Abstract
We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena unknown to the Kaluza literature is revealed: planetary masses are clothed in scalar field, which contributes 25% of the mass-energy of the clothed mass; the scalar potential around a planet is positive, compared with the negative gravitational potential; at laboratory scales, the scalar charge which couples to the scalar field is quadratic in electric charge; a new length scale of physics is encountered for the static scalar field around an electrically-charged mass, L s = μ 0 Q 2 / M ; the scalar charge of elementary particles is proportional to the electric charge, making the scalar force indistinguishable from the atomic electric force. An unduly strong electrogravitic buoyancy force is predicted for electrically-charged objects in the planetary scalar field, and this calculation appears to be the first quantitative falsification of the Kaluza unification. Since the simplest classical field, a long-range scalar field, is expected in nature, and since the Kaluza scalar field is as weak as gravity, we suggest that if there is an error in this calculation, it is likely to be in the magnitude of the coupling to the scalar field, not in the existence or magnitude of the scalar field itself.
Highlights
In 1919, Einstein received a paper from Kaluza [1] showing that the field equations of general relativity, and the field equations of electromagnetism, behave as if the gravitational tensor field gμν, and the electromagnetic vector field, Aμ, are components of a 5-dimensional (5D) tensor gravitational field g~ab
When the geodesic equation is written in 5 dimensions, it is found to contain the standard 4D geodesic equation, along with the Lorentz force law of electromagnetism; there is an additional term for the scalar force that is not identified in nature
The tensor gravitational potential gμν and the vector electromagnetic potential Aμ behave mathematically as if they are components of a 5D gravitational potential g~ab, but that implies the existence of a third field, a scalar potential φ in 4D
Summary
In 1919, Einstein received a paper from Kaluza [1] showing that the field equations of general relativity, and the field equations of electromagnetism, behave as if the gravitational tensor field gμν, and the electromagnetic vector field, Aμ, are components of a 5-dimensional (5D) tensor gravitational field g~ab. We find that the saturation effects in the source terms introduced in [2] act to alter the nature of the scalar coupling in high specific charge environments, so that the Kaluza scalar field may masquerade as the electric force in the parameter regimes of atomic systems. It appears that the scalar potential goes to zero for point particles, suppressing the scalar force altogether for atomic systems.
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