Related papers: Time in classical and quantum mechanics
The question about the appearance of time in the semiclassical limit of quantum gravity continues to be discussed in the literature. It is believed that a temporal Schrodinger equation for matter fields on the background of a classical…
Quantum hydrodynamics is a formulation of quantum mechanics based on the probability density and flux (current) density of a quantum system. It can be used to define trajectories which allow for a particle-based interpretation of quantum…
New insight to the principles of the quantum physics development is given. The correct ways for the construction of new versions of quantum mechanics on the second main postulate base are discussed. The conclusion on the status of the…
Quantum mechanics is challenging even for advanced undergraduate and graduate students. In the Schr\"odinger representation, the wave function evolves in time according to the time dependent Schr\"odinger equation. The time dependence of…
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…
We propose an extension of Quantum Mechanics based on the idea that the underlying "quantum noise" has a non-zero, albeit very small, correlation time $\tau_c$. The standard (non-relativistic) Schrodinger equation is recovered to zeroth…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated…
The notions of time in the theories of Newton and Einstein are reviewed so that certain of their assumptions are clarified. These assumptions will be seen as the causes of the incompatibility between the two different ways of understanding…
The rules of quantum mechanics require a time coordinate for their formulation. However, a notion of time is in general possible only when a classical spacetime geometry exists. Such a geometry is itself produced by classical matter…
A review of some basic facts of classical dynamics shows that time, or precisely duration, is redundant as a fundamental concept. Duration and the behaviour of clocks emerge from a timeless law that governs change.
The nature of time as emergent for a system by separating it from its environment has been put forward by Page and Wootters [D. N. Page and W. K. Wootters, Phys. Rev. D 27, 2885 (1983)] in a quantum mechanical setting neglecting interaction…
We show how quantum mechanics can be understood as a space-time theory provided that its spatial continuum is modelled by a variable real number (qrumber) continuum. Such a continuum can be constructed using only standard Hilbert space…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We apply the many-particle Schr\"{o}dinger-Newton equation, which describes the co-evolution of an many-particle quantum wave function and a classical space-time geometry, to macroscopic mechanical objects. By averaging over motions of the…
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…
For time-dependent systems the wavefunction depends explicitly on time and it is not a pure state of the Hamiltonian. We construct operators for which the above wavefunction is a pure state. The method is based on the introduction of…
We show that generalizations of classical and quantum dynamics with two times lead to fundamentally constrained evolution. At the level of classical physics, Newton's second law is extended and exactly integrated in $1+2$ dimensional space,…
The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical systems seem to evolve in paths of…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…