Related papers: Evolving Constants of Motion
We will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous assertion is due to the fact that a…
A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as…
Differential equations are derived which show how generalized Euler vector representations of the Euler rotation axis and angle for a rigid body evolve in time; the Euler vector is also known as a rotation vector or axis-angle vector. The…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
In most text books of mechanics, Newton's laws or Hamilton's equations of motion are first written down and then solved based on initial conditions to determine the constants of the motions and to describe the trajectories of the particles.…
We discuss the distinction between the notion of partial observable and the notion of complete observable. Mixing up the two is frequently a source of confusion. The distinction bears on several issues related to observability, such as (i)…
We consider linear and quadratic integrals of motion for general variable quadratic Hamiltonians. Fundamental relations between the eigenvalue problem for linear dynamical invariants and solutions of the corresponding Cauchy initial value…
Considering space--time to be non-commutative, we study the evolution of the universe employing the approach of Newtonian cosmology. Generalizing the conservation of energy and the first law of thermodynamics to $\kappa$-deformed…
We argue that the construction of spacetime is personal, specific to each observer, and requires combining aspects of both discovery and creation. What is usually referred to as the block universe then emerges by noting that part of the…
The Lorentz transformations are represented by Einstein velocity addition on the ball of relativistically admissible velocities. This representation is by projective maps. The Lie algebra of this representation defines the relativistic…
In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a non-trivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are…
In this paper, we present an efficient form of Volterra's equations of motion for both unconstrained and constrained multibody dynamical systems that include ignorable coordinates. The proposed method is applicable for systems with both…
We describe a method of construction of gauge-invariant operators (Dirac observables or ``evolving constants of motion'') from the knowledge of the eigenstates of the gauge generator in time-reparametrization invariant mechanical systems.…
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…
A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…
There are theories which implement the idea that the constants of nature may be "time dependent." These introduce new fields representing "evolving constants," in addition to physical fields. We argue that dynamical matter coupling…
Three of the big puzzles of theoretical physics are the following: (i) There is apparently no time evolution in the dynamics of quantum general relativity, because the allowed quantum states must obey the Hamiltonian constraint. (ii) During…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
We propose that the constants of Nature we observe (which appear as parameters in the classical action) are quantum observables in a kinematical Hilbert space. When all of these observables commute, our proposal differs little from the…
We report the discovery of an exact mapping from Galilean time and space coordinates to Minkowski spacetime coordinates, showing that Lorentz covariance and the spacetime construct are consistent with the existence of a dynamical 3-space,…