J. Rogers, SE Ohio
A Political and Epistemological Analysis of Dimensional Physics
Abstract
The choice of energy as the central mediating quantity in modern physics—enshrined formally in the 2019 SI redefinition—was not a discovery about nature. It was a political settlement. Physics had fractured into measurement silos (mechanics, thermodynamics, electromagnetism, quantum mechanics), each with its own base units and institutional identity. When the interdependence of these silos was established, the question of which silo should serve as the hub threatened to fracture the scientific community. Energy, appearing naturally in every silo without belonging exclusively to any, was chosen as a neutral clearing house. The fundamental constants c, h, and k_B are the formally agreed exchange rates between each silo’s currency and the energy hub. This paper argues that this settlement, while diplomatically brilliant, embedded a category error into the foundations of physics: it reified the dimensional axes as ontological, when in fact all measured quantities are projections of a single dimensionless ratio X onto arbitrary human perceptual axes. The constants are not properties of the universe—they are the Jacobians that cancel the arbitrary unit standards humans attached to their measurements.
1. The Silos and Their Origins
Physics did not begin as a unified discipline. It grew from the specific sensory and instrumental apparatus that humans used to interact with the world. We have eyes tuned to wavelength, skin tuned to temperature, muscles tuned to force. Each sense gave rise to a distinct measurement tradition, and each tradition built its own institutional structure.
Mechanics arose from the measurement of mass, length, and time—quantities accessible through the simplest physical interactions. Thermodynamics arose from the measurement of heat and temperature, initially treated as a substance (caloric) entirely separate from mechanical motion. Electromagnetism developed its own base quantities—charge and current—that appeared to describe phenomena with no mechanical analog. Quantum mechanics introduced frequency and action as fundamental, with Planck’s constant relating them. Each silo developed its own unit system, its own standards bodies, its own professional identity.
Crucially, each silo assumed—without ever making the assumption explicit—that its base quantities were fundamentally different kinds of things from the base quantities of the other silos. A kilogram was not a kelvin. A meter was not a second. The axes were treated as ontologically distinct, not merely as different windows onto the same underlying reality.
2. The Discovery of Interdependence
The siloed model collapsed under the weight of its own successes. A series of discoveries in the nineteenth and twentieth centuries established that the silos were not independent—that they were, in fact, measuring the same underlying reality through different instruments:
- The kinetic theory of gases established that temperature is mean kinetic energy. Heat is motion. The thermodynamic and mechanical silos were measuring the same thing.
- Einstein’s E = mc² established that mass and energy are interchangeable. The mechanical and energy domains were not separate.
- Planck’s E = hf established that frequency and energy are proportional. The quantum and electromagnetic silos were measuring the same thing in different units.
- The Boltzmann relation E = k_B T completed the chain, linking temperature directly to energy and hence to mass, frequency, and momentum.
The chain E/E_P = f t_P = m/m_P = T/T_P = l_P/λ = p/p_P = X makes this explicit: every quantity in every silo reduces to the same dimensionless ratio X. All silos are projections of X onto their respective perceptual axes. The axes are not real properties of the universe—they are properties of the measurement apparatus, which is itself a product of evolved human biology.
This created an immediate institutional crisis. If all silos are measuring the same thing, then their base quantities are interconvertible—and one of them could, in principle, serve as the hub from which all others are derived.
3. The Hub Problem and the Threat of Balkanization
The discovery of interdependence forced a choice that was simultaneously scientific and political: which silo’s base quantity should serve as the hub from which all others are derived? The answer would determine whose unit system was “fundamental” and whose was “derived”—a question with enormous consequences for institutional prestige, funding, and the direction of physics education.
Consider what would have happened if each silo had succeeded in making itself the hub. The result would have been five parallel but mutually incompatible descriptions of the universe, each with its own complete and self-consistent set of “fundamental” constants:
- The mass hub: All quantities expressed in kilograms. Temperature would be defined as kg via a constant converting K → kg. Frequency would be defined as kg via a constant converting Hz → kg. Length would be defined as kg via a constant converting m → kg. The mechanical silo’s constants would be “fundamental”; all others would be derived combinations of them.
- The frequency hub: All quantities expressed in Hz. Mass would be defined as 1/s via a constant converting kg → Hz. Temperature would be defined as 1/s. Length would be defined as 1/s. The quantum silo’s constants would be “fundamental.”
- The temperature hub: All quantities expressed in kelvin. Mass would be defined as K via a constant converting kg → K. Frequency would be defined as K. The thermodynamic silo’s constants would be “fundamental.”
