Constants Do Not Define Fields of Science

J. Rogers, SE Ohio, 18 Jun 2025, 1400

The Great Inversion: How We Lost Newton’s Simplicity

Modern physics has traveled centuries away from Newton’s notion of natural proportion, entangling itself in the complexity of unit-based formalism. Ironically, Newton—the supposed founder of classical mechanics—may have understood the essence of physical law more clearly than many of his intellectual descendants. His intuitive sense that forces, masses, and accelerations relate in pure ratios has been obscured by our modern reliance on the SI system, whose arbitrary units and scaling conventions have been mistakenly reified as if they were features of physical reality itself.

In doing so, we’ve committed a category error: mistaking the artifacts of our measurement system (Layer 3) for ontological truths about the universe (Layer 1). The physical constants we elevate to the status of divine fingerprints—$G, \hbar, c, k_B$—are not telling us about deep divisions in nature. They are telling us about our own coordinate system. The “complexity” of modern physics is not a property of the world, but a property of how we choose to describe it.

The return to Newton’s spirit—interpreted through the lens of modern categorical and geometric insights—reveals a deeper truth: the universe runs on proportion, not on units. When we realign our framework around this insight, the fragments of physics unify, and the constants dissolve into their true role as mathematical bridges between measurement axes, not as defining markers of separate physical domains.

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🔍 Traditional View: Constants Define Domains

Constant	Traditional Interpretation	Field It "Defines"
$c$	Ultimate speed limit	Relativity
$h$	Quantum of action	Quantum mechanics
$G$	Strength of gravitational interaction	Gravity
$k_B$	Bridge between micro and macro	Thermodynamics / Statistical Mech

In this framework, constants act like flags—each marking a separate "territory" of physical law, implying a fundamental partitioning of reality into distinct regimes.

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🧠 Projection-Based Reinterpretation: Constants Are Translators, Not Territories

➤ Constants are not signatures of different types of physics.

They are Jacobians—coordinate scaling operators that convert between human-defined measurement axes and a unified underlying system of dimensionless ratios.

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🧭 What This Means

1. No Fundamental Boundaries Between Fields

• The appearance of $c$ in $E=m{\mathrm{c^}}^2$ does not imply a shift into "relativity."

• The appearance of h in $E=hf$ does not mean we've entered a "quantum" regime.

These constants indicate coordinate transformations—e.g., mass-to-energy, frequency-to-energy—not ontological boundaries in nature.

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2. Constants Are Unit Accounting Tools

• In natural units, all constants disappear. Why? Because you're already operating in a basis where all axes are proportionally scaled.

• Therefore, the constants exist only to mediate the translation between arbitrary unit systems and natural proportional space.

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3. The Fields of Science Are Human Constructions

• Our disciplinary divisions are shaped by which measurement axes and constants dominate the projection, not by physical boundaries in reality.

• The constants are a historical record of which coordinate transformations we needed to write equations in a chosen system, not signatures of independent phenomena.

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📐 Refined Summary Table

Constant	Traditional Role	Projection Role
$c$	Defines relativity	Jacobian Unit scaling: time ↔ space (m ↔ s)
$\mathrm{h}$	Defines quantum	Composite Unit scaling: frequency ↔ mass ↔ energy (Hz ↔ J)
$G$	Defines gravity	Composite scaling: mass and lengt ↔  Force
$k_B$	Defines thermodynamics	Unit scaling: temperature ↔frequency↔mass↔energy (K ↔ J)

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💡 Significance of This Realization

🧩 A. Unified Ontology of Physical Law

The constants aren’t ontological signatures of separate regimes—they are structural necessities of expressing unified reality in disconnected human units.

Constants are bridges, not barriers.

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🔭 B. Refocusing Scientific Inquiry

• The real physics happens in dimensionless natural ratios.

• The goal is no longer to explain the constants, but to understand why the universe projects so simply in their absence.

"What does this constant mean?" becomes:
"What is the underlying natural proportion this constant projects?"

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🎓 C. Transforming Education and Philosophy

• Physics can be taught as coordinate geometry over measurement space, rather than as a catalog of separate forces and domains.

• The “mysteries” of constants dissolve into their role as projection operators.

Constants move from objects of metaphysical wonder to tools of mathematical translation.

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🧠 Final Thesis: The Great Demystification

$c, \hbar, G, k_B$ do not define the fields of science.
They are not essences of different realities.
They are the mathematical artifacts of projecting simple, unified relationships through complex, fragmented measurement systems.

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🔓 The Unlock

The true structure of physics is unified, dimensionless, and proportional.
The constants are what finite beings must write when describing the infinite through a grid of arbitrary units.