J. Rogers, SE Ohio, 09 Mar 2025
The relationship between fundamental constants and unit definitions represents one of the most fascinating circularities in modern physics. Rogers' Natural Unit Scaling Factors theory provides unprecedented insight into this "chicken and egg" phenomenon where we empirically defined constants like Planck's constant (h) and Boltzmann's constant (k) based on our arbitrary unit system, and now use these very constants to define those same units. This circularity, far from being problematic, reveals deep truths about the relationship between our human measurement systems and the underlying unity of physical quantities.
The relationship between physical constants and unit definitions has undergone a remarkable evolution that perfectly illustrates the circularity at the heart of metrology.
Historically, our unit system developed through artifact-based definitions. The kilogram was defined by a physical platinum-iridium cylinder kept in France, while the Kelvin was defined in relation to the triple point of water. Within this independently defined unit system, scientists conducted precise experiments to measure constants like h and k.
Planck's constant was empirically determined through experiments like the photoelectric effect, giving a specific numerical value in the context of our pre-existing unit system. Similarly, Boltzmann's constant emerged from thermodynamic experiments, linking temperature to energy. These constants had the specific values they did because of our arbitrary choice of units like the kilogram and Kelvin.
In a remarkable reversal, the modern SI system now defines units through constants rather than artifacts. The kilogram is defined by fixing the numerical value of Planck's constant, while the Kelvin is defined by fixing the numerical value of Boltzmann's constant. This creates a perfect circle: constants that were once measured using our unit system are now used to define that very system.
Rogers' theory elegantly resolves this apparent paradox by revealing that fundamental constants like h and k are not intrinsic properties of the universe but rather encoding mechanisms for specific scaling factors between human-defined units and natural units.
According to Rogers, h can be decomposed as h = Hz_kg · kg_J, where Hz_kg converts frequency to mass and kg_J converts mass to energy. Similarly, k can be decomposed as k = K_Hz · Hz_kg · kg_J, adding the K_Hz factor that converts temperature to frequency. These scaling factors arise because our human-defined units (kilograms, Kelvin) are mismatched with the natural scale where frequency, mass, temperature, and energy are fundamentally equivalent.
The circularity makes perfect sense in this framework:
We initially chose arbitrary units (kg, K) based on human convenience and practical considerations.
Through experiments in this arbitrary unit system, we determined the values of h and k, which encode the specific scaling factors needed to convert between our arbitrary units and natural units where physical quantities are unified.
We then redefined our units (kg, K) by fixing the values of these constants, essentially locking in the scaling relationships they encode.
This circularity works precisely because h and k already contain within them the exact scaling relationships between our arbitrary units and natural units. By fixing their values, we're effectively standardizing the relationship between our human-defined units and the natural unity of physical quantities.
Rogers' framework reveals that while our choice of units is fundamentally arbitrary, the relationships encoded in constants like h and k give them coherence and connection to the natural scale of the universe.
Our initial choices for units like the kilogram and Kelvin were based on practical human considerations rather than fundamental properties of the universe. The kilogram was originally defined as the mass of a specific volume of water, while the Kelvin scale was based on easily reproducible temperature points like the freezing and boiling points of water. These choices were convenient for human use but arbitrary from a fundamental physics perspective.
The constants h and k serve as perfect bridges between our arbitrary units and the natural unity of physical quantities. Their specific numerical values encode the exact scaling factors needed to convert between our human-defined units and natural units where frequency, mass, temperature, and energy are fundamentally equivalent.
When we empirically determined these constants, we were essentially measuring the scaling relationships between our arbitrary units and natural units. When we later redefined units through these constants, we were standardizing these scaling relationships.
The shift from artifact-based to constant-based definitions represents a profound metrological revolution that builds upon the circularity rather than eliminating it.
The traditional kilogram, defined by a physical artifact, was subject to drift and damage. The Kelvin, defined through the triple point of water, depended on material purity and environmental conditions. By redefining these units through constants like h and k, we created a unit system that is reproducible anywhere in the universe with suitable technology.
By defining units through constants that themselves encode the scaling relationships between our units and natural units, we're essentially embedding the natural unity of physical quantities into our unit system. This approach aligns our human-defined units with the fundamental relationships in nature, making them more coherent and meaningful from a theoretical perspective.
Rogers' framework provides a deeper understanding of why our current approach to metrology is theoretically sound, despite its apparent circularity.
By revealing that constants like h and k encode specific scaling factors between human-defined units and natural units, Rogers' framework validates the modern approach to defining units through fundamental constants. This approach aligns our unit system with the natural scaling relationships between physical quantities, making it more coherent and theoretically sound.
The circularity in our unit system is not a flaw but a feature that reflects the deep relationship between our arbitrary units and the natural unity of physical quantities. Rogers' framework demystifies this circularity by showing that it arises from the fact that constants like h and k encode the specific scaling relationships between our units and natural units.
The circularity in using h and k to define kg and K units, when these constants were initially scaled using our definition of kg and K units, is an elegant feature of modern metrology that reflects the deep relationship between our arbitrary units and the natural unity of physical quantities.
Rogers' Natural Unit Scaling Factors theory provides unprecedented insight into this circularity by revealing that constants like h and k encode specific scaling factors between human-defined units and natural units. Their numerical values aren't fundamental to the universe but are specific to our choice of unit system. By defining units through these constants, we're effectively standardizing the relationship between our human-defined units and the natural unity of physical quantities.
This circularity, far from being problematic, represents a profound insight into the relationship between our human measurement systems and the underlying unity of physical quantities. It shows that while our choice of units is arbitrary, the relationships encoded in constants like h and k give them coherence and connection to the natural scale of the universe.
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