Related papers: The Relation Between Classical and Quantum Mechani…
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…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Quantum mechanics is nonlocal. Classical mechanics is local. Consequently classical mechanics can not explain all quantum phenomena. Conversely, it is cumbersome to use quantum mechanics to describe classical phenomena. Not only are the…
The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical statistics range from the philosophical…
The identification of physical subsystems in quantum mechanics as compared to classical mechanics poses significant conceptual challenges, especially in the context of quantum gravity. Traditional approaches associate quantum systems with…
The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and…
Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Although classical mechanics and quantum mechanics are separate disciplines, we live in a world where Planck's constant \hbar>0, meaning that the classical and quantum world views must actually {\it coexist}. Traditionally, canonical…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
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…
In spite of its popularity, it has not been possible to vindicate the conventional wisdom that classical mechanics is a limiting case of quantum mechanics. The purpose of the present paper is to offer an alternative point of view in which…
A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…