# The Duality of Whittaker Potential Theory: Fundamental Representations of Electromagnetism and Gravity, and Their Orthogonality

**Authors:** Mark Titleman  
**arXiv:** [2205.08309](https://arxiv.org/abs/2205.08309)  
**Date:** 2022-05-13  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2205.08309v9/

## Key points

- E. T. Whittaker's papers from 1903 and 1904 have profound implications for physical theory
- Insights into phenomena such as gravitational lensing, gravitational waves, Aharonov-Bohm effect, and elimination of gravitational singularities
- Unification of electrostatic and gravitational attraction through longitudinal waves in the 1903 paper
- Demonstration that electromagnetic waves arise from interference of longitudinal waves or scalar potential functions in the 1904 paper
- Far-reaching implications in modern physics inspiring ongoing research in areas like MOND and universe expansion
- Black holes with vacuum energy interior solutions exhibit a cosmological coupling constant of k=3 leading to mass-proportional growth in Robertson-Walker cosmology equation
- Mass-proportionality and preferred direction of longitudinal waves offer explanations for features of General Relativity and universe expansion
- Expansion occurs through dynamic longitudinal motion within non-local potentials when electromagnetism is distinct from static gravity in intergalactic space
- Whittaker's work introduces new mathematical concepts beyond traditional calculus methods, inviting further exploration into gravity theories such as MOND and expansion dynamics related to intensity or luminosity variations
- Potential for expanding Whittaker's gauge theory through computational advancements like Wick rotation opens up avenues for future research in mathematics and physics

## Summary

E. T. Whittaker's groundbreaking papers from 1903 and 1904 have profound implications for physical theory. Often overlooked as mere mathematical statements, these papers offer insights into various phenomena such as gravitational lensing, gravitational waves, the Aharonov-Bohm effect, and the elimination of gravitational singularities. In his 1903 paper, Whittaker unified electrostatic and gravitational attraction by showing that they result from longitudinal waves with wavefronts propagating parallel to their direction. The subsequent 1904 paper demonstrated that electromagnetic waves arise from the interference of these longitudinal waves or scalar potential functions. These concepts have far-reaching implications in modern physics and continue to inspire ongoing research in areas such as MOND (Modified Newtonian Dynamics) and the expansion of the universe. Recent studies suggest that black holes with vacuum energy interior solutions alongside cosmological boundaries exhibit a cosmological coupling constant of k=3, leading to mass-proportional growth in a Robertson-Walker cosmology equation and serving as a species contributing to cosmological accelerated expansion. The mass-proportionality and preferred direction of longitudinal waves within Whittaker's non-local potentials offer explanations for various features of General Relativity and the expansion of the universe. Expansion occurs through dynamic longitudinal motion within these potentials when electromagnetism is distinct from static gravity in intergalactic space. Whittaker's work represents a significant contribution to classical physics by introducing new mathematical concepts beyond traditional calculus methods. Despite being ahead of its time, his analysis invites further exploration into gravity theories such as MOND and expansion dynamics related to intensity or luminosity variations. The potential for expanding Whittaker's gauge theory through computational advancements like Wick rotation opens up avenues for future research in mathematics and physics. Overall, Whittaker's papers provide a foundation for understanding fundamental aspects of electromagnetism and gravity while offering possibilities for new physical phenomena yet to be explored fully. Their relevance extends beyond their initial publication date, inspiring ongoing investigations into the nature of spacetime and cosmic expansion mechanisms.