This article explores a novel theoretical framework that extends Newton's Law of Universal Gravitation into a Unified Energy Equation. We transition from the classical understanding of force as a function of mass and distance to a perspective where Energy is the primary consideration. The resulting framework offers new insights into phenomena such as Gamma Ray Bursts, Supernovae, and Black Holes by balancing gravitational and radiative components. I propose that these extremes are manifestations of the same underlying principles observed at different Scales, leading to a deeper understanding of cosmic events and the nature of Energy.
Newton's Law of Universal Gravitation, which describes the force between two masses as 1)
F = G \frac{m_1 m_2}{r^2}has long been a cornerstone of classical mechanics. However, modern physics demands a more comprehensive view that encompasses both gravitational forces and radiative energy within a single unified framework. This paper aims to extend Newton's equation into a broader energy-based model, where the relationship between mass, distance, and energy is redefined to include radiative components, utilizing the definitions from The Unifed Theory of Energy, most notably its Energy State Theorem:
“Energy exists in three distinct states: as Radiation, as Gravitation, and as Particulate Motion. Each of these three energy states cannot exist apart from, or without, the other states”
The classical equation describes the gravitational force between two masses and separated by a distance r. By interpreting this force as a manifestation of Energy, I propose the transition to 2)
E = G \frac{m_1 m_2}{r^2}
E = G(r, D, D_T) \left( \frac{M(r)}{r^D} \right) D_T
E = \int_{0}^{r_{\text{Surface}}} G(r, D, D_T) \cdot \frac{M(r) \cdot \rho(r)}{r^{D-2}} \cdot D_T \, dr
E = \int_{D_{\min}}^{D_{\max}} \int_{0}^{\infty} \left[ G(r, D, D_T) \cdot R(r, D, D_T) \right] \cdot \delta(G - R) \, dD_T \, dDwhere G is Gravitation which is Potential Energy, and is only a constant for a constant r (DNE), D is Degree of Surface Interaction and D_T is Scale which also known by Mandelbrot as Topological Dimension.
Here, Energy is not simply a result of gravitational interaction but a fundamental aspect of the system's state.
This reinterpretation allows for a generalized equation, where energy is not merely an emergent property but directly tied to a non-constant Gravitation (G), the mass involved, and the spatial extension as a radiant separation. This shift lays the groundwork for understanding Energy as an intrinsic component of Gravitational systems.
We further refine the Energy Equation to 3)
E = G*{M(r)/{r^D}}where M(r) represents a combined mass over the distance from the theoretical center of that mass to its Surface, ensuring that r cannot be zero in the divisor, and D represents the value relative to the Degree of Surface Interaction, default=2 for “flat-paper mathematics.” This modification acknowledges the physical impossibility of a singularity at the core of massive objects, where r is synthetically set to zero, while still aligning with general relativity's treatment of black holes and other extreme gravitational environments.
This equation also suggests that the mass is intrinsically connected to the spatial distribution of energy surrounding it, integrating both Gravitation and Radiation. The distance 𝑟, interpreted as the extension of the mass's surface from its center, also serves as a variable describing the extent of radiative energy distribution, assuming the particles comprising the mass were stretched to their maximum possible distance from the center.
In typical Mass Structures, however, 𝑟 is also understood as the maximum Surface Depth value, as defined by Definition 11 of The Unified Theory of Energy:
“Surface Depth is the depth of saturation of Radiation into a Mass Structure.”
In our unified framework, Radiation can be described by 4)
R = M(r)/{r^D}representing the spatial extension of energy emanating from Mass. By defining Radiation (R) in terms of mass and distance, which cannot be zero or infinite, we bridge the gap between gravitational forces and radiative phenomena, suggesting that Radiation and Gravitation are two aspects of the same fundamental Energy Equation.
This approach allows us to describe various astrophysical phenomena in terms of the balance between Gravitation and Radiation. For instance, in environments with extreme Radiation and limited Gravitation, , such as Gamma Ray Bursts and Supernovae, we see energetic outflows that can be modeled within this framework. Conversely, in environments where Gravitation dominates and Radiation is limited, , such as Black Holes, the model predicts intense gravitational fields with minimal radiative escape. It would seem, however, that most systems are perfectly in balance, when observed from the correct Scale.
“Scale refers to the relative size of any Radiation Source.”
- Definition 6 of The Unified Theory of Energy
The generalized form of our equation, therefore, is 5)
E=G*Rwhere encapsulates the radiative component defined by the distribution and extent of mass-energy.
This formulation suggests that extreme astrophysical events are not merely anomalies but manifestations of the same principles observed at different scales. The balance of Gravitation, Radiation, and Particulate Motion dictates the system's state, with neither extreme existing in complete isolation. Rather, these systems are interconnected and scale-dependent, with variations in observed behavior arising from changes in the relative contributions of gravitational and radiative energy.
This Unified Energy Framework offers new perspectives on the nature of cosmic phenomena. By treating Gravitation and Radiation as interdependent components of a single Energy Equation, we can better understand the dynamics of extreme events like Gamma Ray Bursts, Supernovae, and Black Holes. The impossibility of complete isolation of gravitation, radiation, or motion implies that these events exist within a continuum, with their characteristics varying according to Scale.
This model challenges traditional boundaries between distinct physical phenomena, proposing that all observed states are part of a unified energy spectrum. Future work will aim to refine this framework and explore its implications for other astrophysical and theoretical domains, potentially offering a pathway to a more cohesive understanding of the universe's fundamental forces.
Newton, I. (1687). Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy). London: Royal Society.
Vera, M. (2020). The Unified Theory of Energy. [PDF]. https://michaelvera.org/Unified_Theory_of_Energy.pdf
Penrose, R. (1965). "Gravitational Collapse and Space-Time Singularities." Physical Review Letters, 14(3), 57-59.
Hawking, S. W., & Ellis, G. F. R. (1973). The Large Scale Structure of Space-Time. Cambridge University Press.
Ashtekar, A., & Bojowald, M. (2006). "Quantum Geometry and the Schwarzschild Singularity." Classical and Quantum Gravity, 23(2), 391-411.
Hayward, S. A. (2006). "Formation and Evaporation of Nonsingular Black Holes." Physical Review Letters, 96(3), 031103.
Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman and Company.
Piran, T. (2005). "The Physics of Gamma-Ray Bursts." Reviews of Modern Physics, 76(4), 1143-1210.
Woosley, S. E., & Janka, T. (2005). "The Physics of Core-Collapse Supernovae." Nature Physics, 1, 147-154.
Blandford, R. D., & Znajek, R. L. (1977). "Electromagnetic Extraction of Energy from Kerr Black Holes." Monthly Notices of the Royal Astronomical Society, 179(3), 433-456.
Mészáros, P. (2006). "Gamma-Ray Bursts." Reports on Progress in Physics, 69(8), 2259-2322.
Fryer, C. L., & Warren, M. S. (2004). "The Collapse of Rotating Massive Stars in Three Dimensions." The Astrophysical Journal, 601(1), 391-404.
Thorne, K. S. (1980). "Multipole Expansions of Gravitational Radiation." Reviews of Modern Physics, 52(2), 299-339.
https://github.com/bubbajoelouis/UnifiedEnergyEquation