Abstract
A transient mass fluctuation, predicted by Lorentz-invariant theories of gravitation wherein inertia is gravitationally induced, can be combined with a synchronous thrust to produce a stationary change in the apparent weight of an object. A substantial effect of this sort—on the order of tenths of a gram or more—should be achievable in laboratory scale apparatus. A detailed derivation of the predicted transient mass fluctuation is given in an appendix.
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1. This does not mean, however, that it is impossible to directly detect the expected weight fluctuations at higher than low audio frequencies. In fact, in preliminary work toward the experiment described below, L. Shen, K. Wanser, and I have detected evidence of the effect at ultrasonic frequencies employing very unusual capacitors (high energy density ceramic multiplate chip capacitors with strongly suppressed first- and second-order electromechanical effects) mounted on an aluminum pedestal which acts as the spring in the system. The minute displacements produced are detected with a laser interferometer. This work will be described fully in a separate paper.
2. Such a transformer can be made with, for example, an Amidon T 300A-26 powdered iron torus. Powdered iron is preferable to ferrite because of its superior flux saturation and energy loss characteristics at the frequencies in question.
3. Einstein[7] was the first to point out (in 1912) that the simplest formalism for the gravitational field that incorporates Machian gravitational induction of inertia is that based on the analogy with the electromagnetic field, that is, a Lorentz-invariant four-vector potential theory. Many years later, Sciama[5] showed explicitly how such a theory could account for well-known inertial reaction effects, provided that the mean matter density of the universe were the “right” value (in fact, just cosmologically “critical” density). Later he showed that a general relativistic tensor formalism yielded the same conclusions[8]. And, as I have pointed out elsewhere[1–3], Nordtvedt's PPN formalism with GRT parameters chosen yields the same result when the effect of cosmic matter is included.
4. Contributions from the Hubble flow tov and thusj are ignored here, since upon integration they vanish by symmetry. Hubble flow does, however, makeρ c a function ofr.
5. The advanced solutions of the wave equation required to account for inertia in the Lorentz gauge can be avoided if one chooses by using the Coulomb gauge with its action-at-a-distance characteristic. Asserting the equivalent of the Coulomb gauge to get instantaneous inertial reaction forces, as Trederet al.[9] point out, suggests an interesting generalization of GRT.
6. This procedure for going from a particle to a continuous media representation is not in general valid, since in all frames, except the rest frame,ρ will involve elements of the stress tensor. Those contributions, however, are of orderv 2 /c 2 and are here ignored.
7. One may find this result troublesome, for one may think thatø is only fixed up to an additive constant. While this is true in linear theories, as discussed below, it is not true in nonlinear theories. Let me also point out here the similarity of Eq. (A12) and the field equations obtained by Trederet al.[9, pp. 70-73] in a “higher-derivative” manifestly Machian Einstein-Cartan theory of gravitation where the same “potential-like” coupling of gravity and matter occurs.
8. Equation (A13) only applies in the instantaneous rest frame of the test particle. In all other frames of reference one obtains a term involving the time derivative of the acceleration. Terms of this sort, of course, are not normally allowed in dynamics. They are the signature of self-forces and radiation reaction effects. But this should come as no surprise, for the effect arises from the gravitational self-energy interaction when inertial reaction forces are stimulated.
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Woodward, J.F. A stationary apparent weight shift from a transient Machian mass fluctuation. Found Phys Lett 5, 425–442 (1992). https://doi.org/10.1007/BF00690424
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DOI: https://doi.org/10.1007/BF00690424