A Machian definition of particle mass in higher-dimensional gravity

Several attempts to construct theories of gravity with variable mass are considered. The theoretical impacts of allowing the rest mass to vary with respect to time or an appropriate curve parameter are examined in the framework of Newtonian and Einsteinian gravity theories. In further steps, scalar-tensor theories are examined with respect to their relation to the variation of the mass and in an ultimate step, an additional coordinate is introduced and its possible relation t...

In a recent paper \cite{novello} we have presented a mechanism to generate mass from gravitational interaction, based on the Mach principle, according to which the inertia of a body is a property of matter as well as of the background provided by the rest-of-the-universe. In \cite{novello} we realized such an idea for a scalar field treating the rest-of-the-universe in its vacuum state. In the present paper we describe a similar mechanism for fermions.

It is shown in this work that all free physical fields should have a nonzero rest mass according to the field theory of gravitation.

First we argue in an informal, qualitative way that it is natural to enlarge space-time to five dimensions to be able to solve the problem of elementary particle masses. Several criteria are developed for the success of this program. Extending the Poincare group to the group C of all angle-preserving transformations of space-time is one such scheme which satisfies these criteria. Then we show that the field equation for spin 1/2 fermions coupled to a self-force gauge field pr...

Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several ways to ra-tionalize these things using an extra dimension. A possible explanation of wave-particle duality is that an observed particle manifests two isometries of flat 5D space in different 4D ways, one with waves and one without.

The purpose of this work is to show that the gravitational interaction is able to generate mass for all bodies. The condition for this is the existence of an energy distribution represented by the vacuum or the cosmological constant term $ \Lambda \, g_{\mu\nu}.$ We review briefly the alternative Higgs mechanism in order to compare both processes.

The earlier paper, Inertial Mass, Its Mechanics - What It Is; How It Operates, developed the mechanics of inertial mass. The present paper is for the purpose of equivalently developing gravitation. The behavior of gravitation is well known, as described by Newton's Law of Gravitation. But just what gravitational mass is, how gravitational behavior comes about, what in material reality produces the effects of gravitational mass, has been little understood. The only extant hy...

Despite the success of the Higgs mechanism to account for the generation of the masses of Standard Model (SM) elementary particles, the ultimate nature and origin of "mass" remain open questions in contemporary physics. From a foundational perspective, mass should be fundamentally related to the gravitational interaction and, according to Mach, to the structure of the Universe. In the present letter, a fully dynamical mass generation mechanism induced by higher-order correcti...

Einstein formulated the general theory of relativity (GR) with an aim to mathematically incorporate Mach's principle. Despite early hopes, it became evident that GR did not follow Mach's proposition. Nevertheless, due to its accurate explanation of various observational results, Einstein refrained from further attempts to formulate Mach's principle. Over time, multiple researchers attempted to develop gravity theories aligned with the Machian model of inertia. However, each o...

Can we give the graviton a mass? Does it even make sense to speak of a massive graviton? In this essay I shall answer these questions in the affirmative. I shall outline an alternative to Einstein Gravity that satisfies the Equivalence Principle and automatically passes all classical weak-field tests (GM/r approx 10^{-6}). It also passes medium-field tests (GM/r approx 1/5), but exhibits radically different strong-field behaviour (GM/r approx 1). Black holes in the usual sens...