The Metrological Blind Spot: How Physical Constants Reveal the Disharmony of Arbitrary Measurement

J. Rogers, SE Ohio

Abstract

For over two centuries, a profound blind spot has existed at the heart of physics. We have simultaneously held two contradictory beliefs: that our base units of measurement (the meter, kilogram, second) are arbitrary human constructs, and that the physical constants (G, c, h) required by our laws are fundamental, discovered properties of the universe. This paper argues that this is a false dichotomy. The constants are not fundamental discoveries; they are the necessary mathematical artifacts that arise directly from the initial, un-harmonized arbitrariness of our units. By deconstructing the constants and revealing their function as Jacobian conversion factors, we demonstrate that they are the "epicycles" of modern physics, correcting for a poorly chosen (anthropocentric) origin for our measurement system. This reframing shows that physical laws are, at their core, simple dimensionless ratios between natural proportions. This perspective dissolves long-standing "irreducible mysteries" surrounding mass, gravity, and the values of the constants, revealing that the ultimate unity in physics is not a unification of forces, but the harmonization of our axes of measurement.

1. Introduction: The Great Disconnect

The foundation of modern science rests on the International System of Units (SI). From its inception, the architects of this system understood and acknowledged the arbitrary nature of its base units. The meter, originally defined as one ten-millionth of the distance from the pole to the equator, and the kilogram, the mass of a specific metal artifact, were understood to be choices of convenience, not cosmic truths.

In parallel, theoretical physics embarked on a journey of discovery, unveiling laws that appeared to govern the cosmos. A curious feature of these laws was the persistent appearance of constants of proportionality—Newton's G, the speed of light c, Planck's constant h. These numbers were treated as profound discoveries, fundamental features of reality whose precise values were a message from the universe.

This created a cognitive firewall. On one side, metrologists managed a system they knew was arbitrary. On the other, physicists revered the constants that arose from using that system as fundamental. The great blind spot of modern science has been the failure to recognize that these two facts are not independent, but are cause and effect. The constants are not a message from the universe; they are a direct and unavoidable mathematical consequence of the initial, arbitrary choices made by the metrologists.

2. The Nature of the Constants: Discovery or Correction?

The traditional view posits that constants are immutable properties of nature. We propose that they are, instead, unit scaling operators. They are the mathematical machinery required to harmonize our disparate and badly-scaled measurement axes. Their function is not to describe nature, but to correct our description.

Consider the speed of light, c. Its numerical value (299,792,458 in m/s) is not a "speed limit" imposed by the cosmos, but a measure of our own scaling error. It is the conversion factor that documents how badly our human-scale meter is scaled relative to our planetary-scale second. If we had chosen our units in harmony with the geometry of spacetime, this ratio would be 1. The constant c is the Jacobian that transforms measurements between our flawed coordinate chart and a natural one.

Similarly, Newton's constant G and Planck's constant h are more complex operators, or "epicycles," that reconcile our macroscopic, arbitrary units of mass, length, and time with the natural scales of gravity and quantum mechanics. Their incredibly small numerical values are not a sign of the weakness of these forces, but a measure of the vast scaling mismatch between our human-world units and the phenomena they describe.

3. A Rational Deconstruction of the Math: Gravity as a Case Study

The validity of this viewpoint is not a matter of philosophy, but is demonstrated by a direct, step-by-step breakdown of the mathematical operations. Let us examine the formula for gravitational time dilation:

        $$\frac{\mathrm{\Delta }t}{t_0}=\frac{GM}{c^{2}r}$$      

The standard narrative explains this via the curvature of spacetime caused by mass. However, let us analyze what the constants are doing. The controlling term G/c² is a composite operator. We can deconstruct it by examining the conversion factors between SI and natural units (the Planck units, l_P, m_P, etc.), which function as the basis vectors of the Jacobian matrix:

        $$\frac{G}{c^2}=\frac{(l_P^3\mathrm{/}{m}_P{t}_P^2)}{(l_P^2\mathrm{/}{t}_P^2)}=\frac{l_P}{m_{\mathrm{P}}}$$      

The entire complex operation G/c² simplifies to a single instruction: "scale the result by the ratio of the length-converter to the mass-converter." Substituting this back into the law reveals the true physics hidden by our units:

        $$\frac{\mathrm{\Delta }t}{t_0}=\left(\frac{l_P}{m_P}\right)\frac{M}{r}\hspace{0.25em} ⟹\hspace{0.25em} \frac{\mathrm{\Delta }t}{t_0}=\frac{M\mathrm{/}{m}_P}{r\mathrm{/}{l}_{\mathrm{P}}}$$      

The physical law is not the complicated dimensional formula. The physics is a simple, dimensionless statement: the fractional change in time is the ratio of mass in natural units to length in natural units. This is a direct statement about a time field, where "mass" is not the cause of the effect, but is our name for the measurement of the effect itself. The elaborate story of spacetime curvature is a narrative we invented to explain the operational effects of the G/c² scaling factor.

4. The Unity of Measurement: Harmonizing the Axes

This framework redefines the quest for unification in physics. The ultimate unity is not between forces, but between our very axes of measurement. The identity that emerges in a harmonized, natural unit chart is:

        $$T=f=m=E=p=F=1\mathrm{/}L$$      

This is not a list of equivalences; it is a statement of identity. It reveals that we have given a half-dozen different names to the same underlying reality—processes in time—simply because we were measuring it along different, un-harmonized axes. Mass is the measure of this process at rest; energy is the measure of its total activity; temperature is the statistical measure of a collection of such processes.

This solves centuries of misunderstanding. "Spooky action at a distance" is an illusion. Newton's law of gravitation, when deconstructed, describes the local interaction of two time fields (m1/r and m2/r). The constant G is merely the set of instructions that scales this local interaction into our arbitrary SI unit of force.

Physics has been trapped in a "Matrix" of its own SI units. The system works, and the simulation is convincing, leading us to mistake the rules of the simulation (the constants) for the rules of reality. The process outlined here is the act of seeing the underlying code.

5. Conclusion: From Irreducible Mystery to Rational Clarity

We knew our units were arbitrary, but we failed to consider that the constants were the price of that arbitrariness. This blind spot created a narrative of irreducible mystery around the nature of mass and the values of the constants.

By recognizing the constants as the mathematical tools for harmonizing our measurement system, these mysteries dissolve. The constants are not a cosmic message; they are a historical record of our own metrological choices. The deepest truths are not found in the seemingly random values of G, c, and h, but in the simple, elegant relationships that emerge only when these scaling artifacts are understood and factored out. The real work of fundamental physics, then, is not just to measure the world, but to perfect the language we use to do so, until the harmony of the underlying reality is revealed.