- The length hub: All quantities expressed in meters. Mass, frequency, and temperature would all be defined as derived from spatial measurement.
Each hub would have generated its own complete set of “fundamental constants”—all of which would be nothing but the Jacobians of that hub’s particular projection of X onto its chosen axis. The constants of one hub would be algebraic combinations of the constants of another hub, related by exactly the same physics but expressed in mutually incomprehensible unit conventions.
Crucially, no hub’s constant set would be more or less fundamental than any other. They would all be equally arbitrary—all equally dependent on the human choice of base unit. A physicist from a civilization that had adopted the frequency hub would look at the constants c, h, k_B of our energy-hub system and see them as composite expressions of their own “fundamental” constants—just as we see theirs. The same physical law would look algebraically different in every hub’s language. Science would have fractured into five mutually incompatible dialects, each describing the same dimensionless reality X but hiding it under different unit conventions.
4. The Political Settlement: Energy as Neutral Hub
The scientific community avoided this balkanization through a political settlement of remarkable diplomatic elegance: the choice of energy as the universal mediating quantity. Energy was the ideal neutral hub for a precise reason—it appeared naturally in every silo’s own equations, without belonging exclusively to any of them.
- Mechanics already had kinetic energy (½mv²) and potential energy as internal concepts.
- Thermodynamics was built around heat energy and the first law.
- Electromagnetism described field energy density and photon energy.
- Quantum mechanics defined the photon energy E = hf and the zero-point energy.
Because every silo already spoke energy as a second language, adopting it as the common currency required no silo to admit subordination to another. The mechanical silo kept its kilogram, meter, and second. The thermal silo kept its kelvin. The quantum silo kept its hertz. Energy simply sat in the middle as the universal translator, and the fundamental constants became the fixed translation rates between each silo’s native currency and the joule.
The constants can now be read directly as treaty terms:
- c = 299,792,458 m/s: the exchange rate between the mechanical silo’s length‑time units and the energy hub (via mass‑energy equivalence, c² converts kg to joules).
- h = 6.626 × 10⁻³⁴ J·s: the exchange rate between the quantum silo’s frequency units and the energy hub (E = hf converts Hz to joules).
- k_B = 1.380 × 10⁻²³ J/K: the exchange rate between the thermodynamic silo’s temperature units and the energy hub (E = k_B T converts kelvin to joules).
The 2019 redefinition of the SI system is the formal ratification of this treaty. By fixing the exact numerical values of c, h, k_B, e, and N_A, the international standards bodies did not discover new physics. They permanently established the exchange rates between the silo currencies and the energy hub. The kilogram, meter, second, and kelvin are now defined through these exchange rates—they are derived from the hub’s constants, not independently established. The joule is the anchor; everything else is defined relative to it.
5. The Error: Mistaking the Treaty for Ontology
The political settlement achieved its diplomatic goal: physics remained unified, the silos retained their identities, and the constants provided a common language. But it left physics with a category error that has persisted for over a century: the constants were mistaken for fundamental properties of the universe rather than agreed‑upon exchange rates between human measurement conventions.
The numerical value of c is not a fact about light. It is a fact about how many meters humans assigned to a second of travel time, given the historical accident of defining the meter from the Earth’s circumference and the second from the Babylonian base‑60 division of the day. A civilization that had chosen different unit standards would have a different numerical value for c—while observing exactly the same physics. The constant c is the Jacobian that converts between the human second and the human meter; its value is fixed by those human choices, not by nature.
Similarly, h is not a fundamental quantum of action that the universe contains. It is the conversion factor between the human Hz (cycles per second) and the human joule (kilogram‑meter‑squared per second‑squared). Its numerical value is determined entirely by our choices of the kilogram, meter, and second—and by the political decision to route quantum‑mechanical quantities through the energy hub. If the quantum silo had won and made frequency the hub, the constant converting energy to frequency would have been 1/h rather than h—and physicists from that world would wonder at the mysterious fundamental significance of 1/h.
The fundamental constants are not mysterious numbers that the universe generated. They are the Jacobians of the energy hub—the scaling factors that cancel the arbitrary human unit standards from the dimensionless ratio X. Their apparent mysteriousness is a projection of the political compromise, not a feature of the territory.
6. Newton’s Natural Proportions and Planck’s Bridge
The framework developed here is not radical. It is a restatement of what Newton already knew. Newton’s laws are statements about proportions—F ∝ ma, not F = ma. The equals sign and the dimensional constant G came later, introduced by those who needed to express the proportion in human units for the purpose of numerical prediction and engineering. The proportion itself is dimensionless: it describes a pure geometric relationship between ratios. Newton called these “natural proportions” explicitly. He knew the difference between the proportion and the act of measuring it in human units.
