
TL;DR
This paper introduces a novel space-time--time geometry combining Kaluza's and Weyl's theories, describing particle motion with evolving mass and charge influenced by a scalar field, and proposes new physical interpretations and applications.
Contribution
It develops a new geometric framework called space-time--time that unifies electromagnetic and gravitational interactions with unique residual curvature properties and dynamic particle characteristics.
Findings
Particle mass and charge evolve along geodesics.
Four forces govern particle motion, including a novel phi-force.
Application potential in atomic electron orbital modeling.
Abstract
Space-time--time is a natural hybrid of Kaluza's five-dimensional geometry and Weyl's conformal space-time geometry. Translations along the secondary time dimension produce the electromagnetic gauge transformations of Kaluza--Klein theory and the metric gauge transformations of Weyl theory, related as Weyl postulated. Geometrically, this phenomenon resides in an exponential-expansion producing ``conformality constraint'', which replaces Kaluza's ``cylinder condition''. The curvature tensors exhibit a wealth of ``interactions'' among geometrical entities with physical interpretations. Unique to the conformally constrained geometry is a sectionally isotropic, ultralocally determined ``residual curvature'', useful in construction of an action density for field equations. A space-time--time geodesic describes a test particle whose rest mass m and electric charge q evolve according to…
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Taxonomy
TopicsMultidisciplinary Warburg-centric Studies
