Related papers: Functional methods underlying classical mechanics,…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…
A ubiquitous feature of quantum mechanical theories is the existence of states of superposition. This is expected to be no different for a quantum gravity theory. Guided by this consideration and others we consider a framework in which…
We show that the quantum wavefunctional can be seen as a set of classical fields on the 3D space aggregated by a measure. We obtain a complete description of the wavefunctional in terms of classical local beables. With this correspondence,…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
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…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
We show that the quantum wavefunction, interpreted as the probability density of finding a single non-localized quantum particle, which evolves according to classical laws of motion, is an intermediate description of a material quantum…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…
We consider the quantum-to-classical transition for macroscopic systems coupled to their environments. By applying Born's Rule, we are led to a particular set of quantum trajectories, or an unravelling, that describes the state of the…
A rigorous \textit{ab initio} derivation of the (square of) Dirac's equation for a single particle with spin is presented. The general Hamilton-Jacobi equation for the particle expressed in terms of a background Weyl's conformal geometry is…
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
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,…
Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…
Classical and quantum physics represent two distinct theories; however, quantum physics is regarded as the more fundamental of the two. It is posited that classical mechanics should arise from quantum mechanics under certain limiting…
The relationship between classical and quantum mechanics is explored in an intuitive manner by the exercise of constructing a wave in association with a classical particle. Using special relativity, the time coordinate in the frame of…
The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…
After a revision of the main features of the structure of the Dirac electron a plausible definition of elementary particle is stated. It is shown that this definition leads in the classical case to a picture which produces a very clear…