Gravity
My Ph.D. thesis included a conceptual path from classical Newtonian mechanics to General Relativity (See Publications). One of the challenges in teaching General Relativity is the need to start with base level of mathematical understanding (mainly differential geometry and Riemannian geometry ). Once the student possess a minimum working knowledge of these, they are introduced to geodesic equations and gravitational curvature of space. Lastly, Einstein’s field equations are introduced with Schwarzschild’s metric. Only after these initial concepts are grasps, does one work their way back to classical Newtonian mechanics at the limit of “flat” space.
My desire was, and still is, to show a fully developed path from classical to GR, instead of GR to classical. Without question General Relativity is one of the greatest theoretical feats of the twentieth century. In no way is my intention to tear it down, but to enhance. Obviously there is a weakness in GR with its ability to predict the world of quantum, and so as with Quantum in its ability to predict in the world of GR. As one who enjoys the history related to the birthing of General Relativity and Quantum mechanics, I have often pondered if the newly developed math of the time (Riemannian geometry and linear algebra) were not available, would a different path to GR and Quantum have been developed.
It is with this frame of mind I attempted to insert myself within their time period (albeit with a century’s worth of geniuses) and work a path without these two mathematical tools. I personally have found this challenge beyond my reach, but none-the-less it has produced some interesting models. My favorite, and possibly most promising model is starting a derived scalar field and calculating predictions based on Newtonian physical laws applied over the field. From this application of Newtonian mechanics over a scalar field amazing correlations and accurate predictions are made. Including gravitational time dilation, orbital advances, GPS clock adjustments needed, photon red/blue shifts, and possibly even gravitational waves (though a vector field is better suited than a scalar).
The same scalar field when applied to quantum (from a classical approach) produces interesting results. The field, though a classical field, produces discreteness, which at small (quantum level) distances becomes dominate. For those with interest, I have attempted to place a logical path below from concept to practice of the classical based approach to a unified theory.
Classical Approach to a Unified Theory
Special Relativity (brief review of bridging from classical to SR)
Newtonian Mechanics Over the Scalar Field
Newtonian Mechanics Applied to the Hydrogen Atom Over the Scalar Field