It is shown that probabilistic treatment of quantum mechanics can be coordinated with causality of all physical processes. The physical interpretation of quantum-mechanical phenomena such as process of measurement and collapse of quantum state is given.
The paper is concentrated on the special changes of the conception of causalityfrom quantum mechanics to quantum information meaning as a background the revolution implemented by the former to classical physics and science after Max Born’s probabilistic reinterpretation of wave function. Those changes can be enumerated so: (1) quantum information describes the general case of the relation of two wave functions, and particularly, the causal amendment of a single one; (2) it keeps the physical description to be causal by the conservation of quantum information and in accordance with Born’s interpretation; (3) it introduces inverse causality, “backwards in time”, observable “forwards in time” as the fundamentally random probability density distribution of all possible measurements of any physical quantity in quantum mechanics; (4) it involves a kind of “bidirectional causality” unifying (4.1) the classical determinism of cause and effect, (4.2) the probabilistic causality of quantum mechanics, and (4.3) the reversibility of any coherent state; (5) it identifies determinism with the function successor in Peano arithmetic, and its proper generalized causality with the information function successor in Hilbert arithmetic.
A history of the discovery of `new' quantum mechanics and the paradoxes of its probabilistic interpretation are briefly reviewed from the modern point of view of quantum probability and information. Modern quantum theory, which has been developed during the last 20 years for the treatment of quantum open systems including quantum noise, decoherence, quantum diffusions and spontaneous jumps occurring under continuous in time observation, is not yet a part of the standard curriculum of quantum physics. It is argued that the conventional formalism of quantum mechanics is insufficient for the description of quantum events, such as spontaneous decays say, and the new experimental phenomena related to individual quantum measurements, but they have all received an adequate mathematical treatment in quantum stochastics of open systems. Moreover, the only reasonable probabilistic interpretation of quantum mechanics put forward by Max Born was, in fact, in irreconcilable contradiction with traditional mechanical reality and causality. This led to numerous quantum paradoxes, some of them due to the great inventors of quantum theory such as Einstein and Schrödinger. They are reconsidered in this paper from the modern point of view of quantum stochastics and information. The development of quantum measurement theory, initiated by von Neumann, indicated a possibility for resolution of this interpretational crisis by divorcing the algebra of the dynamical generators and the algebra of the actual observables, or Bell's be ables. It is shown that within this approach quantum causality can be rehabilitated in the form of a superselection rule for compatibility of the actual histories with the potential future. This rule, together with the self-compatibility of the measurements ensuring the consistency of the histories, is called the nondemolition, or causality principle in modern quantum theory. The application of this rule in the form of dynamical commutation relations leads to the derivation of the von Neumann projection postulate, and also to the more general reductions, instantaneous, spontaneous, and even continuous in time. This gives a dynamical solution, in the form of the quantum stochastic filtering equations, of the notorious measurement problem which was tackled unsuccessfully by many famous physicists starting with Schrödinger and Bohr. It has been recently proved that the quantum stochastic model for the continuous in time measurements is equivalent to a Dirac type boundary-value problem for the secondary quantized input `offer waves from future' in one extra dimension, and to a reduction of the algebra of the consistent histories of past events to an Abelian subalgebra for the `trajectories of the output particles'. This supports the corpuscular-wave duality in the form of the thesis that everything in the future are quantized waves, while everything in the past are trajectories of the recorded particles.
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.
Quantum mechanics admits a “linguistic interpretation” if one equates preliminary any quantum state of some whether quantum entity or word, i.e. a wave function interpret-able as an element of the separable complex Hilbert space. All possible Feynman pathways can link to each other any two semantic units such as words or term in any theory. Then, the causal reasoning would correspond to the case of classical mechanics (a single trajectory, in which any next point is causally conditioned), and the probabilistic reasoning, to the case of quantum mechanics (many Feynman trajectories). Frame semantics turns out to be the natural counterpart of that linguistic interpretation of quantum mechanic
Abstract Quantum mechanics (QM) has led to spectacular technological developments, including the discovery of new constituents of matter and new materials: however, there is still no consensus regarding its interpretation and limitations. Some scientists and scientific writers promote some exotic interpretations and evoke quantum magic. In this paper we point out that magical explanations mean the end of the science. Magical explanations are misleading and counterproductive. We explain how a simple probabilistic local causal model is able to reproduce quantum correlations in Bell tests. We also discuss the difficulties of mathematical modeling of the physical reality and dangers of incorrect mental images. We examine in detail when and how a probabilistic model may completely describe a random experiment. We give some arguments in favor of the contextual statistical interpretation of QM. We conclude that we still do not know whether quantum theory provides a complete description of physical phenomena and we explain how it may be tested. We also point out, that there remain several open questions and challenges in QM, in quantum field theory and in the Standard Model. Moreover, there is still no consensus about how to reconcile quantum theory with general relativity and cosmology.