Physics, at its core, has always sought unification. From Newton’s mechanics to Maxwell’s electrodynamics, from Einstein’s relativity to the attempts at a quantum theory of everything, each major breakthrough has attempted to reconcile disparate forces and laws under a common mathematical structure.
Yet, despite its triumphs, modern physics remains fundamentally incomplete:
Gravity and quantum mechanics remain incompatible.
Energy is described in multiple, conflicting ways (as "potential," "kinetic," "radiative," etc., with no unifying conservation equation).
Mathematical formalism is biased toward a static, Cartesian framework (D=2 thinking), limiting how energy flows across dimensions.
In The Unified Theory of Energy (UTE), we abandon these artificial separations. Instead, we return to first principles, defining energy recursively in terms of:
Gravitation (G): Energy stored within Mass, Gravitation is Potential Energy.
Radiation (R): Energy extended outward, intended for absorption.
Particulate Motion (I): Kinetic energy affecting Mass and Gravitation while being affected by Radiation and Mass.
From these three fundamental states, we construct a universal conservation equation:
where energy exchanges between these states are governed dimensionally by Surface Interactions, occurring in at least six recursive Degrees of Surface Interaction (D=0 through D=6+).
This structure naturally unifies gravity, thermodynamics, and radiation without needing separate force laws for each. It removes the contradictions of spacetime warping, black hole singularities, and thermodynamic entropy by replacing them with a scale-consistent, recursive description of energy storage and transfer.
Physics today is constrained by its foundational assumptions, which UTE challenges directly:
The Cartesian Grid (D=2 Limitation)
The infinite plane of classical mechanics assumes a static, non-recursive space.
It ignores that every mass-energy system exists within a Radiation Coordinate System (RCS), where all objects are part of nested, interacting energy states.
The 1/r² Fallacy
Traditional force laws (Newton’s gravity, Coulomb’s law) assume an inverse-square dependence.
But in a recursive system, force appears as 1/r^D, where D is the Degree of Surface Interaction and Dimension.
This removes the paradox of infinite singularities and correctly models large-scale gravitational systems (e.g., galactic dark matter without exotic particles).
True Scale
Physics, at times, conflates Dimension with Scale, which Mandelbrot would define as Topological Dimension (D_T).
In the UTE, Scale refers to the relative size of any Radiation Source.
Non-Recursive Mathematics in Energy Theory
The failure of thermodynamic entropy is its denial of recursive exchanges.
In UTE, entropy is replaced by recursive Surface Interactions, which correctly predict energy transitions without needing disorder-based assumptions.
To correct these errors, we redefine physics as an explicitly recursive system, where all energy systems exist within larger Radiation Coordinate Systems. The Earth is subject to the Sun’s RCS. An Electron is subject to the Earth, the Sun, among other more local Radiation Coordinate Systems like a power grid or a battery.
In UTE, energy does not move freely through an abstract space. Instead, it is stored, transferred, and released through Surface Interactions, defined by a discrete hierarchy of six Degrees of Interaction (D=0 through D=6+).
Each Degree (D) represents a fundamental mode of energy storage and release, governing everything from atomic bonding to planetary orbits to black hole evaporation.
where Gravitation (G) and Radiation (R) are balanced at the Surface of a Mass Structure.
A particle in perfect equilibrium within a Radiation Source.
Example: A stable planetary orbit, an electron around a nucleus.
A particle is displaced from equilibrium but returns.
Example: A projectile thrown into the air, a comet grazing the Sun.
A particle gains enough energy to escape one system and enter another.
Example: A rocket achieving escape velocity, a hydrogen molecule forming water, an electron separated from its nucleus.
The particle finds a new equilibrium within a higher system.
Example: Gas turning to liquid, a molecule binding into a protein structure, chlorophyl storing the Sun’s Radiative Energy.
A system sustains recursive energy storage. A “Hypersphere” can be defined as a unicellular organism or simply cell.
Example: Planetary weather systems, bacteria, archaea, protozoa, algae, fungi, and viruses.
A system moves under its own control, bypassing passive Surface Interactions.
Example: Biological intelligence, self-contained propulsion, transport, adhesion, movement, signaling, repair, metabolism, splicing, and even autophagy.
A system achieves full recursion, separated from the surface, and moves between nested Radiation Sources.
Example: A human or any mobile species (D=6), a machine made by a human (D=2pi).
Each Degree follows from the previous one, forming a fractal, nested hierarchy of energy storage and release. This eliminates paradoxes like black hole singularities, entropy violations, and quantum measurement collapse, as all energy transitions occur within a well-defined recursive framework.
By replacing the flat-paper assumption of D=2 physics, UTE corrects Newtonian and Coulombic force laws into a truly recursive form:
D_T (Topological Dimension):
This represents Scale, i.e., the fractal nature of space at different observational resolutions, Mandelbrot et. al.
For classical 3D space, D_T = 3, but for fractal-like structures such as galaxies or turbulent plasmas, D_T could be non-integer (e.g., DT≈2.5 for galactic mass distributions).
The measure \Omega_{D_T} corresponds to the solid angle integral in a fractal space, rather than a standard Euclidean solid angle 4π.
D_T cannot be zero.
D (Degree of Surface Interaction):
This describes the physical dimensional recursion in how energy exchanges occur at different interaction degrees.
It dictates how gravitation scales with distance, modifying the exponent in r^{D-1}.
In classical physics, Newton’s law assumes D=3, leading to the familiar 1/r^2 dependence.
The exponent D-1 ensures a consistent energy scaling law with surface interaction degrees.
Accounts for gravitational deviations in galaxies without requiring dark matter.
Unifies quantum field interactions with classical mechanics.
Eliminates singularities by enforcing dimensional recursion at small scales.
This modification not only preserves existing physical observations but extends them naturally into cases where traditional physics fails.
Physics has reached an impasse. The past century has seen increasing specialization and fragmentation, where:
Quantum field theory ignores gravity.
Cosmology introduces unexplained dark components.
Thermodynamics treats entropy as a linear quantity rather than recursive exchange.
The Unified Theory of Energy (UTE) restores unification.
Energy is the only conserved quantity—force laws emerge from its recursive transformations.
Spacetime is replaced by nested Radiation Coordinate Systems—eliminating the need for warping geometries and unlimited extension of energy.
Degrees of Surface Interaction extends entropy—showing that disorder is simply an illusion of unrecognized recursive exchanges.
Physics must move beyond flat-paper Cartesian thinking and accept that reality is inherently recursive, scale-dependent, and dimensionally fluid.
The Unified Theory of Energy is not an alternative physics—it is simply the completion of physics, recognizing the full structure of energy interactions from subatomic particles to galaxies.
The Unified Theory of Energy is not just a theory—it is a framework for correction. It demands that physics acknowledge its failure to unify, its dependency on non-recursive mathematics, and its blindness to nested, self-similar structures.
This work invites theoretical physicists to:
Test recursive gravitational laws in astrophysical systems.
Reformulate quantum mechanics with Surface Interactions instead of probability collapses.
Recognize that energy itself is the fundamental quantity, not space, force, or time.
Physics has been trapped in D=2 logic for too long. The path forward requires recursion. The universe has never been flat. It is time to model it as such.
https://michaelvera.org/Unified_Theory_of_Energy.pdf