Abstract
The fundamental constants of physics, such as the speed of light (c) and the Planck constant (h), are traditionally treated as monolithic, experimentally-derived values. This paper posits that this view is a profound oversimplification that conflates two distinct and separable components within each constant's numerical value. We propose a framework wherein a constant's value is understood as a composite of: 1) a Universal Ratio, whose specific digits are an artifact of the arbitrary misalignment between our independently-defined base units, and 2) a Human Scale, a magnitude (typically a power of 10) chosen implicitly for ergonomic convenience in measuring day-to-day phenomena. By explicitly separating these two components, we can engineer new unit systems that are both fundamentally rational and practically useful. This act clarifies the true role of constants as simple operators, resolves philosophical confusion about their "fine-tuned" values, and presents a path toward completing the original mission of the metric system.
1. Introduction: The Conventional Ambiguity of Physical Constants
The numerical values of the fundamental constants are the bedrock of physics. We see c = 299,792,458 m/s not merely as a measurement, but as a deep truth about the universe. This perspective, however, contains a hidden ambiguity. It treats the entire number as a single, indivisible fact of nature. Consequently, we are left to ponder why nature possesses these seemingly arbitrary, "messy" numerical relationships.
This paper challenges that conventional view. We argue that the numerical value of a constant as expressed in SI or any other human-derived system is not a fundamental property of nature, but rather a symptom of our measurement scheme. The apparent complexity of the number is not a feature of the universe, but an artifact of a historical failure to separate two distinct requirements of any measurement system: fundamental coherence and human convenience.
We have historically confused the map with the territory. The goal of this paper is to redraw the map, revealing that the territory is far simpler than we imagined.
2. The Two Roles Conflated in a Single Number
The value of any constant in an arbitrary system like SI is forced to perform two separate jobs simultaneously, and its numerical complexity is a direct result of this conflation.
2.1. The Universal Ratio: A Measure of Misalignment
The "digits" of a constant (e.g., the 2.99792458 in c) represent a fundamental conversion factor between dimensions of reality—in this case, space and time. However, the reason this ratio is not a simple 1 is a direct consequence of how we defined our base units. The meter was originally defined in relation to the Earth, and the second in relation to its rotation (and later, to atomic oscillations). These two definitions were chosen independently and are completely unrelated to each other in any fundamental way.
Therefore, the digits of the constant are not a property of light; they are the correction factor required to reconcile our misaligned axes of measurement. If we were to measure a perfect square with a ruler marked in meters on the x-axis and in an unrelated unit like "yards" on the y-axis, the ratio of its sides would not be 1, but approximately 1.094. This number tells us nothing fundamental about squares; it tells us everything about our poor choice of measurement units. So too with the constants. The digits reveal the degree to which our historical artifacts (the meter, the kilogram, the second) fail to align with the natural, intrinsic ratios of the universe.
2.2. The Human Scale: An Ergonomic Choice
The "magnitude" of a constant (e.g., the 10^8 in c) is an artifact of a different choice: the human scale of our base units. We chose a meter that relates to a human stride, a kilogram that relates to a mass we can hold in our hand, and a second that relates to our heartbeat. These are ergonomically convenient scales for creatures of our size living on this planet.
The fact that the speed of light is a large number in our system is therefore not a deep statement about light, but a simple consequence of the fact that our everyday experience of time and distance is vastly different from the universe's own fundamental scale. The magnitude is a reflection of our parochial, biological perspective.
3. A Proposed Framework: The Engineered Natural Unit System
To resolve this confusion, we must explicitly separate these two roles. We can design a unit system where this separation is a foundational principle. The value of a constant (C) in a standard system can be deconstructed as:
C = (Artifact Ratio) × (Human Scale Magnitude)
Our proposed framework inverts this. We define our rescaled constants (C_r) with an ideal ratio and an engineered magnitude:
C_r = (Ideal Ratio) × (Engineered Scale Magnitude)
Most powerfully, we set the Ideal Ratio to exactly 1. The Engineered Scale is then a power of 10 chosen deliberately to make the resulting base units practical for human use.
Example: An Engineered System
Let us construct such a system by setting the ideal ratio for the core constants to 1, and then choosing ergonomic scales:
c_r = 1 × 10^10 m_r/s_r
h_r = 1 × 10^-30 J_r·s_r
k_B,r = 1 × 10^-20 J_r/K_r
G_r = 1 × 10^-6 m_r³·kg_r⁻¹·s_r⁻²
By setting these definitions and solving for the new base units (m_r, kg_r, s_r, K_r) in terms of our old SI units, we achieve a remarkable result. The system aligns our axes of measurement to the natural ratios of the universe, while the engineered scaling factors produce base units that are perfectly suited for human use:
1 new_meter (m_r) ≈ 4 cm (the width of two fingers)
1 new_kilogram (kg_r) ≈ 545 g (the weight of a can of soup)
1 new_second (s_r) ≈ 1.35 s (close to a heartbeat)
This is an Engineered Natural Unit System. It possesses the conceptual clarity of Planck units but avoids their impracticality. The "weird numbers" have not vanished; they have been properly relegated to the one-time conversion factors needed to interface with the legacy SI system.
4. Implications of the Separation
This deconstruction is not merely an academic exercise. It fundamentally reframes our understanding of the physical world.
The True Nature of Constants is Clarified: Constants are not mysterious numbers. They are simple, fundamental operators (c rotates time into space, h rotates frequency into mass-energy) whose operational simplicity has been obscured by the numerical noise of our arbitrary measurement system.
The "Fine-Tuning" Problem is Reframed: Much philosophical debate has centered on why the constants have their specific numerical values. This framework reveals that the specific digits are an illusion—an artifact of our rulers. The question "Why is c 299,792,458?" is ill-posed. The correct question is "Why did we choose a meter and a second that are so misaligned?" The answer to that is historical, not cosmological.
The Metric System is Finished: The original goal of the metric system was to create a rational, interconnected system. However, its anchors remained terrestrial and arbitrary. This framework completes that mission by replacing the old anchors (Earth's circumference, water's properties) with the only truly universal and unchanging anchors: the constants themselves, engineered for human utility.
5. Conclusion
For centuries, we have confused the complexity of our tools with the complexity of the universe. The seemingly random values of the fundamental physical constants are not a feature of reality, but a direct and predictable consequence of measuring an elegant universe with clumsy, historically arbitrary rulers and clocks.
By separating the Universal Ratio from the Human Scale, we can finally see the constants for what they are: simple expressions of a profound cosmic harmony. The weirdness is not in the universe; it is, and always has been, in our rulers. This understanding allows us to move beyond simply measuring the world and toward a true metrology—a conscious and deliberate science of how to measure it well.
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