相关论文: Dialogue on Classical and Quantum between mathemat…

Following an article by John von Neumann on infinite tensor products, we develop the idea that the usual formalism of quantum mechanics, associated with unitary equivalence of representations, stops working when countable infinities of…

We propose a reformulation of quantum mechanics in which the distinction between definite and indefinite becomes the fundamental primitive. Inspired by suggestions of Heisenberg, Schrodinger and Dyson that the past can't be described in…

Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…

Measurement theory in classical mechanics is investigated in the formulation of classical mechanics by Koopman and von Neumann (KvN), using Hilbert space. It is shown that the classical and the quantum measurements give different "relative…

Heisenberg's uncertainty principle is often cited as an example of a "purely quantum" relation with no analogue in the classical limit where $\hbar \to 0$. However, this formulation of the classical limit is problematic for many reasons,…

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…

Duality transformations within the quantum mechanics of a finite number of degrees of freedom can be regarded as the dependence of the notion of a quantum, i.e., an elementary excitation of the vacuum, on the observer on classical phase…

The implications of the physical theory of quantum mechanics on the question of realism is much a subject of sustaining interest, while the background questions among physicists on how to think about all the theoretical notion and…

Frauchiger and Renner recently cast doubt on the universal applicability of Quantum Mechanics [1]. In the following, it is pointed out that their conclusion of one of three common-sense conditions, demanded for Quantum Mechanics, being…

In spite of all {\bf no-go} theorems (e.g., von Neumann, Kochen and Specker,..., Bell,...) we constructed a realist basis of quantum mechanics. In our model both classical and quantum spaces b are rough images of the fundamental {\bf…

Using quantum-classical analogies, we find that dynamical pictures of quantum mechanics have precise counterparts in classical mechanics. In particular, the Eulerian and Lagrangian descriptions of fluid dynamics in classical mechanics are…

The scientific fields of quantum mechanics and signal-analysis originated within different settings, aimed at different goals and started from different scientific paradigms. Yet the development of the two subjects has become increasingly…

In this work, we present several aspects of the interplay between classical and quantum theories. After reviewing the equivalence between positivity and complete positivity in the commutative setting, we introduce and analyze intermediate…

Thought experiments are where logical reasoning meets storytelling, catalysing progress in quantum science and technology. Schr\"odinger's famous cat brought quantum science to the public consciousness, while Deutsch's thought experiment to…

This paper is an introduction to the eleven works of the special issue on Quantum and Classical Frontiers of Noise. The weather, and its butterfly effect, is the typical example that explain why many natural phenomena are, in fact, not…

We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…

Intuitively, the more powerful a theory is, the greater the variety and quantity of ideas can be expressed through its formal language. Therefore, when comparing two theories concerning the same subject, it seems only reasonable to compare…

A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…

An attempt is made to give a heuristic explanation of the distinguished role of measurement in the quantum theory. We question the notion of "naive" reductionism by stressing the difference between an isolated quantum and classical object.…

This is an informal introduction to the ideas of decoherence and emergent classicality, including a simple account of the decoherent histories approach to quantum theory. It is aimed at undergraduates with a basic appreciation of quantum…