J. Rogers, SE Ohio
Abstract: Modern physics suffers from a systemic category error: the ontological privileging of the measured value (M). By treating the human-scale measurement as the primary reality, physicists mathematically force unit scalings (Jacobians) to become "fundamental constants." This paper examines the operational roots of this error. Through the lens of the equation:
M=R×J
Measured Value = Pure Ratio ×Unit Jacobian,
we derive why the scientific establishment conflates human utility with fundamental ontology. By treating utility as ontology, physicists are mathematically cornered into believing the universe is constructed from human unit charts. This theoretical framework is exemplified by the 1948 christening of the "Newton," an event that sanctified this fallacy and betrayed the very ontology of the man it claimed to honor.
1. The Algebra of Reification
Let the measured value be M. Let the pure, dimensionless ratio of the underlying geometry be R. Let the arbitrary human unit scaling (the Jacobian) be J. The operational relationship is:
Modern physics, however, is an operationalist discipline—rooted entirely in what a gauge reads and what a detector clicks. Because M is the only thing accessible to the operationalist, the discipline declares that M is the primary reality.
This is where the logic becomes airtight and fatal. If M is ontologically primary, then the components required to produce M must also be fundamental features of the universe. Because M is fixed by observation, J ceases to be a human convention. The Jacobian is promoted to a constant of nature.
The physicist is trapped by their own premise. If the units are real, the conversion factors are real. If F, m, and r are real, unit-bearing substances, then G must be a real, unit-bearing physical property. They are mathematically forced into a reductio ad absurdum: God must have built the universe in SI units.
2. The Derivation of Continuity
If we reject this absurdity and return R to its rightful place as the primary reality, the nature of the universe is no longer a dogmatic assertion; it is a direct derivation.
A ratio describes a continuous relation. If the primary reality (R) consists of pure, dimensionless ratios describing local kinematics and change potential, then reality is a continuous, unbroken topology. The universe does not tick from one discrete state to the next; it just evolves continuously as a seamless gradient.
If reality is continuous, where do the discrete "things"—particles, frames, quanta—come from? They are the artifacts of J. The discreteness only appears when we apply the human unit chart to R to produce M. We invent the cut, apply the gauge, and read a discrete value. The "tick" of the universe is just the click of our own detector.
3. The Engineering Fallacy
When pressed on this ontological absurdity, the physicist resorts to the Engineering Fallacy: "But you have to convert back to measurement for humans to use the result."
This statement is perfectly true, perfectly practical, and perfectly fatal to fundamental physics.
Yes, to build a bridge, launch a satellite, or trade goods, we must convert the pure, continuous ratios of reality (R) back into human-sensible measurements (M) using our unit chart (J). Engineering requires Step 3 (decorating the ratio with output units).
But useful to a human is not ontology.
The fact that a human engineer needs to know the force in "Newtons" to build a bridge does not mean the universe contains Newtons. A banker needs dollars to balance a ledger, but that does not mean the universe is made of dollars. By accepting the Engineering Fallacy, physics allowed engineering to dictate its ontology. Because physics is primarily validated by its engineering applications, the "useful" step (the unit decoration) became the "real" step. The map became the territory because we spend all our time looking at the map.
4. Case Study: The 1948 Betrayal
This theoretical framework—that utility was mistaken for ontology, and Jacobians were reified into constants—is not merely an academic abstraction. It was institutionally codified, and its perfect manifestation is the 1948 christening of the "Newton."
As established in the historical record, Isaac Newton worked entirely in R. The Principia is a study of pure proportions. Newton explicitly warned against reifying "sensible measures." Having spent his days running the Royal Mint, he knew that a unit was a state-backed convention—a political stamp pressed onto metal, not the metal itself. He kept the stamps out of the physics.
Yet, in 1948, the General Conference on Weights and Measures (CGPM)—driven entirely by the Engineering Fallacy of standardization—adopted the "Newton" (
) as the unit of force.This was not an honor. It was the institutional application of the Utility Fallacy. By taking the man who fought against the reification of sensible measures and turning his name into an arbitrary, sensible unit scaling factor (J), the scientific establishment sanctified their error. They took the master of Step 2 and turned him into a Step 3 accounting token.
Now, every time a physicist calculates "10 Newtons," they invoke the name of the man who would have vehemently opposed treating that number as a fundamental feature of the universe. The 1948 naming convention effectively sealed the reification of the Jacobian, masking an accounting ledger as a law of nature.
5. Conclusion
People think the units are the physics because they confuse the operational utility of human measurement (M) with the continuous engine of reality (R). They defend this confusion by citing the practical need to convert back to units, failing to recognize that operational utility does not confer ontological primacy.
To do honest physics, we must strip the Jacobians from our equations, return to the pure ratios of Step 2, and accept that while we must occasionally convert back to units to build our human bridges, we must never, ever mistake those units for the continuous, uncut reality that actually exists.
