The Constants as Artifacts: A Parable of Incoherent Coordinates in Physics

J. Rogers, SE Ohio

Abstract

The fundamental constants of nature (c, h, G, k_B) are traditionally regarded as profound, empirically discovered properties of the universe. This paper argues that this view is a category error. We present a simple parable—the "Cube Measurement Problem"—to demonstrate that such constants are not features of reality, but are necessary mathematical artifacts, or "gaskets," that arise when we attempt to describe an invariant, coherent reality using arbitrary, incoherent systems of measurement. By mapping this parable directly onto the structure of modern physics, we show that the great constants are not deep mysteries to be explained, but are correction factors that reveal the mismatch between our chosen human units (SI) and the universe's native, coherent coordinate system (the Planck chart). This reframes the entire scientific endeavor from explaining the constants to recognizing them as pointers to a more fundamental, constant-free description of reality.

1. Introduction: The Unexamined Problem of Measurement

Physics seeks to create a unified description of an invariant reality. Yet, the foundational tools of this description—our units of measurement (the meter, the kilogram, the second)—are anything but unified or invariant. They are the products of independent and arbitrary historical conventions. This raises a fundamental, yet largely unexamined, question: How can a coherent reality be described by an incoherent system of measurement?

The standard answer is the introduction of fundamental physical constants. These constants make our equations work, ensuring dimensional consistency and predictive accuracy. We have since reified these constants, treating them as sacred, fundamental features of the universe whose precise values are a deep mystery. This paper posits that this reification is a profound error, born from a failure to distinguish the map from the territory.

2. A Parable: The Cube Measurement Problem

To illustrate this error, let us imagine a pre-scientific society attempting to develop a theory of volume. Their system of measurement is based on local, historical accidents:

• Width is measured in wibs, defined by the length of the king's thumb.  To  measure width in any other way is to insult the king.

• Height is measured in hogs, defined by the height of a specific cathedral door. Measuring height in any other way disrespects the church. 

• Depth is measured in duns, defined by the depth of a town's primary well. Measuring depth in any other way is disrespectful to the history of the town founder that dug that well by hand. 

These three units are arbitrary, independent, and entirely unrelated to one another. It is unthinkable to consider unifying lengths.  The very idea that you could convert the kings thumb into a church door is ridiculed.   Now, a natural philosopher in this society wishes to calculate the volume of a cube in a standardized, universal unit, such as the cubic meter. The simple geometric formula V = W × H × D is useless, as it yields the nonsensical unit of "wib-hog-duns."

To make the system work, they must introduce a "Volumetric Conversion Constant," K. The operational formula for volume becomes:

Volume in barrels  = Width (wibs) × Height (hogs) × Depth (duns) × K

The constant K would be determined experimentally to have a specific value, for instance, K = 0.0247 barrels / (wib·hog·dun).

Now, imagine the physicists of this society becoming obsessed with this constant. They might ask:

• "Why does K have this precise numerical value? Is it a fundamental property of three-dimensional space?"

• "Could a universe exist with a different value of K?"

• "Can we derive K from a more fundamental theory of 'wib-hog-dun geometry'?"

This line of inquiry is, to us, self-evidently absurd. We can see clearly that K is not a property of geometry. It is a mundane conversion factor whose entire existence is necessitated by their poor, incoherent choice of units. K is a gasket, a necessary adapter to connect their mismatched parts.

3. The Inescapable Analogy: Mapping the Parable to Physics

The "deeper insanity" of the wib-hog-dun theorists is the exact conceptual state of modern physics. We have simply replaced one set of arbitrary units with another.

The mapping is one-to-one and devastatingly clear:

Parable Analogy	Modern Physics Equivalent
Arbitrary Units (Wibs, Hogs, Duns)	SI Units (Meters, Kilograms, Seconds, Kelvin)
Volumetric Constant K	Fundamental Constants (G, c, h, k_B)
"Wib-Hog-Dun Theory"	The Standard Model's quest to explain constants' values.
Invariant Geometry of a Cube	The Invariant Laws and Ratios of the Universe

When physics asks, "Why does c equal 299,792,458 m/s?", it is asking the exact same kind of question as "Why does K equal 0.0247?". The question is not profound; it is a category error.

4. The Solution: The Planck Cube and Coherent Coordinates

The solution to the Cube Measurement Problem is not to develop a deeper theory of K, but to abandon the incoherent coordinate system. If the society discovered the universe had a natural, self-consistent unit of length (let us call it the "Planck Length"), they could measure width, height, and depth in this single unit.

In this natural, coherent system, the formula for volume would revert to its pure, geometric form:

Volume (natural units) = Width (natural) × Height (natural) × Depth (natural)

The constant K does not need to be explained; it vanishes. It is revealed as an artifact of the old, broken system.

This is precisely the role of the Planck chart in physics. The system of Planck units, where c=1, h=1, and G=1, is not a mathematical shortcut. It is a shift to the universe's native, coherent coordinate system. In this system, the "great" constants disappear, revealing the simple, underlying geometry of the laws of nature.

5. The Constants as Diagnostic Error Messages

The constants are not telling us deep truths about the universe. They are telling us about the flaws in our measurement system. They are diagnostic messages:

• c is an error message stating: "Your unit of length and your unit of time are mis-scaled relative to each other. Here is the correction factor."

• h is an error message stating: "Your unit of energy and your unit of frequency are mis-scaled relative to each other. Here is the correction factor."

• G is an error message stating: "Your units of mass/energy and spacetime geometry are mis-scaled relative to each other. Here is the correction factor."

For over a century, we have been treating these crucial error messages as if they were the profound output of the program. We have built entire fields of study to interpret the meaning of the error message, rather than doing what any engineer would do: read the message and fix the faulty configuration.

6. Conclusion: A New Architecture for Physical Law

The Cube Measurement Problem forces a radical re-evaluation of what a physical constant is. The constants are not part of the physics; they are the gaskets that seal our arbitrary measurements to the invariant natural ratios of the universe. The complexity and mystery we attribute to them are not features of reality, but are the shadows cast by our own incoherent tools of perception.

This framework suggests a new path forward. The goal of fundamental physics should not be to explain the numerical values of the constants. It should be to identify the pure, dimensionless ratios of the Planck chart—the true, constant-free physics—and to teach a new generation of scientists to see the universe not through the distorted lens of our historical units, but in the clear, coherent light of its own native language.