God is in the Gap: From the Physics of Objects to the Physics of Relationships

J. Rogers, SE Ohio

Abstract

The current stagnation in theoretical physics is a symptom of an ontological error: the reification of measurement artifacts. The Standard Framework operates under a philosophy of "Naive Realism," treating arbitrary human units (mass, length, time) as fundamental constituents of reality and the constants connecting them as mysterious universal laws. This paper proposes a "Relational Framework," arguing that valid physics is found not in these values, but in dimensionless invariant proportions. By exposing constants (including  G, c, and h) as mere off-diagonal "Jacobians"—conversion factors for our coordinate charts—we reveal that physical laws are not external dictates, but geometric tautologies of a unified field.

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1. The Standard Framework: The Cult of the Noun

The prevailing paradigm of modern physics, despite its mathematical sophistication, rests on a philosophical foundation of Naive Realism. It views the universe as a container filled with distinct "things"—particles, forces, and fields—that possess intrinsic, observer-independent properties.

In this framework, the act of measurement is misinterpreted as the discovery of fundamental truths. When we measure the speed of light or the gravitational constant, the Standard Framework assumes we are uncovering the "source code" of the cosmos.

• The Error: It mistakes the map for the territory. It assumes that because we have a ruler for "mass" and a ruler for "time," Mass and Time must be distinct elemental substances.

• The "God" of the Standard Model: Here, the "God of the Gaps" is the Constant. Why is 

  $G$

   

  $6.67\times {10}^{-11}$

  ? Why is the ratio of energy to frequency a specific number? The Standard Framework offers no explanation other than "that’s just how the universe is." It treats these scaling factors as magic numbers that must be measured and accepted as brute facts.

This approach turns physics into Accounting. The goal is to catalog every particle and force, measuring them against arbitrary human standards (the SI units), and inventing "glue" (constants) to make the ledger balance.

2. The Relational Framework: The Truth of the Verb

The Relational Framework rejects the reification of units. It asserts that the universe is not made of "things" (nouns), but of "processes" (verbs). Mass, Length, Time, and Energy are not separate elements; they are different projections of a single geometric process.

In this view, the constants are demoted. They are no longer fundamental laws; they are Jacobians.

• $c$

   is simply the translation error between our perception of space and our perception of time.

• $G$

   is the translation error between our perception of mass and our perception of curvature.

• The Quantum Scale (

  $h$

  ): This is not a mystical entity; it is merely the notation required to scale Energy to Frequency in our specific unit chart.

The Relational Framework posits that if you strip away the human unit chart, the constants disappear (becoming 1), and you are left with the Invariant Proportions.

3. Comparison: The Prison of the Obvious vs. The Freedom of Geometry

The distinction between these two frameworks is the difference between a user interacting with a desktop interface and a programmer understanding the code.

Feature	Standard Framework (Naive Realism)	Relational Framework (Invariant Physics)
Ontology	The universe is made of Objects (Particles, Mass, Fields).	The universe is made of Relationships (Ratios, Proportions, Geometry).
Role of Units	Fundamental dimensions of reality.	Arbitrary coordinate charts (masks).
The Constants (	"God": Mysterious, fundamental numbers that dictate reality.	"Notation": Jacobians/Scaling factors that correct for human unit choices.
Physical Law	Equations ( $F=ma$ ) describe how separate things interact.	Equations describe identities; properties are the same thing scaled differently.
The "Gap"	The unknown space between particles where forces act.	The Invariant Ratio itself—the dimensionless geometry where the physics actually lives.

4. The Periodic Table of Tautologies

In the Standard Framework, equations like 

$E=m{c}^2$

 or 

$E\propto f$

 are treated as discoveries of how two different things relate.

In the Relational Framework, these are recognized as tautologies.

• Because Mass and Energy are the same geometric process, 

  $c^2$

   is just the unit conversion required to say "Mass is Energy."

• Because Energy and Frequency are the same geometric process, the quantum constant is just the unit conversion required to say "Energy is Frequency."

We can construct a "Periodic Table of Physical Laws" based not on materials, but on these unit-dependent identities. By normalizing all variables to the Planck scale (the limit of the chart), we see that:

Every "law" of physics is simply a cross-multiplication of these ratios. The physics is not in the variable, nor in the constant, but in the equivalence of the ratios. 21 physical law of the 20th century can be discovered by simply taking those equivalence chain a pair of elements at a time and substituting the non reduced Planck definition of the constants for the non reduced Planck units and simplifying to convert back from just unit scaling to "Physical Law".

5. Conclusion

The standard view has led to a crisis of complexity, where we invent new particles to explain the discrepancies in our measurements. We are measuring the distortion of our own lens and calling it "Dark Matter" or "Dark Energy."

The Relational Framework argues that "God" (the fundamental truth) is not found in the things we measure, but in the gap—the dimensionless relationship that persists regardless of the unit chart. By understanding constants as mere notation for our own scaling, we stop looking for magic numbers and start seeing the unified geometry of the universe. Valid explanations are not built on constants; they are built on the invariant proportions that render the constants unnecessary.