Gravity and the Quantum Vacuum Inertia Hypothesis I. Formalized Groundwork for Extension to Gravity

It has been shown [1,2] that the electromagnetic quantum vacuum makes a contribution to the inertial mass, mi, in the sense that at least part of the inertial force of opposition to acceleration, or inertia reaction force, springs from the electromagnetic quantum vacuum (see also [3] for an earlier attempt). Specifically, in the previously cited work, the properties of the electromagnetic quantum vacuum as experienced in a Rindler constant acceleration frame were investigated, and the existence of an energy-momentum flux was discovered which, for convenience, we call the Rindler flux (RF). The RF, and its relative, Unruh-Davies radiation, both stem from event-horizon effects in accelerating reference frames. The force of radiation pressure produced by the RF proves to be proportional to the acceleration of the reference frame, which leads to the hypothesis that at least part of the inertia of an object should be due to the individual and collective interaction of its quarks and electrons with the RF. We call this the quantum vacuum inertia hypothesis. We demonstrate that this approach to inertia is consistent with general relativity (GR) and that it answers a fundamental question left open within GR, viz. is there a physical mechanism that generates the reaction force known as weight when a specific non-geodesic motion is imposed on an object? Or put another way, while geometrodynamics dictates the spacetime metric and thus specifies geodesics, is there an identifiable mechanism for enforcing the motion of freely-falling bodies along geodesic trajectories? The quantum vacuum inertia hypothesis provides such a mechanism, since by assuming the Einstein principle of local Lorentz-invariance (LLI), we can immediately show that the same RF arises due to curved spacetime geometry as for acceleration in flat spacetime. Thus the previously derived expression for the inertial mass contribution from the electromagnetic quantum vacuum field is exactly equal to the corresponding contribution to the gravitational mass, mg. Therefore, within the electromagnetic quantum vacuum viewpoint proposed in [1,2], the Newtonian weak equivalence principle, mi = mg, ensues in a straightforward manner. In the weak field limit it can then also be shown, by means of a simple argument from potential theory, that because of geometrical reasons the Newtonian gravitational force law must exactly follow. This elementary analysis however does not pin down the exact form of the gravitational theory that is required but only that it should be a theory of the metric type, i.e., a theory like Einstein’s GR that can be interpreted as curvature of spacetime. While the present analysis shows that our previous quantum vacuum inertial mass analysis is consistent with GR, the extension of these two analyses to components of the quantum vacuum other than the electromagnetic component, i.e. the strong and weak vacua, remains to be done.