Related papers: Classical Extensions, Classical Representations an…
In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More…
Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is…
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the…
The unitary implementation of a symmetry group $G$ of a classical system in the corresponding quantum theory entails unavoidable deformations $\TG$ of $G$, namely, central extensions by the typical phase invariance group U(1). The…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
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…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
Angular momentum in classical and quantum mechanics is carried out beyond textbooks frames. We compare angular distribution of particle position with classical probabilistic approach. Addition of angular momenta is also discussed together…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
An expansion for quantum statistical mechanics is derived that gives classical statistical mechanics as the leading term. Each quantum correction comes from successively larger permutation loops, which arise from the factorization of the…
The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We propose a mechanism for the enhancement of vacuum fluctuations by means of a classical field. The basic idea is that if an observable quantity depends quadratically upon a quantum field, such as the electric field, then the application…
A correspondence of classical to quantum physics studied by Schr\"{o}\-dinger and Ehrenfest applies without the necessity of technical conjecture that classical observables are associated with Hermitian Hilbert space operators. This…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
A holistic extension of classical propositional logic is introduced in the framework of quantum computation with mixed states. The concepts of tautology and contradiction are investigated in this extensions. A special family of quantum…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…