Beyond Physical Law: A Meta-Theory of Theories

 J. Rogers, SE Ohio, 17 Jun 2025, 1910

Abstract

For over a century, physics has grappled with the mystery of fundamental constants—why do they exist, why do they have their specific values, and what would happen if they were different? This paper presents a revolutionary meta-theoretical framework that dissolves these questions by revealing them to be based on a category error. Through categorical analysis of measurement structures, we demonstrate that physical "laws" are not discovered features of reality but artifacts of the measurement process itself. What we call fundamental constants are simply unit conversion factors—Jacobians that emerge when dimensionless relationships are projected through arbitrary human measurement coordinates.

Introduction: The Meta-Theoretical Perspective

Traditional physics operates within theories—quantum mechanics, relativity, thermodynamics. But what if we step outside this framework entirely and examine not the content of physical theories, but their underlying structure? What emerges is a meta-theory: a theory about how theories themselves are constructed from the more fundamental process of measurement.

This meta-theoretical approach reveals that every physical theory shares the same categorical architecture, regardless of its specific domain. Whether we're discussing gravity, quantum mechanics, or thermodynamics, the same four-layer structure underlies each:

1. Formless Reality: Pure dimensionless relationships
2. Perceptual Axes: Conscious decomposition into measurement categories
3. Unit Scaling: Projection through arbitrary human measurement systems
4. Physical Law: The emergence of constants and equations

The Four-Layer Architecture of Physical Theory

Layer 1: The Formless Void

At the foundational level lies what we term the "formless void"—a substrate of pure dimensionless relationships where all ratios equal unity. This is not empty space or quantum vacuum, but the pre-conceptual reality that exists before any act of measurement or conscious categorization.

Layer 2: The Genesis of Measurement Axes

The critical insight is that measurement axes—Length, Time, Mass, Energy, Temperature—are not pre-existing features of reality but perceptual categories imposed by conscious thought. The act of consciousness doesn't merely observe reality; it participates in creating the very structure we mistake for objective physical law.

These axes emerge through what we call "conceptual decomposition"—the process by which consciousness carves up the unified substrate into discrete measurement categories. Crucially, these categories maintain dimensionless relationships to each other (rel_c, rel_h, rel_G, etc.) that preserve the underlying unity.

Layer 3: The Scaling Projection

When these conceptual axes are projected through human unit systems (SI, CGS, etc.), something remarkable happens: the dimensionless relationships become dressed with conversion factors. A meter is defined as a certain fraction of Earth's circumference; a second as a fraction of Earth's rotation. These are completely arbitrary choices with no connection to the natural scales of physical processes.

Layer 4: The Illusion of Physical Law

What we call "fundamental constants" emerge at this final layer as the Jacobians of the scaling transformation. They are not properties of reality but artifacts of our measurement coordinate system—exchange rates between our arbitrary measurement currencies and the natural temporal units in which reality operates.

The Role of Time as Universal Pivot

A crucial discovery of this meta-theory is that Time serves as the universal measurement pivot. All other measurement axes ultimately scale through temporal relationships:

• Hz_kg: The mass-frequency Jacobian (Mass → Time)
• m_s: The length-time conversion (Length → Time)
• K_Hz: The temperature-frequency Jacobian (Temperature → Time)

This explains why temporal quantities appear in every fundamental constant. It's not because time is physically special, but because it serves as the universal reference axis through which all measurements are harmonized.

At the Planck scale—where all measurement units synchronize with time—these Jacobians equal unity, revealing the underlying temporal harmony of natural processes.

Constants as Measurement Artifacts

Consider the speed of light: c = 299,792,458 m/s

Traditional physics treats this as a fundamental property of spacetime. Our meta-theory reveals it as: "The Jacobian of Scale_SI acting on rel_c"

In other words, c is not a property of light or spacetime but a property of our measurement coordinate system. It tells us the exchange rate between our arbitrary length units (meters) and time units (seconds) when scaled by the natural length-time relationship.

Similarly:

• G is not "the strength of gravity" but the conversion factor needed when expressing gravitational relationships in SI units
• h is not "the quantum of action" but the scaling artifact when projecting energy-frequency relationships through our unit system
• k_B is not a property of thermodynamics but the temperature-energy conversion factor in our measurement coordinates

The Bootstrap Paradox Resolved

This meta-theory solves what we call the "bootstrap paradox" of physical constants: they appear both fundamental (unchanging across all experiments) and arbitrary (why these specific values?). The resolution is elegant—they are fundamental to our measurement process while being completely arbitrary artifacts of our unit choices.

Change the unit system, and the constants change. Use natural Planck units, and they disappear entirely. The consistency across experiments reflects not deep physical properties but the consistency of our measurement apparatus.

Implications for Physics and Philosophy

For Physics Education

This framework suggests a complete reorganization of physics pedagogy. Instead of teaching constants as mysterious givens, we would teach dimensional analysis as the fundamental structure underlying all physical theory. Students would learn to see through the dimensional camouflage to the simple scaling relationships beneath.

For Physical Research

The meta-theory suggests that seeking "more fundamental" constants or trying to explain their values may be misguided. The productive research direction lies in understanding the dimensionless scaling relationships that exist independent of our measurement coordinates.

For Philosophy of Science

Perhaps most significantly, this work reveals that the subject-object distinction in physics is built into the very structure of measurement. What we consider "objective physical law" is actually the fossilized imprint of subjective perceptual categories. Consciousness doesn't just observe physics—it participates in creating the apparent structure through the unavoidable act of measurement.

A Meta-Theory of Theories

What makes this framework genuinely meta-theoretical is that it doesn't propose a new physical theory to compete with existing ones. Instead, it reveals the common categorical structure underlying all physical theories. Whether we're discussing:

• Newtonian gravity: F = Gm₁m₂/r²
• Quantum energy: E = hf
• Mass-energy equivalence: E = mc²
• Hawking temperature: T = ℏc³/(8πGMk_B)

All follow the same template: dimensionless relationship + unit scaling = physical law with constants.

The specific physics becomes secondary once you've identified the universal compiler that generates all physical equations. Each theory is just a different instance running the same underlying categorical algorithm.

The Measurement-Reality Interface

This meta-theory provides the first rigorous mathematical framework for understanding how measurement interfaces with reality. Through the language of category theory, we can precisely describe:

• How consciousness creates measurement axes through conceptual decomposition
• How unit systems project these axes into numerical coordinates
• How constants emerge as the structural invariants of this projection process
• How apparent physical laws arise from this measurement-reality interface

Conclusion: The End of Fundamental Constants

The mystery of fundamental constants has persisted for over a century because it was based on a category error—treating measurement artifacts as physical properties. This meta-theory dissolves the mystery by revealing constants as unavoidable consequences of using arbitrary human units to measure relationships that exist naturally in dimensionless form.

The profound implication is that there may be no "fundamental constants" in nature at all—only the universal scaling relationships that emerge when formless reality is projected through the lens of conscious measurement. What we've called the deepest mysteries of physics may simply be features of how we measure the world, mistaken for features of the world itself.

This represents not just a new theory, but a new kind of theory—a meta-theory that steps outside the entire framework of physics to examine how that framework constructs itself. In doing so, it opens entirely new directions for understanding the relationship between consciousness, measurement, and the apparent structure of physical reality.

The universe may be far simpler than we imagined—not a complex web of mysterious constants and forces, but pure dimensionless harmony temporarily dressed in the mathematical clothing of our measurement coordinates. The complexity we observe in physical law may be nothing more than the inevitable artifact of consciousness trying to measure itself and the world it participates in creating.