It is worth noting that Newton occupied a unique biographical position for understanding this distinction. As Master of the Mint—the right hand of the Crown in establishing and defending the standards of measurement and coinage for an empire—he was professionally engaged with the arbitrary human construction of unit standards on a daily basis. He understood that the pound sterling, like the pound weight, was a human institutional agreement maintained by enforcement, not a natural constant. He spent thirty years prosecuting those who debased the coinage, because he understood that the standard’s value lay entirely in its agreed‑upon integrity, not in any intrinsic property of the metal.
Planck’s contribution in 1899 was to find the specific Jacobians that connect Newton’s dimensionless proportions to our particular human unit chart. The Planck length l_P, mass m_P, time t_P, and temperature T_P are not a “natural” unit system that the universe prefers—they are the conversion factors that cancel the human meter, kilogram, second, and kelvin from measurements of X. Planck thought he had discovered a better unit chart. He had actually found the definition of our own. The Planck units are erasers, not rulers: dividing a measured length by l_P does not convert to a more natural scale, it cancels the meter entirely and leaves the pure number X.
The 2019 SI redefinition closes this historical arc. By fixing c, h, k_B, e, and N_A, the standards bodies formally adopted the Planck Jacobians as the operational definition of the unit chart itself. The human unit standards (kilogram, meter, kelvin) are now defined through the Jacobians rather than through independent physical artifacts. This is the treaty ratification: the Jacobians are officially the exchange rates, and the unit standards are officially derived from them.
7. The Operational Definition of Physics
Once the political history is seen clearly, the operational structure of physics becomes transparent. It consists of exactly three steps:
- Remove input units: Cancel the arbitrary human unit standards from the measured quantities by dividing by the appropriate Planck Jacobians. This converts dimensional measurements (in meters, kilograms, kelvin, etc.) into the dimensionless ratio X. This step is pure accounting—it has no physical content.
- Do the physics as a pure ratio: Work with dimensionless ratios only. This is the only step that involves the eternal, unit‑free relationships—Newton’s natural proportions, expressed in X. This is the only step that is physics. It is the step the rock performs when it orbits, without any measurement, any calculation, any observer.
- Decorate with output units: Multiply by the appropriate Planck Jacobians (or any chosen unit standards) to express the result in human‑readable units. This step is also pure accounting.
Step 2 is the only physics. Steps 1 and 3 are the interface between the dimensionless reality and our arbitrary measurement conventions—they are the domain of the political settlement, the constants, the hub. The energy hub, the Planck Jacobians, the SI constants—all of these live in Steps 1 and 3. They have no presence in Step 2.
This framing resolves a persistent confusion in foundational physics. Problems that appear to be Step 2 problems—the fine‑tuning of constants, the mysterious values of c, h, k_B, the unification of the silos—are actually Step 1 and Step 3 problems. They are artifacts of the political settlement that chose energy as the hub and fixed the exchange rates. They have no presence in the dimensionless Step 2. The universe does not fine‑tune its constants; it has none. We fine‑tuned ours, and then forgot that we did.
8. Conclusion
The choice of energy as the hub of modern physics was a political triumph and an epistemological error. It preserved the unity of physics by providing a neutral clearing house that no silo could claim as its own—preventing the balkanization of science into five mutually incompatible hub‑systems, each with its own set of incommensurable “fundamental” constants. It was the least bad option available to a community that had already committed to treating the dimensional axes as real.
But energy is not more fundamental than mass, frequency, temperature, or wavelength. It is one projection of X among equals—the one that happened to be least contentious as a political hub. The constants c, h, k_B are not properties of the universe; they are the exchange rates of the energy hub, determined jointly by the political settlement and by our historical accidents of unit choice. They appear fundamental only because the political settlement succeeded so completely that physicists forgot it had occurred.
The deeper resolution is to dissolve the hub entirely. The chain E/E_P = f t_P = m/m_P = T/T_P = l_P/λ = p/p_P = X demonstrates that all dimensional quantities are projections of a single dimensionless ratio X onto human perceptual axes. X exists prior to measurement. It is the physical reality. The measurement—the assignment of a number of meters, kilograms, or kelvin—is the abstraction, not the other way around. A rock in orbit does not measure; it does not calculate; it does not perceive. Yet it orbits exactly, in perfect proportion, with no access to c, h, or k_B. It performs Step 2 only. It always has.
Physics will be complete when it works where the rock works—in Step 2, without a hub, without constants, without axes. The energy hub was a necessary political stage in the development of science. It is not the destination.
