Related papers: Foundations of Relational Particle Dynamics
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
Pure shape dynamics (PSD) is a novel implementation of the relational framework originally proposed by Julian Barbour and Bruno Bertotti. PSD represents a Leibnizian/Machian approach to physics in that it completely describes the dynamical…
Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…
We show that a universal propagation scale can emerge from purely relational, scale-invariant $N$-body dynamics formulated on shape space, i.e. the space of configurations modulo translations, rotations, and dilatations. Although pure shape…
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…
In this paper we review some aspects of relativistic particles' mechanics in the case of a non-trivial geometry of momentum space. We start with showing how the curved momentum space arises in the theory of gravity in 2+1 dimensions coupled…
I here investigate what is arguably the most significant residual challenge for the proposal of phenomenologically viable "DSR deformations" of relativistic kinematics, which concerns the description of composite particles, such as atoms.…
Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the…
Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
We present the N=2 supersymmetric formulation for the classical and quantum dynamics of a nonrelativistic charged particle on a curved surface in the presence of a perpendicular magnetic field. For a particle moving on a constant-curvature…
It is proved by means of the dynamical effects of special relativity that velocity caused by accelerating process is not a relative concept. The influence of accelerating process should be considered in space-time theory. Besides the…
A general relativistic description of a disk rotating at constant angular velocity is given. It is argued that conceptually this direct approach poses fewer problems than the special relativistic one. For observers on the disk, the geometry…
Relational particle mechanics models bolster the relational side of the absolute versus relational motion debate, and are additionally toy models for the dynamical formulation of General Relativity and its Problem of Time. They cover two…
The concept of a physical space, which actualizes Euclidean geometry, is not confined to the statics of solids but extensible to the phenomena where Newtonian mechanics is valid, defining its concept of time. The laws of propagation of…
We consider the behavior of macroscopic bodies within the framework of relative locality, which is a recent proposal for Planck scale modifications of the relativistic dynamics of particles which are described as arising from deformations…
In the current debate referring to the construction of a tenable background independent theory of Quantum Gravity we introduce the notion of topos-theoretic relativization of physical representability and demonstrate its relevance…
We introduce a new geometric framework for relativistic particle dynamics based on contact geometry and suitable for treating dissipative processes like particle decay. The dynamics is formulated on a nine--dimensional extended phase space…
I investigate useful shape quantities for the classical and quantum mechanics of the relational quadrilateral in 2-d. This is relational in the sense that only relative times, relative ratios of separations and relative angles are…
Shape Dynamics is a 3D conformally invariant theory of gravity which possesses a large set of solutions in common with General Relativity. When looked closely, these solutions are found to behave in surprising ways, so in order to probe the…