Related papers: The Unfinished Search for Wave-Particle and Classi…
Wave-particle duality, a fundamental principle of quantum mechanics, encapsulates the complementary relationship between the wave and particle behaviors of quantum systems. In this paper, we treat quantum coherence and classical…
Finding a physically consistent approach to modelling interactions between classical and quantum systems is a highly nontrivial task. While many proposals based on various mathematical formalisms have been made, most of these efforts run…
The superposition of quantum states lies at the heart of physics and has been recently found to serve as a versatile resource for quantum information protocols, defining the notion of quantum coherence. In this contribution, we report on…
Individual quantum objects display inseparable coexisting wave-like properties and particle-like properties; such inseparable coexistence can seem paradoxical and mind-boggling. The apparent paradox is resolved by the unified theory of…
The measurement problem in quantum mechanics originates in the inability of the Schr\"odinger equation to predict definite outcomes of measurements. This is due to the lack of objectivity of the eigenstates of the measuring apparatus. Such…
Since the dawn of quantum theory, coherence was attributed as a key to understand the weirdness of fundamental concepts like the wave-particle duality and the Stern-Gerlach experiment. Recently, based on a resource theory approach, the…
We propose a new quantum approach for describing a system of $n$ interacting particles with variable mass connected by an unknown field with variable form ($n$-VMVF systems). Instead of assuming any particular nature for variation of the…
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…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
Quantum physics, which describes the strange behavior of light and matter at the smallest scales, is one of the most successful descriptions of reality, yet it is notoriously inaccessible. Here we provide an approachable explanation of…
The Koopman-von Neumann (KvN) formalism recasts classical mechanics in a Hilbert space framework using complex wavefunctions and linear operators, akin to quantum mechanics. Instead of evolving probability densities in phase space (as in…
We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument, may be rigorously resolved within the…
I review arguments demonstrating how the concept of "particle" numbers arises in the form of equidistant energy eigenvalues of coupled harmonic oscillators representing free fields. Their quantum numbers (numbers of nodes of the wave…
In this paper we continue the study, started in [1], of the operatorial formulation of classical mechanics given by Koopman and von Neumann (KvN) in the Thirties. In particular we show that the introduction of the KvN Hilbert space of…
We give a review of the most important results on optimal tomography as mathematical wave-pattern recognition theory emerged in the 70's in connection with the problems of optimal estimation and hypothesis testing in quantum theory. In…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
Descriptions of classical mechanics in Hilbert space go back to the work of Koopman and von Neumann in the 1930s. Decades later, van Hove derived a unitary representation of the group of contact transformations which recently has been used…
This paper revisits the textbook 'particle in a box', but from the point of view of Koopman-von Neumann (KvN) mechanics. KvN mechanics is a way to describe \emph{classical} dynamics in a Hilbert space. That simple fact changes the usual…
A gauge-invariant wave equation for the dynamics of hybrid quantum-classical systems is formulated by combining the variational setting of Lagrangian paths in continuum theories with Koopman wavefunctions in classical mechanics. We identify…