The Epistemological Catastrophe of Dimensioned Physics: How the Reification of Arbitrary Ratios Manufactured the Illusion of Physical Mechanisms

Abstract Modern physics is founded upon a two-stage epistemological error that has fundamentally distorted our ontology of the universe. The first error is the reification of a measurement—a dimensionless ratio between a physical state and an arbitrary human unit standard—into an intrinsic, independent physical property (e.g., “Mass” or “Energy”). The second error is the subsequent reification of the mathematical correction factors—the conversion ratios between these arbitrarily chosen unit standards (e.g., c, G, h)—into physical mechanisms and coupling constants that purportedly govern the interactions between these fabricated properties. By exposing this double reification, we demonstrate that the “fundamental constants” are not physical laws or entities, but merely the error bars between our disjointed coordinate grids. Returning to a unit-free, dimensionless substrate resolves the fragmentation of physics and unifies seemingly distinct forces as mere geometric projections of a single, invariant reality.

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1. Introduction: The Fragmentation of the Substrate

The history of modern physics is characterized by an increasing fragmentation of reality into distinct ontological silos: mass, energy, length, time, charge. Each silo possesses its own designated properties, its own mathematical formalisms, and its own academic departments. When physics discovers that these silos must interact—such as when mass appears to influence the geometry of space, or when energy appears in discrete chunks—it invokes “fundamental constants” (c, G, h) as the physical bridges between them.

This paper argues that this fragmentation is not a feature of the universe, but an artifact of a catastrophic epistemological error. The universe is a unified, dimensionless substrate (denoted here as X). The perceived division of X into independent properties, and the subsequent need for physical mechanisms to relate them, arises entirely from mistaking the shadows of our own measurement apparatus for the reality of the object casting them.

2. The First Reification: From Ratio to Property

Measurement is not a process of extracting an intrinsic physical property from an object; it is the process of projecting a dimensionless state onto an arbitrary human-defined axis.

Let X represent the pure, dimensionless state of a physical system. To quantify X for human use, we divide it by an arbitrary baseline—a unit standard (U). The measurement M is therefore strictly defined as a ratio: $$M = \frac{X}{U}$$

For example, the mass of an object is the ratio of its dimensionless geometric state to the Paris kilogram (kg); its length is the ratio of its spatial extent to the Paris meter (m). The measurement M is a useful human coordinate, but it possesses no independent ontological status. It is a shadow cast by X onto the wall of our chosen grid.

The First Reification occurs when we unconsciously invert this relationship. Instead of recognizing M as a projection of X, we treat M as an intrinsic property of the object. We say the object “has mass” or “has energy,” bringing the shadow inside the object and treating the coordinate as a substance.

Once M is reified as an independent property, the universe appears to be populated by distinct, disconnected substances. Mass is no longer a measurement of X on the kilogram grid; it is a distinct physical entity. Energy is no longer a measurement of X on the Joule grid; it is a completely different physical entity.

3. The Second Reification: From Error Bars to Physical Mechanisms

Because the unit standards (kg, m, s) were chosen arbitrarily and independently—based on the circumference of the Earth, the density of water, and the duration of a day—they do not naturally align. When we project the unified substrate X onto these disjointed grids, we introduce an artificial mismatch in the dimensions.

To make the mathematics of these disjointed projections balance, we must introduce conversion factors that translate between the arbitrary grids. For example, to convert a measurement on the time-grid (s) to a measurement on the space-grid (m), we require the conversion factor c (meters per second). To convert a measurement on the mass-grid (kg) to a measurement on the space-grid (m), we require the factor G/c² (meters per kilogram).

These conversion factors are precisely the ratios of our arbitrary unit standards to one another. They are the “error bars” of our coordinate system—the mathematical patches required to correct the misalignment of our human axes.

The Second Reification occurs when physics mistakes these coordinate correction factors for physical mechanisms. Having reified Mass and Space as separate, independent properties (First Reification), physicists are forced to ask: “How does the property of Mass reach out and affect the property of Space?”

They look at the equation for geometric gradient (e.g., the Schwarzschild radius r_s = 2(G/c²)M) and declare that G/c² is the physical mechanism—the “coupling constant” that dictates the strength by which Mass curves Space.

This is an ontological absurdity. G/c² has dimensions of [Length/Mass]. It is literally the ratio of the human meter stick to the human kilogram block. It does not exist in the universe; it exists solely to correct the error of measuring a unified X with two arbitrarily scaled, misaligned rulers. We have taken the mathematical patch required to fix our own bookkeeping error, and canonized it as a fundamental law of nature.

4. The Contrapositive Proof

The validity of this critique can be demonstrated through the strict application of formal logic to the axiom of scale invariance.

Axiom 1 (Scale Invariance): If a feature is physical (intrinsic to the universe), then it is invariant to unit scaling. (P → Q)

By the law of contraposition, this yields: Contrapositive: If a feature is not invariant to unit scaling, then it is not physical. (¬Q → ¬P)

The numerical values of c, G, and h change completely depending on whether one uses SI, CGS, or Planck units. In Planck units, they vanish into the number 1. They are the very definition of features that are ¬Q (not invariant to unit scaling).

Therefore, by the uncompromising geometry of logic, c, G, and h are ¬P (not physical).

They cannot be physical mechanisms, coupling constants, or fundamental features of reality. They belong strictly to the category of unit scaling itself. To accept the axiom of scale invariance while simultaneously treating the constants as physical entities is a direct logical contradiction. Physics has spent a century reifying its own error bars.

5. The Restoration of the Substrate

To correct this double reification, we must return to the operational definition of physics in three steps:

1. Remove Input Units: Cancel the arbitrary human unit standards by dividing by the appropriate Planck Jacobians (e.g., m/m_P, r/l_P).
2. Do the Physics as a Pure Ratio: Work entirely with the dimensionless equivalence chain (X = m/m_P = E/E_P = ft_P). This is the only step that involves the eternal, unit-free relationships. Gravity, for instance, is not a force mediated by G; it is simply the geometric gradient of m/m_P over r/l_P.
3. Decorate with Output Units: Multiply by the appropriate unit standards to express the result in human-readable coordinates.

In this framework, the illusion of independent properties vanishes. Mass and energy are not two different substances that must be bridged by c²; they are the exact same X projected onto different axes. Gravity is not a physical curvature caused by G/c²; it is a pure gradient that emerges naturally from the density of X, while G/c² is relegated to its true status as a Step 3 decoration—a mere unit conversion factor.

6. Conclusion

The ontological crisis of modern physics—the incompatibility of quantum mechanics and general relativity, the mystery of the cosmological constant, the search for the “true” value of fundamental constants—stems from a singular epistemological failure. We took a ratio between a thing and a ruler, and called it a property. We then took the mismatch between our rulers, and called it a physical law.

By recognizing that c, G, and h are merely the error bars between our arbitrary coordinate charts, we do not lose the mathematics of the standard model; we merely strip it of its false ontology. Beneath the bookkeeping lies the dimensionless substrate, unified, invariant, and requiring no mystical mechanisms to hold it together. The universe does not need conversion factors to know how to behave; it only needs geometry.