The Unexamined Axiom: Natural Units, Fundamental Constants, and the Single-Scale Assumption in Modern Physics

 The standard framework version has to be written as an internal critique: speaking the language of mainstream physics, using its assumptions, and then showing that those assumptions are never examined. Here is a concise “inside-the-standard-framework” rewrite.

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J. Rogers, SE Ohio

1. The Quiet Axiom of a Single Scale

Contemporary high‑energy physics operates with a tacit but universal working assumption: there exists a single natural scale that underlies all physical quantities, and in that scale the fundamental constants can be set to 1 “without loss of generality.”

Every graduate student learns to switch to “natural units” by the simple replacements

$$c=1,\hslash =1,k_B=1,G=1$$

and is told, correctly, that this simplifies the algebra and clarifies the structure of field theories and thermodynamics. In these units:

• Light cones become 45‑degree lines with no numerical $c$.

• Quantum commutation relations lose explicit $\hbar$.

• Temperature and energy differ by no conversion factor.

This practice implicitly asserts that all of these constants are nothing more than conversion factors between human unit conventions and an underlying, unified, single physical scale. It is not treated as a conjecture. It is treated as a given.

What is almost never done is to take this seriously as an ontological claim and ask: if there is a single underlying scale, what does that imply about the status of “fundamental constants,” measurement, and metrology?

2. Natural Units as “Convenience,” Constants as “Fundamental”

In the standard story, a paradoxical stance is adopted:

• On the one hand, the community says: “Set $c=\hslash =k_B=1$. They’re just conversion factors.”

• On the other hand, the same constants are referred to as “fundamental constants of nature,” are used to define the latest SI, and are presented to the public as deep, irreducible facts about reality.

This two‑level treatment leads to three consequences.

1. Inside calculations, constants are demoted to bookkeeping artifacts. The physics, it is said, is in the dimensionless combinations.

2. In pedagogy and interpretation, the same constants are re‑elevated to a quasi‑metaphysical status, as if they directly encoded properties of the universe.

3. At the conceptual level, the underlying single‑scale assumption is never examined as a structural claim about what the world is like—it is used but not analyzed.

A student who simply follows instructions and sets $c=\mathrm{1\; is}$ welcomed.

A student who asks, “If we can consistently set $c=\hslash =k_B=1$, what, exactly, is the ontological status of these constants and of our unit system?” is quietly redirected.

A student who pushes and demands that this be treated with the same rigor as any other axiom risks being labeled “not focusing on real physics" and pushed out of physics programs.

3. Measurement, Units, and the “Non‑Problem” That No One Touches

From within the standard framework, it is common to speak of a “measurement problem” in quantum mechanics and then, in the next breath, to rely on natural units that strip away explicit scales and hide all unit conversions.

Yet the very act of moving to natural units already encodes a strong claim:

• That all physically meaningful content resides in dimensionless ratios.

• That the constants we write in SI are conversion factors between our arbitrary unit chart and an underlying natural scale.

• That “measurement,” in practice, is nothing but reading off coordinates in a chosen unit chart after the theory has been written in a unit‑free form.

If this is correct—and standard practice assumes it is as an axiom—then the deep conceptual questions about constants and measurement are not at the periphery of physics. They are baked into how field theories, thermodynamics, and gravity are actually constructed.

But these questions are not part of the curriculum. They are not treated as legitimate research topics for students. They are not framed as open problems at all. They live in an uncomfortable space: used every day, defended as “just convenience,” and quarantined from foundational scrutiny.

4. The Enforcement Mechanism: Rhetoric and Gatekeeping

From inside the standard framework, the enforcement is subtle but real:

• A graduate student who learns to fluently work in natural units is praised for “thinking like a physicist.”

• The same student, if they insist on treating “$c=1$” as a nontrivial structural statement about reality—and attempt to systematize the role of constants, unit systems, and scale—will be told to “stop worrying about units” and “focus on real problems.”

• Persistent insistence on foundational rigor around natural units is read not as intellectual seriousness but as a misunderstanding of the culture’s hierarchy of questions.

The result is not a formal policy but a cultural filter. Students who accept the axiom uncritically advance. Students who want to examine it with the same rigor they bring to Lagrangians or renormalization are quietly selected out as “not suited to theoretical physics.”

From the inside, this feels like maintaining standards. Viewed objectively, it is a mechanism for protecting an unexamined assumption from scrutiny.

