Related papers: Time variation of a fundamental dimensionless cons…
Time evolutions whose infinitesimal generator is a fractional time derivative arise generally in the long time limit. Such fractional time evolutions are considered here for random walks. An exact relationship is given between the…
In contemporary physics space and time are intertwined entities so that kinematical and dynamical quantities are expressed in the four-dimensional space-time. This formulation seems to contradict our every-day experience and perception…
Inspired by the discrete evolution implied by the recent work on loop quantum cosmology, we obtain a discrete time description of usual quantum mechanics viewing it as a constrained system. This description, obtained without any…
We formulate a simple extension of general relativity which incorporates space-time variations in the Newtonian gravitation 'constant', $G$, and the fine structure 'constant', $\alpha $, which generalises Brans-Dicke theory and our theory…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
The dimensional structure of space-time is investigated according to physical and mathematical methods. We show that ther are various empirical and theoretical restrictions on the number of independent dimensions of space-time, consequently…
We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized…
The variation of fine structure constant with the variation of velocity of light has been studied considering contribution to the permeability and permittivity of the vacuum and incorporating contribution of fractal potential originated…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
We review the observational information on the constancy of the fine structure constant alpha. We find that small improvements on the measurement of ^{187}Re lifetime can provide significant progress in exploring the range of variability…
We show in detail some results, outlined in a previous paper regarding the case of Brownian motion (BM), about the distribution of the $n$th-passage time of a one-dimensional diffusion obtained by a space or time transformation of BM,…
A cosmological time variable is emerged from the hamiltonian formulation of unimodular theory of gravity to measure the evolution of dynamical observables in the theory. A set of constants of motion has been identified for the theory on the…
Time crystals, a unique non-equilibrium quantum phenomenon with promising applications in current quantum technologies, mark a significant advance in quantum mechanics. Although traditionally studied in atom-cavity and optical lattice…
We briefly review the recent experimental results on possible variations of the fine structure constant $\alpha$ on the cosmological time scale and its position dependence. We outline the theoretical grounds for the assumption that $\alpha$…
We present a model of discrete quantum evolution based on quantum correlations between the evolving system and a reference quantum clock system. A quantum circuit for the model is provided, which in the case of a constant Hamiltonian is…
We numerically investigate the long--time evolution of density perturbations after the first appearance of caustics in an expanding cosmological model with one--dimensional `single--wave' initial conditions. Focussing on the time--intervals…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Even though quantum systems in energy eigenstates do not evolve in time, they can exhibit correlations between internal degrees of freedom in such a way that one of the internal degrees of freedom behaves like a clock variable, and thereby…
Neutrino speed experiments could be viewed not only as tests of Lorentz invariance but also as measurements of limiting propagation speed for all standard model species below certain depth where no direct metrological information is…
We present a dynamical framework for modeling the motion of point-like charged particles, with or without mass, in general external electromagnetic fields. A key feature of this formulation is the treatment of time coordinate as a dynamical…