Rigid motions and generalized Newtonian gravitation

Foundations of Physics, 1995

We give a precise and modern mathematical characterization of the Newtonian spacetOne structure (N). Our formulation clarifies the concepts of absohtte space, Newton's relative spaces, and absolute tone. The concept of reference frames (which are "timelike" vector fieMs on N) plays a fundamental role in our approach, and the classification of all possible reference frames on ~ is O,vestigated in detail. We succeed #i identifying a Lorentzian structure on ~1 and we study the classical electrodynamics of Maxwell and Lorentz relative to this structure, obtahffng the #nportant result that there exists only one #1trinsic generalization of the Lorentz force law which is compatible with Maxwell equations. This is at variance with other proposed #1trinsic generalizations of the Loreutz force law appearing #z the literature. We present also a formulation of Newtonian gravitational theoo, as a curve spacetime theory and discuss its meaning. 2.1. Geometrical Structure 2.2. Newtonian Dynamics 3. Reference and Moving Frames 3.1. Reference Frames 3.2. Moving Frames 3.3. Newtonian Space and Newtonian Time. Relative Rest Spaces 3.4. Galileo's Principle of Relativity

—Starting from the origin of Einstein's general relativity (GR), the request of Mach on the theory's structure has been the core of the foundational debate. That problem is strictly connected with the nature of the mass-energy equivalence. It is well known that this is exactly the key point that Einstein used to realize a metric theory of gravitation having an unequalled beauty and elegance. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories request a better understanding of the Equivalence Principle (EP). The MOND theory by Milgrom proposes a modification of Newtonian dynamics, and we consider a direct coupling between the Ricci curvature scalar and the matter Lagrangian showing that a nongeodesic ratio m i /m g can be fixed and that Milgrom's acceleration is retrieved at low energies.

Journal of Mathematical Physics, 2011

A theorem due to Bob Geroch and Pong Soo Jang ["Motion of a Body in General Relativity." Journal of Mathematical Physics 16(1), (1975)] provides the sense in which the geodesic principle has the status of a theorem in General Relativity (GR). Here we show that a similar theorem holds in the context of geometrized Newtonian gravitation (often called Newton-Cartan theory). It follows that in Newtonian gravitation, as in GR, inertial motion can be derived from other central principles of the theory.

Zeitschrift für Naturforschung A, 1991

This paper aims to examine if the classical tests of General Relativity (GR) can be predicted by a simpler approach based on minimal changes in the Newtonian gravity. The approach yields a precession of the perihelion of Mercury by an amount 39.4"/century which is very close to the observed Dicke-Goldenberg value (39.6"/century), but less than the popularly accepted value (43"/ century). The other tests exactly coincide with those of GR. Our analysis also displays the genesis as well as the role of geometry in the description of gravitational processes. The time dependent spherically symmetric equations, which are mathematically interesting, call for a further study. The model also allows unambiguous formulation of conservation laws. On the whole, the paper illustrates the limited extent to which a second rank tensor analogy (nonlinear) with flat background Faraday-Maxwell electrodynamics can be pushed in describing gravitation

Zeitschrift für Naturforschung A, 1992

This supplement to Z. Naturforsch. 46 a, 1026 (1991) provides additional material that should be combined with the contents of that paper. The combined content then provides a model of gravitation which is complete in essential details. Its main features are that it (i) predicts all the local GR tests accurately but (ii) does not exhibit Schwarzschild singularity, (iii) allows the wellknown Birkhoff's theorem to hold and (iv) has well defined conservation laws in virtue of the maximal group of motions admissible on the flat background spacetime

Can Newtonian mechanics be derived from relativity theory? Physicists agree that classical mechanics constitutes a limiting case of relativity theory. By contrast some philosophers claim that this cannot be the case because of the incommensurability between both theories. In this article I focus on the alleged incommensurability associated with the term 'mass'. Contradicting Kuhn and Feyerabend I affirm that the mass of moving objects is a relativistic invariant, Thus 'mass' preserves the reference through the change of theory. A result that can be considered devastating to the thesis of incommensurability.

International Journal of Geometric Methods in Modern Physics 16 , 1950015, 2019

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 geometry of spacetime of a moving object is described by a metric obtained from the potential of the force field acting on it. We introduce a generalization of Newton's First Law - the Generalized Principle of Inertia stating that: An inanimate object moves inertially, that is, with constant velocity, in its own spacetime whose geometry is determined by the forces affecting it}. Classical Newtonian dynamics is treated within this framework, using a properly defined Newtonian metric with respect to an inertial lab frame. We reveal a physical deficiency of this metric (responsible for the inability of Newtonian dynamics to account for relativistic behavior), and remove it. The dynamics defined by the corrected Newtonian metric leads to a new \emph{Relativistic Newtonian Dynamics} for both massive objects and massless particles moving in any static, conservative force field, not necessarily gravitational. This dynamics reduces in the weak field, low velocity limit to classical Newtonian dynamics and also exactly reproduces the classical tests of General Relativity, as well as the post-Keplerian precession of binaries.

1992

It has been suggested that re-expressing relativity in terms of forces could provide fresh insights. The formalism developed for this purpose only applied to static, or conformally static, space-times. Here we extend it to arbitrary space-times. It is hoped that this formalism may lead to a workable definition of mass and energy in relativity.

This is the third in a series of papers on a new theory of relativity [Phys. Essays 4, 68 (1991); ibid [ 194; "Relativistic Kinematics IV,," submitted to Phys. Essays]. This paper presents, in detail, an application of the new theory of relativity to relativistically modify Newton's gravitational force law. The new relativistic gravitational force law thus obtained gives a simple correction factor, 1 - (v/c) 2, to Newton's gravitational force law; it contains Newton's gravitational force law as a low-speed limit. However, the new relativistic theory of gravitation differs from Einstein's general relativity of gravitation. We also discuss experimental tests of general relativity and wish to emphasize that these experimental tests are not reliable as originally claimed.

2016

Masses (elementary particles) curve space positively. They sense (are affected by) curvature, created by other masses, and move accordingly. How, specifically, this occurs, is an open issue, as is the issue of inertia. Our elementary particle model, presented here, enables us to resolve these issues, show mass to be merely a practicality, and prove Newton's First and Second Laws. We show that contraction (curving) of space by a mass (GR's gravitation) creates a gradient in light velocity. A particle senses this gradient and is forced into free fall. This free fall is attributed to the currently unexplained attraction between masses. We also prove Newton's Law of Gravitation and the equivalence of gravitational and inertial masses. Part 2 of this paper shows that the spin of a particle induces space torsion that results in space contraction (positive curving) which is GR's gravitation.