Related papers: Propositional Quantum Mechanics
We show that QM can be represented as a natural projection of a classical statistical model on the phase space $\Omega= H\times H,$ where $H$ is the real Hilbert space. Statistical states are given by Gaussian measures on $\Omega$ having…
Feynman path integrals formalism for non-relativistic quantum mechanics is revisited. A comparison is made with the cases of light progagation (Huygens principle) and Brownian motion. The difficulties for a physical model behind Feynman…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in…
It is possible to completely explain all aspects of quantum mechanics by expressing the relations between physical properties in terms of complex conditional probabilities (Phys. Rev. A 89, 042115(2014)). These fully deterministic…
After some historical remarks concerning Schroedinger's discovery of wave mechanics, we present a unified formalism for the mathematical description of classical and quantum-mechanical systems, utilizing elements of the theory of operator…
The classical notions of continuity and mechanical causality are left in order to refor- mulate the Quantum Theory starting from two principles: I) the intrinsic randomness of quantum process at microphysical level, II) the projective…
In this paper we discuss the relevance of the algebraic approach to quantum phenomena first introduced by von Neumann before he confessed to Birkoff that he no longer believed in Hilbert space. This approach is more general and allows us to…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex…
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…
In 1926, Dirac stated that quantum mechanics can be obtained from classical theory through a change in the only rule. In his view, classical mechanics is formulated through commutative quantities (c-numbers) while quantum mechanics requires…
We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation…
This paper addresses the central question of what a coherent concept of probability might look like that would do justice to both classical probability theory, axiomatized by Kolmogorov, and quantum theory. At a time when quanta are…
The tensor product postulate of quantum mechanics states that the Hilbert space of a composite system is the tensor product of the components' Hilbert spaces. All current formalizations of quantum mechanics that do not contain this…
It is demonstrated how quantum mechanics emerges from the stochastic dynamics of force-carriers. It is shown that the quantum Moyal equation corresponds to some dynamic correlations between the momentum of a real particle and the position…
It is shown that Schroedinger's equation may be derived from three postulates. The first is a kind of statistical metamorphosis of classical mechanics, a set of two relations which are obtained from the canonical equations of particle…
Standard quantum mechanics is an idealisation based on infinite-precision objects: point states, exact probabilities, and sharp measurements. Yet every real experiment has finite resolution, and for macroscopic systems we never have access…
We give a tutorial exposition of the analogue of the filtering equation for quantum systems focusing on the quantum probabilistic framework and developing the ideas from the classical theory. Quantum covariances and conditional expectations…
The usual conjectures of quantum measurements approaches, inspired from the traditional interpretation of Heisenberg's ("uncertainty") relations, are proved as being incorrect. A group of reconsidered conjectures and a corresponding new…