arXiv subjects

L. L. Williams

Publications and source records attributed to L. L. Williams.

5 recordsLinked to original sources

arXiv2021

A new class of monopole solutions in five-dimensional general relativity and the role of negative scalar field energy in vacuum solutions

Using numerical algebra tools, new classes of monopole solutions are obtained to the static, spherically-symmetric vacuum field equations of five-dimensional general relativity. First proposed by Kaluza, 5D general relativity unites gravity and classical electromagnetism with a scalar field. These monopoles correspond to bodies carrying mass, electric charge, and scalar charge. The Reissner-Nordström limit allows us to constrain the signature of the fifth component to be spacelike, but valid solutions are obtained for either sign of the scalar field. We find that Kaluza vacuum solutions imply the scalar field energy density is the negative of the electric field energy density, so the total electric and scalar field energy of the monopole is zero. Yet the new solutions provide reasonable Reissner-Nordström and Coulomb limits in mathematical form, with varying possibilities for the scalar field. The vanishing of the total electric and scalar field energy density for vacuum solutions seems to imply the scalar field can be understood as a negative-energy foundation on which the electric field is built.

gr-qc↗

arXiv2021

Inductive rectilinear frame dragging and local coupling to the gravitational field of the universe

There is a drag force on objects moving in the background cosmological metric, known from galaxy cluster dynamics. The force is quite small over laboratory timescales, yet it applies in principle to all moving bodies in the universe. It means it is possible for matter to exchange momentum and energy with the gravitational field of the universe, and that the cosmological metric can be determined in principle from local measurements on moving bodies. The drag force can be understood as inductive rectilinear frame dragging. This dragging force exists in the rest frame of a moving object, and arises from the off-diagonal components induced in the boosted-frame metric. Unlike the Kerr metric or other typical frame-dragging geometries, cosmological inductive dragging occurs at uniform velocity, along the direction of motion, and dissipates energy. Proposed gravito-magnetic invariants formed from contractions of the Riemann tensor do not appear to capture inductive dragging effects, and this might be the first identification of inductive rectilinear dragging.

gr-qc↗

arXiv2021

Maxwellian mirages in general relativity

Maxwellian approximations to linear general relativity are revisited in light of relatively recent results on the degrees of freedom in the linear gravitational field. The well-known Maxwellian formalism obtained in harmonic coordinates is compared with a Maxwellian formalism obtained under a coordinate choice where each of the metric components corresponds to each of the coordinate-invariant degrees of freedom of the linear gravitational field. The coordinate freedom of general relativity can be exploited to cast the field equations into Maxwellian form, but such forms can be mere mirages of the coordinate choice -- mirages such as vector gravitational waves. A coordinate choice that yields perfectly-Maxwellian field equations, will yield a force equation that is not Lorentzian. If field definitions are chosen to obtain Lorentz-like terms in the force equation, then Maxwellian forms are compromised in the field equations. Many treatments of gravito-electromagnetism will make inconsistent ordering choices between the field equations and force equations, or else truncate terms of relevant order from the force equation. Often such mistakes reflect an attempt to force exact Maxwellian analogs simultaneously in both the field equations and the force equation, with the result that terms dropped are as large as those kept.

gr-qc↗

arXiv2021

Null-result test for effect on weight from large electrostatic charge

We report test results searching for an effect of electrostatic charge on weight. For conducting test objects of mass of order 1 kilogram, we found no effect on weight, for potentials ranging from 10 V to 200 kV, corresponding to charge states ranging from $10^{-9}$ to over $10^{-5}$ coulombs, and for both polarities, to within a measurement precision of 2 grams. While such a result may not be unexpected, this is the first unipolar, high-voltage, meter-scale, static test for electro-gravitic effects reported in the literature. Our investigation was motivated by the search for possible coupling to a long-range scalar field that could surround the planet, yet go otherwise undetected. The large buoyancy force predicted within the classical Kaluza theory involving a long-range scalar field is falsified by our results, and this appears to be the first such experimental test of the classical Kaluza theory in the weak field regime where it was otherwise thought identical with known physics. A parameterization is suggested to organize the variety of electro-gravitic experiment designs.

gr-qc↗

arXiv2020

Long-range scalar forces in five-dimensional general relativity

Kaluza first observed that the vacuum Einstein equations written in 5 dimensions (5D) reproduce exactly 4D general relativity and classical electrodynamics, when derivatives of the 5D metric with respect to the 5th coordinate are set to zero. The 15th component of the 5D metric is a 4D long-range scalar field, and the 4D limit emerges as the scalar field goes to one. Here we report new analysis, results, and force effects from the long-range Kaluza scalar field. These considerations reveal a strong electro-gravitic buoyancy force arising from a gravitational coupling between the electric charge of a body and the scalar field around a planet. A new, third characteristic lengthscale for the electro-gravitic fields of a body of mass $M$ and charge $Q$ is identified, $μ_0 Q^2/M$, to go along with the Reissner-Nordstrom lengthscales, $GM/c^2$ and $Q\sqrt{Gμ_0 /c^2}$. At atomic scales, 5D covariance of the source terms requires that the electric, scalar, and gravitational forces all become proportional to electric charge. We discuss these results relative to foundational work by Dicke on long range scalar interactions and the Brans-Dicke scalar-tensor theory, including how interaction with the scalar implies a variable rest mass, and the energetics of the joint scalar-gravitational interaction. We discuss the problems of tuning the only available free parameter, the invariant 5D length element of the sources, to neutralize the scalar force and avoid the otherwise-large scalar force predictions. We conclude that large classical forces are a testable prediction of 5D general relativity sufficient to falsify the 5D hypothesis. Yet the emergence of a new physical interaction lengthscale is suggestive of further unexplored physics of the long range scalar field.

gr-qc↗