Historical research guide · 0864 · 2004
Inertia and Gravitation as Vacuum Effects — the case for Passive Gravitational Mass
Alfonso Rueda
In one minute
Alfonso Rueda argues that inertial mass and passive gravitational mass can arise from the same vacuum interaction. In the quantum-vacuum inertia hypothesis, a charged constituent accelerated through the electromagnetic zero-point field sees an asymmetric field and receives a reaction proportional to acceleration. Rueda then applies the equivalence principle to an object held above a gravitating body: freely falling local frames pass the stationary object, and the proposed vacuum reaction appears as weight. The companion derivation identifies the two masses through the same spectrum-and-coupling integral and obtains a radial inverse-square field in its weak-field argument. It also proposes a measurement: weigh a cold microwave cavity, then its separated pieces; the assembled cavity should carry the mass of its resonant zero-point modes. This paper presents a model and a test design, not that measurement.
Connection
This is chapter 3’s explicit bridge from inertia to weight. Its cavity comparison supplies a definite experimental result: a measured assembled-minus-parts mass excess at stated temperature and mode cutoff, or no such excess. That makes the proposal testable without treating a familiar equality of masses as an explanation by itself.
From the source
The starting result, from the earlier work this paper builds on, is that the electromagnetic quantum vacuum makes a contribution to inertial mass. Calculated in a uniformly accelerated frame, the zero-point radiation develops an event-horizon asymmetry that produces a force opposing the acceleration, proportional to the acceleration in the low-velocity limit, and vanishing in unaccelerated frames because the zero-point spectrum is Lorentz invariant. The authors name this the quantum vacuum inertia hypothesis.Companion paper, section 1 and section 2
The extension to weight is a symmetry argument, not a new postulate. An object held fixed above a gravitating body is, as seen from the freely falling local Lorentz frames that stream past it, undergoing constant proper acceleration. By local Lorentz invariance the vacuum in those falling frames is the same vacuum as in the accelerated case, so the same asymmetry and the same reaction force must arise. What appears as inertial mass in the accelerated case is what appears as passive gravitational mass in the gravitational one, given by the same integral over the zero-point spectrum weighted by the object’s coupling function.Companion paper, section 4, equations 23 and 24
The weak equivalence principle therefore stops being an assumption. Within general relativity the equality of inertial and gravitational mass has to be put in by hand — Rindler’s phrase, quoted in the paper, is that the proportionality for different materials is really a very mysterious fact. On this account the two are not merely equal, they are identical: accelerating through the vacuum and standing still while the vacuum falls past you are the same physical situation.Companion paper, section 4, closing paragraphs, and conclusion 1
Newton’s law of gravitation follows in the weak-field limit without further input. Once the gravitating body distorts the vacuum in the same way acceleration does, the resulting field is central and radial by spherical symmetry, scales linearly with the source mass, has field lines that begin and end only where mass is present, and adds vectorially — which by ordinary potential theory leaves only the inverse-square form.Companion paper, section 7
The account supplies a mechanism general relativity leaves out. Geometrodynamics fixes the metric and therefore the geodesics, but says only that departing from a geodesic produces an inertia reaction force; it offers no physical origin for that force. Here the origin is the same vacuum asymmetry in both cases — true acceleration gives the inertia reaction force, being held stationary in a curved metric gives weight. The authors are careful to add that this says nothing yet about active gravitational mass, the ability of matter to bend spacetime in the first place.Companion paper, sections 5 and 8, and section 10
There is a proposed measurement, and it is unusually clean. Treat the interior of a microwave cavity as the archetype: its contribution to mass is the summed zero-point energies of the cavity’s own resonant modes, up to the plasma frequency of the electrons in the walls, divided by the speed of light squared — a quantity with no free parameters. Weigh the assembled cavity at the lowest temperature achievable, then disassemble it and weigh the parts. The assembled cavity should come out very slightly heavier. The predicted excess is small even for a large cavity, which is the whole difficulty, but a positive result would establish the reality of the zero-point field.Companion paper, section 3, equations 15 and 21, and conclusions 6 and 7
The way in
https://doi.org/10.1063/1.1787321How to cite it
Alfonso Rueda (2004) Inertia and Gravitation as Vacuum Effects — the case for Passive Gravitational Mass doi:10.1063/1.1787321