Related papers: The dynamical nature of time
Dynamical features of tagged particles are studied in a one dimensional $A+A \rightarrow kA$ system for $k=0$ and 1, where the particles $A$ have a bias $\epsilon$ $(0 \leq \epsilon \leq 0.5)$ to hop one step in the direction of their…
We consider the ambiguity associated with the choice of clock in time reparameterization invariant theories. This arbitrariness undermines the goal of prescribing a fixed set of physical laws, since a change of time variable can completely…
A careful study is made of the operational meaning of the time symbols appearing in the space-time Lorentz transformation. Four distinct symbols, with different physical meanings, are needed to describe reciprocal measurements involving…
Understanding different aspects of time is at the core of many areas in theoretical physics. Minimal models of continuous stochastic and quantum clocks have been proposed to explore fundamental limitations on the performance of timekeeping…
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…
We consider the characteristic time operator $\mathsf{T}$ introduced in [E. A. Galapon, Proc. R. Soc. Lond. A, 458:2671 (2002)] which is bounded and self-adjoint. For a semibounded discrete Hamiltonian $\mathsf{H}$ with some growth…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
This paper investigates the mathematical representation of time in physics. In existing theories time is represented by the real numbers, hence their formal properties represent properties of time: these are surveyed. The central question…
This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
The relationship between 'information' and 'time' is explored in order to look for a 'solution' to the 'Problem of Time'. 'Time' is found to be the result of the conversion of energy into 'information'. The 'time' number or label we assign…
This paper provides an enjoyable example through which several concepts of classical mechanics can be understood. We introduce an equation that models the motion of a cat in the presence of a person. The cat is considered as a point…
The measurement of time durations or instants of ocurrence of events has been frequently modelled ``operationally'' by coupling the system of interest to a ``clock''. According to several of these models the operational approach is limited…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
Preparing general relativity for quantization in the Hamiltonian approach leads to the `problem of time,' rendering the world fundamentally timeless. One proposed solution is the `thermal time hypothesis,' which defines time in terms of…
The physics that is traditionally formulated in one--time-physics (1T-physics) can also be formulated in two-time-physics (2T-physics). The physical phenomena in 1T or 2T physics are not different, but the spacetime formalism used to…
In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in…
In this paper we treat the so called clock paradox in an analytical way by assuming that a constant and uniform force F of finite magnitude acts continuously on the moving clock along the direction of its motion assumed to be rectilinear.…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…