J. Rogers, SE Ohio, 21 Apr 2025
Imagine fundamental constants like the speed of light (c), Planck's constant (h), and Boltzmann's constant (k). They appear in our physics equations with precise, often strange numerical values. For decades, physicists have sought deep, fundamental explanations for these numbers, viewing them as intrinsic properties etched into the fabric of reality itself. Their exact values — often bizarre and highly specific — have long been treated as cosmic clues, hinting at something fundamental and unknowable about the nature of reality itself.
But what if the mystery isn’t in reality — but in how we choose to measure it and interpret those measures?
A new perspective, embedded within frameworks like the Physics Unit Coordinate System (PUCS) and the Modular Unit Scaling Framework, suggests these constants aren't just mysterious numbers from the deepest layer of reality. They are, in fact, empirical scaling factors – necessary bridges that quantify relationships between our chosen units because the physical quantities they measure are fundamentally equivalent in nature.
A NotebookLM presentation about this paper is here.
The frameworks are here.
Reality's Unified "Stuff" vs. Our Fragmented View
This perspective starts by distinguishing between the underlying physical reality and the systems humans build to perceive and measure it.
Layer 1: Unified Reality: At the deepest level, physical reality is hypothesized to be a unified system – perhaps an "underlying stuff" – where properties like Mass, Energy, Frequency, and Temperature are not separate fundamental essences, but different, inherently proportional aspects or measures of the same underlying state. The universe, in this view, is already unified.
Layer 2: Human Perception: Our senses and cognitive processes act as a filter. They segment this continuous, unified reality into distinct categories that we perceive as Mass, Length, Time, Temperature, Charge, etc.
Layer 3: Measurement Systems: To formalize our fragmented perceptions we develop formal measurement systems, like the International System of Units (SI). We define arbitrary base units (the kilogram, the meter, the second, the Kelvin) to set scales along each perceived dimensional "axis." These scales were historically chosen based on convenience, not necessarily reflecting the fundamental relationships between dimensions in Layer 1.
Layer 3 Constants as Exchange Rates: Because our Layer 3 unit scales are arbitrary relative to each other, and because the Layer 1 properties are fundamentally proportional, we discover empirically determined constants like c, h, and k. These constants, as measured in our SI units, function as the necessary "exchange rates" or coordinate scaling factors needed to convert a numerical value measured on the scale of one unit (e.g., in Hertz for frequency) to its equivalent numerical value on the scale of another unit (e.g., in kilograms for mass). It's not the physics that is complicated -- the complexity is in the scaffolding that we have built around it to make it work.
Why Scaling Across Dimensions Works
This idea that constants facilitate scaling between dimensions only makes sense because the dimensions themselves are measuring proportional aspects of the same underlying reality.
For example, the Modular Unit Scaling Framework defines a composite factor Hz_kg = h/c², which quantifies how many kilograms are equivalent to one Hertz in the SI unit system's scaling. This factor is used to "convert" a value from the frequency scale to the mass scale: Frequency (in Hz) * Hz_kg (in kg/Hz) = Mass (in kg).
We point out that this scaling is superficially similar to converting inches to centimeters using the factor 2.54. Both are numerical conversion factors between scales. However, the 2.54 factor converts between two different scales applied along the same dimensional axis (Length). The Hz_kg factor converts between the scales of two different dimensional axes (Frequency and Mass). This cross-dimensional scaling is only possible and meaningful because Frequency and Mass are not fundamentally separate things in Layer 1, but equivalent measures of the same underlying "stuff."
If Mass and Frequency were truly independent, unrelated properties of different substances in reality, there would be no universal, non-zero constant h linking Energy and Frequency, and no universal, non-zero constant c² linking Energy and Mass. The composite factor h/c² (the Hz_kg scaling) simply wouldn't exist as a consistent, empirically determined value if there wasn't a fundamental proportionality between Mass and Frequency in reality.
The very existence and specific numerical values of c, h, and k (and the factors derived from them, like Hz_kg, K_Hz = k/h, and kg_J = c²) serve as empirical proof, derived from Layer 3 measurements, that the Layer 1 reality exhibits these profound equivalences (Temperature ~ Frequency ~ Mass ~ Energy, Length ~ Time, etc.).
