Related papers: Fundamental forces and their dynamics
Riemann's principle "force equals geometry" provided the basis for Einstein's General Relativity - the geometric theory of gravitation. In this paper, we follow this principle to derive the dynamics for any static, conservative force. The…
Shape dynamics is a completely background-independent universal framework of dynamical theories from which all absolute elements have been eliminated. For particles, only the variables that describe the shapes of the instantaneous particle…
It is shown, that a free motion of microparticles (elementary particles) in the gravitational field is multivariant (stochastic). This multivariance is conditioned by multivariant physical space-time geometry. The physical geometry is…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
In this essay we wish to seek a unifying thread between the basic forces. We propose that there exists a universal force which is shared by all that physically exists. Universality is characterized by the two properties: (i) universal…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
Gravity is a phenomenon which arises due to the space-time geometry. The main equations that describe gravity are the Einstein equations. To understand the consequences of these field equations we need to calculate the free particle…
We give an introductory overview of the classical Poincar\'e gauge theory of gravity formulated on the spacetime manifold that carries the Riemann-Cartan geometry with nontrivial curvature and torsion. After discussing the basic…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
General relativity postulates the Minkowski space-time to be the standard flat geometry against which we compare all curved space-times and the gravitational ground state where particles, quantum fields and their vacuum states are primarily…
We present a gravitational quantum dynamics theory that combines quantum field theory for particle dynamics in space-time with classical Einstein's general relativity in a non-Riemannian Finsler space. This approach is based on the…
In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the…
The gravity is classically formulated as the geometric curvature of the space-time in general relativity which is completely different from the other well-known physical forces. Since seeking a quantum framework for the gravity is a great…
We study some universal features of gravity in higher dimensions and by universal we mean a feature that remains true in all dimensions $\geq4$. They include: (a) the gravitational dynamics always follows from the Bianchi derivative of a…
Il is argued that the generalisation of the mechanical principles to other variables than localisation, velocity and momentum leads to the laws of generalized dynamics under the condition of continuous and derivable space time. However,…
Geometrical formulation of classical mechanics with forces that are not necessarily potential-generated is presented. It is shown that a natural geometrical "playground" for a mechanical system of point particles lacking Lagrangian and/or…
Here show that, pure affine actions based solely on the Riemann curvature tensor lead to Einstein field equations for gravitation. The matter and radiation involved are general enough to impose no restrictions on material dynamics or vacuum…
Classical mechanics for individual physical systems and quantum mechanics of non-relativistic particles are shown to be exceptional cases of a generalized dynamics described in terms of maps between two manifolds, the source being…
General relativity postulates that the gravity field is defined on a Riemannian manifold. The field equations are $R^\mu_\nu = 0$ i.e. Ricci's curvature tensor vanishes. The field equations have to be augmented by natural physical…