Related papers: Multi-Time Equations, Classical and Quantum
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…
Equations of motion for single particle under two proper time model and three proper time model have been proposed and analyzed. The motions of particle are derived from pure classical method but they exhibit the same properties of quantum…
The possibility of physics in multiple time dimensions is investigated. Drawing on recent work by Walter Craig and myself, I show that, contrary to conventional wisdom, there is a well-posed initial value problem--deterministic, stable…
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
A consistent classical and quantum relativistic mechanics can be constructed if Einstein's covariant time is considered as a dynamical variable. The evolution of a system is then parametrized by a universal invariant identified with…
In the covariant canonical approach to classical physics, each point in phase space represents an entire classical trajectory. Initial data at a fixed time serve as coordinates for this ``timeless'' phase space, and time evolution can be…
The time-dependence of correlation functions under the influence of classical equations of motion is described by an exact evolution equation. For conservative systems thermodynamic equilibrium is a fixed point of these equations. We show…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…
We survey the equations of continuous-time quantum walks on simple one-dimensional lattices, which include the finite and infinite lines and the finite cycle, and compare them with the classical continuous-time Markov chains. The focus of…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
The treatment of time in relativity does not conform to that in quantum theory. To resolve the discrepancy, a formalization of time is introduced in an accompanying paper, starting from the assumption that the treatment of time in physics…
Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amount of details. In the chronological order we present results…
The time development of equal-time correlation functions in quantum mechanics and quantum field theory is described by an exact evolution equation for generating functionals. This permits a comparison between classical and quantum evolution…
Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in…
We consider defining time as a function of a cyclical field, an abstraction of a clock. The definition of time corresponds to a novel interpretation of the relationship between space-time coordinates of observers at different locations in…
We analyze the issue of dynamical evolution and time in quantum cosmology. We emphasize the problem of choice of phase space variables that can play the role of a time parameter in such a way that for expectation values of quantum operators…
The origin and nature of time in complex systems is explored using quantum (or 'Feynman') clocks and the signals produced by them. Networks of these clocks provide the basis for the evolution of complex systems. The general concept of…
The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global…