The document under review

Running head: "Inverse-Square Scaling Constants: kₑ and G" "A Comparative Analysis of Inverse-Square [S]caling Constants Dimensional, Geometric, and Structural Inversion Between Electrostatic and Gravitational Fields Principle of Physical Consistency (PPC v5.0) — Independent Research"

"In the formulation of classical field mechanics, a striking structural correlation emerges when analyzing the mathematical frameworks governing long-range forces. Specifically, the relationship between Coulomb's constant (kₑ) and the Newtonian gravitational constant (G) reveals a profound geometric symmetry. While sta[nd]ard academic paradigms treat these constants as independent scaling factors for entirely distinct physical phenomena, a systematic examination of their mathematical placement, dimensional formulas, and operational vectors suggests a deeply interconnected, mirrored relationship. This paper provides a rigorous audit of the structural mirroring, dimensional divergence, and theoretical frameworks that attempt to bridge these two fundamental constraints of physical reality."

"A direct correlation is established through the exact structural mirroring between Coulomb's Law for electrostatic force and Newton's Law of Universal Gravitation. Upon critical examination of their mathematical expressions, the identical behavior of field propagation through three-dimensional space becomes undeniable. Coulomb's Law: F = kₑ (q₁ q₂) / r² Newton's Gravitation[al L]aw: F = G (m₁ m₂) / r² Through this comparison, I identified that both equations dictate a force (F) that decreases proportional to the square of the distance (r²) between two point sources. The constant kₑ acts as the specific proportionality factor converting the product of two electric charges (q₁ q₂) into a force, while G serves as the proportionality factor converting the product of two masses (m₁ m₂) into a force. Because of this exact mathematical symmetry, the spatial properties of the fields generated by these constants —including field lines, flux, and potential energy gradients—are mathematically identical in their geometric structure."

"Despite an identical geometric layout, a significant divergence occurs when analyzing the magnitudes and dimensional metrics assigned to these constants within standard measurement systems. Coulomb's constant (kₑ) possesses an approximate value of 8.99 × 10⁹ N·m²/C², with a fundamental dimensional formula of [M¹ L³ T⁻⁴ I⁻²]. Conversely, the gravitational constant (G) possesses an approximate value of 6.67 × 10⁻¹¹ N·m²/kg², with a fundamental dimensional formula of [M⁻¹ L³ T⁻²]. From the mainstream scien[tific] perspective, this immense disparity in magnitude—where the electrostatic attraction between an electron and a proton exceeds their gravitational attraction by a factor of roughly 10³⁹—is interpreted as evidence of the extreme weakness of gravity relative to electromagnetism. However, a deeper dimensional inversion becomes apparent when evaluating how each constant interacts with mass (M). In kₑ, the mass dimension is positive and linear (M¹), whereas G inherently requires the inverse of mass (M⁻¹) to scale the force properly. This inverse relationship regarding the fundamental parameter of mass suggests that the constants do not merely differ in scale, but function as precise dimensional opposites."

"Extending the analysis to the physical action of these forces, I observed that Coulomb's constant behaves functionally as an inverted version of the gravitational constant. This operational inversion manifests clearly in the directional vectors produced by each system. The prevailing view in mainstream physics holds that gravity is a universally attractive phenomenon, pulling masses together and acting as a compressive, [co]ntractive vector in the macro-cosm. In contrast, while electrostatic forces can be attractive, the macro-physical world is fundamentally stabilized by repulsion. The structural integrity of matter relies directly on the massive outward, repulsive pressure of electron clouds, preventing atomic structures from collapsing into one another. This line of reasoning is supported by logical analysis: if G represents the force of accumulation drawing matter inward, kₑ provides the fundamental spatial resistance pushing outward, establishing the essential physical boundaries of matter."

"A logical thought process confirms that Coulomb's constant is not an isolated, standalone value, but rather a direct function of the medium through which it propagates. In standard electrodynamics, it is defined by the property of the vacuum via the relationship: kₑ = 1 / (4πε₀). Within this definition, ε₀ represents the permittivity of free space, which measures the underlying resistance of the vacuum to the formation of an electric field. Be[ca]use ε₀ sits in the denominator, Coulomb's constant is explicitly an inverse measure of space's electrical permittivity. When mapping this mechanical behavior to spatial acceleration, an alternative unified framework can be deduced. In a dielectric or fluid-medium framework, kₑ represents the structural stiffness or electrical pressure of the medium. Conversely, the gravitational constant can be modeled as the compliance, displacement, or localized breakdown of that same medium under the influence of mass or density differentials."

"The historical pursuit of a unified field theory underscores the validity of treating these constants as interconnected components of a single system rather than isolated coincidences. The prevailing a[ca]demic perspective notes that during the early 20th century, theorists sought to merge electromagnetism and gravitation geometrically. In the Kaluza-Klein framework, the introduction of a hidden fifth spatial dimension demonstrated that Maxwell's equations for electromagnetism and Einstein's field equations for gravitation emerge naturally from the same geometric source. In this context, kₑ and G are not independent constants, but distinct geometric projections of a single, multi-dimensional force."

"The observed facts align with alternative physical models that seek to explain downward acceleration without relying on the mainstream paradigm of bent spacetime. In these alternative frameworks, the physical movement of objects is governed mechanically by relative density and buoyancy within a given medium. These properties di[cta]te whether an object rises or sinks, and at what rate. Crucially, the directional vector—the determination of which way is "down"—is provided by an overarching electrostatic gradient, which is measurable as the Earth's natural atmospheric potential gradient. In this model, Coulomb's constant plays a foundational role by defining the electrical permittivity of the space, directly linking the electrical characteristics of the medium to the downward vector acting on matter."

"The structural, dimensional, and operational parameters of Coulomb's constant and the gravitational constant reveal a highly synchronized, inverted relationship. Mathematically, they utilize identical inverse-square geometry to propagate vectors through space. Vectorially, the[y] act as counter-balances, where one dictates contractive accu[m]ulation and the other governs repulsive spatial resistance. Whether analyzed through the mainstream lens of multi-dimensional geometry or the localized mechanics of dielectric and density gradients, the data indicate that kₑ and G are not unrelated constants, but perfectly mirrored bookends of field mechanics. PPC v5.0 — Independent Research"