Related papers: Evolving Constants of Motion
In recent times there has been considerable interest in scenarios for quantum gravity in which particle kinematics is affected nonlinearly by the Planck scale, with encouraging results for the phenomenological prospects, but also some…
Physics explains the laws of motion that govern the time evolution of observable properties and the dynamical response of systems to various interactions. However, quantum theory separates the observable part of physics from the…
Traditional clock synchronisation on a rotating platform is shown to be incompatible with the experimentally established transformation of time. The latter transformation leads directly to solve this problem through noninvariant one-way…
We investigate the static solutions with rotational symmetry in the nonprojectable Ho\v rava theory in \(2+1\) dimensions. We consider all inequivalent terms of the effective theory, including the cosmological constant. We find two distinct…
We study the relation between two evolution pictures that are currently considered for totally constrained theories. Both descriptions are based on Rovelli's evolving constants approach, where one identifies a (possibly local) degree of…
Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory one…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We revisit Duff, Okun, and Veneziano's divergent views on the number of fundamental constants and argue that the issue can be set to rest by having spacetime as the starting point. This procedure disentangles the resolution in what depends…
The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and…
It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as…
For a relativistic charged particle moving in a constant electromagnetic field, its velocity 4-vector has been well studied. However, despite the fact that both the electromagnetic field and the equations of motion are purely real, the…
We present constants of motion for the finite-dimensional Lohe type aggregation models with frustration and we apply them to analyze the emergence of collective behaviors. The Lohe type models have been proposed as possible non-abelian and…
Interacting systems consisting of two rotators and a pendulum are considered, in a case in which the uncoupled systems have three very different characteristic time scales. The abundance of unstable quasi periodic motions in phase space is…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz…
Widespread unjustified views on the role of the observer, the individuality of quantum processes, the relation between decoherence and irreversibility, Bell's quest for `beables', the direction of time, and the concept of experience are…
We analytically work out the long-term, i.e. averaged over one orbital revolution, time variations of some direct observable quantities Y induced by classical and general relativistic dynamical perturbations of the two-body pointlike…
Since the advent of quantum mechanics we have mainly been concerned with its predictions from the perspective of an external observer. This is in strong contrast to the theory of general relativity, where the physics is governed by the…
A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function only. The motion of test particles is…
The peculiarities of rotating frames of reference played an important role in the genesis of general relativity. Considering them, Einstein became convinced that coordinates have a different status in the general theory of relativity than…
A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be…