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We describe both quantum particles and classical particles in terms of a classical statistical ensemble, characterized by a probability distribution in phase space. By use of a wave function in phase space both can be treated in the same…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Quantum mechanics rests on the assumption that time is a classical variable. As such, classical time is assumed to be measurable with infinite accuracy. However, all real clocks are subject to quantum fluctuations, which leads to the…
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…
Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…
The transition from quantum to classical statistics is studied in light of Huggett's finding that the empirical data do not support the usual claim that the distinction between classical and quantum objects consists in the capacity of…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
In recent years, the non-relativistic quantum dynamics derived from three assumptions; i) probability current conservation, ii) average energy conservation, and iii) an epistemic momentum uncertainty [A. Budiyono and D. Rohrlich,…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…
Gaussian quantum systems exhibit many explicitly quantum effects but can be simulated classically. Using both the Hilbert space (Koopman) and the phase-space (Moyal) formalisms we investigate how robust this classicality is. We find…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The one particle quantum mechanics is considered in the frame of a N-body classical kinetics in the phase space. Within this framework, the scenario of a subquantum structure for the quantum particle, emerges naturally, providing an…
Quantum uncertainty relations have deep-rooted significance on the formalism of quantum mechanics. Heisenberg's uncertainty relations attracted a renewed interest for its applications in quantum information science. Robertson derived a…
Statistical classical mechanics and quantum mechanics are developed and well-known theories that represent a basis for modern physics. The two described theories are well known and have been well studied. As these theories contain numerous…
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,…
Classical statistical average values are generally generalized to average values of quantum mechanics, it is discovered that quantum mechanics is direct generalization of classical statistical mechanics, and we generally deduce both a new…
We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…
We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong''…