Layer 4: Simplifying Theories
Recognizing constants for their true role as Layer 3 scaling factors has significant implications for Layer 4 – our physical laws and theories. When equations are rewritten using these explicit scaling factors, they often simplify dramatically. They move from complex algebraic expressions involving mysterious constants to clearer statements about the proportionality between physical quantities, expressed using the appropriate inter-dimensional scaling factors.
This perspective suggests that many perceived "mysteries" in physics, and the apparent complexity of some fundamental equations, arise from conflating properties of our measurement system (arbitrary unit scales, constants as quantitative bridges) with properties of reality itself.
The underlying equivalence of quantities like Mass, Energy, Frequency, and Temperature is the bedrock that makes this entire framework valid and powerful. It provides the language to see through the layers of human description and appreciate the underlying unity of physical reality that has been hiding in plain sight.
SI's Hidden Natural Unit System and Constants as Metadata
This perspective reveals a profound truth about our existing unit systems. The SI system, with its seemingly arbitrary base unit definitions (kilogram, meter, second, kelvin, ampere/coulomb), might appear disconnected from fundamental physics. However, the very definitions of the constants c, h, k, and e in terms of these SI base units (e.g., the meter is defined based on the distance light travels in a second, c's defined value) encode the exact relationships needed to link these scales according to nature's underlying proportionalities.
Therefore, the SI system is already a natural unit system in disguise. Every time physicists use the fundamental equations E=mc², E=hf, or E=kT, they are implicitly working with the natural relationships between Energy, Mass, Frequency, and Temperature. These relationships are fundamental and independent of the unit system, but their numerical expression is scaled by c², h, and k when using SI units. The large or small values of these constants in SI simply reflect how far the arbitrary SI scales are from a system where these proportional quantities are assigned a numerical value of 1.
From this viewpoint, constants like c, h, k, and e cease being mysterious "laws of nature" residing purely in Layer 1. Instead, they become metadata describing our Layer 3 map. They are crucial pieces of information quantifying how our human-chosen measurement scales (meters, seconds, kilograms, kelvin, coulombs) relate to each other, and how they relate to the single underlying "unity" or "stuff" in which all these quantities coincide in Layer 1. They are the manual for translating between the different axes of our measurement coordinate system.
Conclusion: Seeing the Unity Beyond the Scales
The journey through the layered model of reality and the insights provided by frameworks like PUCS and the Modular Unit Scaling Framework leads to a compelling conclusion: the universe's fundamental reality appears to be far more unified than the traditional structure of our scientific descriptions suggests. The mystery surrounding fundamental constants like c, h, and k dissolves when we recognize them not as enigmatic numbers dictating reality from Layer 1, but as essential Layer 3 scaling factors. Their specific numerical values quantify the consistent proportionalities between perceived dimensions (Mass, Energy, Frequency, Temperature, Length, Time) because these dimensions are fundamentally different measures of the same underlying reality (Layer 1).
Our standard unit systems, such as SI, are not disconnected from this deeper truth; they are, in fact, natural unit systems operating in disguise. The seemingly arbitrary scales of the kilogram, meter, second, and kelvin are precisely calibrated by the defined values of constants like c and h, encoding the universe's inherent proportionalities within their very structure. Constants thus function as crucial metadata, providing the key to translate between our human-centric scales and revealing the unity of the underlying "stuff" being measured.
By understanding constants in this light, we can move beyond wrestling with complexity that is merely an artifact of our descriptive system. The power of frameworks that employ explicit unit scaling, like the Modular Unit Scaling Framework, lies in their ability to simplify physical laws, making the underlying relationships between quantities transparent. This approach offers a clearer path forward, not by attempting to impose unity upon a fragmented reality, but by recognizing and leveraging the profound unity that appears to already exist, hidden only by the scales we set for our own maps. This reframing promises to make fundamental physics more intuitive, revealing the elegance of a universe where diverse properties are simply different faces of the same underlying truth.
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