Related papers: Quantum mechanics is the square root of a stochast…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
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 amplitude, Born rule,…
We give a partial answer to the question whether the Schrodinger equation can be derived from the Newtonian mechanics of a particle in a potential subject to a random force. We show that the fluctuations around the classical motion of a one…
The present contribution is based on the assumption that the probabilistic character of quantum mechanics does not originate from uncertainties caused by the process of measurement or observation, but rather reflects the presence of…
This paper proposes an interpretation of quantum mechanics, relying on the time-symmetric stochastic dynamics of quantum particles and on non-classical probability theory. Our main purpose is to demonstrate that the wave function and its…
With the decline of the Copenhagen interpretation of quantum mechanics and the recent experiments indicating that quantum mechanics does actually embody 'objective reality', one might ask if a 'mechanical', conceptual model for quantum…
The Bohmian formulation of quantum mechanics is used in order to describe the measurement process in an intuitive way without a reduction postulate in the framework of a deterministic single system theory. Thereby the motion of the hidden…
We consider for clarity the simple case of the one dimensional non-relativistic Schr\"{o}dinger equation and regard it as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
Non-relativistic quantum mechanics for a free particle is shown to emerge from classical mechanics through an invariance principle under transformations that preserve the Heisenberg position-momentum inequality. These transformations are…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
Quantum mechanics postulates the existence of states determined by a particle position at a single time. This very concept, in conjunction with superposition, induces much of the quantum-mechanical structure. In particular, it implies the…
This article sets up a formalism to describe stochastic thermodynamics for driven out-of-equilibrium open quantum systems. A stochastic Schr\"odinger equation allows to construct quantum trajectories describing the dynamics of the system…
By assuming that the kinetic energy,potential energy,momentum,and some other physical quantities of a particle exist in the field out of the particle,the Schrodinger equation is an equation describing field of a particle,but not the…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
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…
The fundamental principle of quantum mechanics is that the probabilities of physical outcomes are obtained from the intermediate states and processes of the interacting particles, considered as happening concurrently. When the interaction…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
We consider a linear Boltzmann equation that arises in a model for quantum friction. It describes a particle that is slowed down by the emission of bosons. We study the stochastic process generated by this Boltzmann equation and we show…