Narrow Results

Recently a mechanism to generate mass from gravitational interaction, based on 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 was presented in Refs. 1, 2. In these papers such an idea was realized for scalar and spinor fields treating the rest-of-the-universe in its vacuum state. In the present paper, using an extended version of Mach principle, the same strategy will be applied to show how the Heisenberg–Nambu–Jona-Lasinio non-linear equation for fermions Ψ arises as a consequence of the gravitational interaction of Ψ with the rest-of-the-universe.

Chae’s analyses on GAIA observations of wide binary stars have fortified the paradigm of extended gravity with particular attention to MOND-like theories. We recall that, starting from the origin of Einstein’s general relativity, the request of Mach on the structure of the theory has been the core of the foundational debate. This issue is strictly connected with the nature of the mass–energy equivalence. This was exactly the key point that Einstein used to derive the same general relativity. On the other hand, the current requirements of particle physics and the open questions within extended gravity theories, which have recently been further strengthened by the analyses of GAIA observations, request a better understanding of the Equivalence Principle. By considering a direct coupling between the Ricci curvature scalar and the matter Lagrangian, a nongeodesic ratio between the inertial and gravitational masses can be fixed and MOND-like theories are retrieved at low energies.

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal.

The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence, the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless.

Thence emerges a scale-invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation thereof, embodied in “energy-momentum super tensors”, follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the general relativity-based standard paradigm could not address.

Recently a mechanism to generate mass from gravitational interaction, based on 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 was presented in Refs. 1, 2. In these papers such an idea was realized for scalar and spinor fields treating the rest-of-the-universe in its vacuum state. In the present paper, using an extended version of Mach principle, the same strategy will be applied to show how the Heisenberg-Nambu-Jona-Lasinio non-linear equation for fermions Ψ arises as a consequence of the gravitational interaction of Ψ with the rest-of-the-universe.