Related papers: Classical mechanics without determinism
We prove a theorem showing that quantum mechanics is not directly a stochastic process characterizing Brownian motion but rather its square root. This implies that a complex-valued stochastic process is involved. Schr\"odinger equation is…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Any time-dependent solution of Schr\"{o}dinger equation may be always correlated to a solution of Hamilton equations or to a statistical combination of their solutions; only the set of corresponding solutions is somewhat smaller (due to…
It is shown that quantum mechanics can be regarded as what one might call a "fuzzy" mechanics whose underlying logic is the fuzzy one, in contradistinction to the classical "crisp" logic. Therefore classical mechanics can be viewed as a…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In this paper, we show how classical statistical field theory techniques can be used to efficiently perform the numerical evaluation of the non-perturbative Schwinger mechanism of particle production by quantum tunneling. In some…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Based on the concept of ensemble, it is proved in the manuscript that the probability amplitude function can also been used to describe the classical statistical system. The motion equations of probability amplitude functions of classical…
In this paper we apply the formalism of the analytical signal theory to the Schrodinger wavefunction. Making use exclusively of the wave-particle duality and the principle of relativistic covariance, we actually derive the form of the…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
We show that the Schr\"odinger equation can be solved exactly based only on classical least action. Fundamental postulates of quantum mechanics can in turn be derived directly from this construction. The results extend to the relativistic…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
In this paper a didactic approach is described which immediately leads to an understanding of those postulates of quantum mechanics used most frequently in quantum computation. Moreover, an interpretation of quantum mechanics is presented…
Geometric (Schrodinger) quantization of nonrelativistic mechanics with respect to different reference frames is considered. In classical nonrelativistic mechanics, a reference frame is represented by a connection on a configuration space…
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…
Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum…