravitational and electrostatic self-interactions of its wave function. This not only contradicts the superposition principle of quantum mechanics but also contradicts the findings of the experiments. Therefore, wave function is not a definition of a physical area, but rather a transient phase of a material.Each moment has a single localized particle with mass and charge, so the wave function is not auto-introduced. Therefore, it has been argued that the classical ergodic model may not correspond to quantum mechanics for determining constant motion of the particles. Based on the negative result, we say the wave function is a random and unsatisfactory explanation of the particles' quantum motion in nature.In this view, the square of the absolute value of the wave function not only gives the particles' potential in certain locations but also the potential where the cell is. The proposed Latest wave-function description offers a natural practical other than orthodox interpretation, and also suggests that the Broglie-Bohm theory and the interpretation of many worlds are incorrect, and the theories of dynamic collapse They are heading in the right direction by accepting collapse of wave function.