5. What an Honest Standard-Framework Paper Would Admit

A reformulated, fully “orthodox” paper that tells the truth from within the standard paradigm would say something like:

• Modern high‑energy physics assumes that there is a single underlying scale in which $c=\mathrm{\hslash }=k_B=\mathrm{1,\; and\; that\; all\; physically\; meaningful\; content\; is\; in\; dimensionless\; ratios.}$

• This assumption is used operationally but almost never treated as an explicit, examinable axiom.

• The status of “fundamental constants” is therefore internally ambiguous: they are treated as both mere conversion factors and deep properties of nature, depending on context.

• The community tacitly discourages students from pursuing this ambiguity as a serious research direction, even though it sits at the base of how theories are formulated.

Such a paper would not need to step outside standard mathematics, nor invoke any new ontology. It would simply demand that the field own its own axiom: either treat the single‑scale, natural‑unit assumption as a foundational claim subject to analysis, or stop pretending that constants are simultaneously “mere conversion factors” and “fundamental” entities.

Until that happens, the standard framework will continue to carry a silent contradiction: it uses a unified scale every day in practice, while culturally punishing anyone who tries to examine what that really means.

Here is a compact reference section you can attach to the paper as written “from inside” the standard framework, supporting the main claims about natural units, constants, and instrumentalism.

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References

Baez, J. C. “A Prehistory of n‑Categorical Physics.” University of California, Riverside (2009). Discusses categorical structures in physics and the role of higher categories in organizing physical theories.[math.ucr]​

Carnap, R. Logical Foundations of Probability. University of Chicago Press, 1950. Classic statement of logical empiricism and verificationism, shaping the “no metaphysics, only prediction” ethos that fed into instrumentalist attitudes in physics.wikipedia+1

Hossenfelder, S. Lost in Math: How Beauty Leads Physics Astray. Basic Books, 2018. Critique of modern high‑energy theory’s reliance on aesthetic criteria (naturalness, elegance) and its detachment from empirical test, including discussion of how certain foundational questions are implicitly ruled out.arxiv+1

“Instrumentalism.” Wikipedia, The Free Encyclopedia (accessed 2026). Overview of instrumentalism in philosophy of science as the view that theories are instruments for prediction rather than descriptions of unobservable reality, including its historical development via Mach, Duhem, and logical positivism.[en.wikipedia]​

Stein, H. “Instrumentalism.” In: The Philosophy of Science: An Encyclopedia, pp. 327–345. Summarizes modern forms of scientific instrumentalism and their relation to realism, including how instrumentalist stances shift what questions are treated as legitimate.[bpb-us-e2.wpmucdn]​

van Fraassen, B. C. The Scientific Image. Oxford University Press, 1980. Presents constructive empiricism, arguing that theories need only be “empirically adequate,” reinforcing the idea that ontological questions (e.g. “what is mass really?”) lie outside the proper aim of physics.plato.stanford+1

“What Does the Philosophy of Physics Add to Human Knowledge?” Aeon (2025). Explains how Bohr’s instrumentalist tendencies and the Copenhagen tradition encouraged a view of physics as an instrument for prediction rather than a route to understanding “the fundamental nature of reality.”[aeon]​

“Instrumentalism – Bibliography.” PhilPapers (accessed 2026). Curated bibliography of work on instrumentalism, constructive empiricism, and related antirealist positions in philosophy of science, documenting that “no‑ontology” approaches are themselves philosophical commitments.[philpapers]​

“Instrumentalist’s New Clothes.” Philosophy of Science 78(5), 2011. Develops a modern form of instrumentalism and defends it as a viable position, illustrating how sophisticated versions of “theories as tools” remain influential in contemporary philosophy of science.[cambridge]​

“Instrumentalism and Relativity.” Philosophy of Science (JSTOR article). Historical analysis of instrumentalist interpretations in the context of relativity, showing how foundational questions were reframed as non‑questions under an instrumentalist lens.[jstor]​

“Scientific Realism.” Stanford Encyclopedia of Philosophy (2011, rev.). Standard reference contrasting realism with instrumentalism and related antirealist views, clarifying that “just predicting observables” is a substantive, contested philosophical stance, not a neutral default.[plato.stanford]​

“Instrumentalism – Chapter 15 (CDN PDF).” Survey article on instrumentalism and constructive empiricism, emphasizing that treating theories as mere instruments changes what kinds of questions are considered meaningful or fundable in science.[bpb-us-e2.wpmucdn]​