Politics, Power, and Science: The Epistemology Encoded in Physical Law: A Kantian Reading of Modern Physics

Wednesday, November 12, 2025

The Epistemology Encoded in Physical Law: A Kantian Reading of Modern Physics

J. Rogers, SE Ohio

"Our physics doesn't describe the universe. It describes how we measure it."

Abstract

This paper presents a meta-theoretical analysis of the mathematical structure of modern physics. We argue that the formalism of our most fundamental theories—when properly interpreted—encodes a Kantian epistemological framework: physical constants are features of our measurement apparatus, not properties of nature; dimensional equations relate phenomena to phenomena, not phenomena to reality; and the "thing-itself" remains necessarily inaccessible to direct inquiry. We demonstrate that equations like E=mc² and F=Gm₁m₂/r² are not directly statements about the universe, but statements about the relationship between our conceptual projections of the universe and the actual invariant physics that is true in every unit chart. Using Planck's original 1899 formulation (with h, not ℏ), we show that natural units collapse arbitrary phenomenal separations. The geodesic equation of General Relativity is shown to describe motion without invoking "force," revealing gravity as a geometric necessity in the space of phenomena. This analysis suggests that progress in fundamental physics requires developing mathematical languages that minimize arbitrary phenomenal projections—topological, information-theoretic, or other frameworks that describe structural invariants rather than measurement-dependent quantities.

1. Introduction: What Our Mathematics Is Actually Saying

Modern physics has achieved extraordinary predictive success while remaining philosophically opaque about what its equations mean. This paper argues that the mathematical formalism itself—when examined carefully—reveals a profound epistemological claim: we do not and cannot measure reality directly; we measure projections of reality onto our conceptual axes.

This is not a new physical theory. This is an analysis of what our existing theories tell us about the limits of physical knowledge.

1.1 The Kantian Framework

Immanuel Kant distinguished between:

Noumena (things-in-themselves): Reality as it exists independently of observation

Phenomena: Reality as it appears to us through the structure of our perception and cognition

Kant argued that we can never know noumena directly—we only access phenomena, which are shaped by the a priori forms of intuition (space and time) and categories of understanding (causality, substance, etc.).

This paper's thesis: The mathematical structure of modern physics encodes precisely this epistemological framework. What we call "physical laws" are relationships between phenomenal projections. What we call "constants" are conversion factors between different projections. What we call "the universe" is, in our equations, necessarily the thing-we-cannot-measure-directly.

Kant's insight sharpened: Kant distinguished between pure space and time (the a priori forms of intuition that make experience possible) and empirical space and time (pure intuition filled with sensory content). Our "conceptual axes" (length, mass, time) are not identical to pure space/time—they are the operationalization of pure intuition into a measurement scheme. We measure because we must structure experience spatially and temporally; our choice of meters, kilograms, and seconds is the empirical realization of this necessity. This is because that is how our senses perceive the universe.

Moreover, Kant's categories of understanding are encoded in physical formalism: the concept of "force" manifests the category of causality; the concept of "mass" manifests the category of substance. When we discover that "force" is not fundamental but geometric, we are discovering that even the categories themselves are projections onto the phenomenal structure.

1.2 Terminological Clarifications

To ensure precision throughout this analysis, we distinguish four conceptual layers:

Term	Definition	Example
Noumenon (thing-itself)	Reality as it exists independently of measurement; the "unified process"	The substrate of physical reality
Phenomena	Structured appearances accessible to measurement	Energy, mass, spacetime curvature
Conceptual axes	The cognitive/mathematical dimensions onto which we project phenomena	Length (meters), mass (kilograms), time (seconds)
Measurement artifacts	The conversion factors required by our choice of axes	Constants (c, G, h), dimensional equations

The hierarchy flows: Noumenon → Phenomena → Conceptual axes → Measurement artifacts. Our equations operate at the level of measurement artifacts, relating phenomena projected onto conceptual axes. They tell us nothing directly about the noumenon.

2. The Measurement Apparatus: Conceptual Axes and Their Artifacts

2.1 Bridgman's Insight: Dimensions as Epistemic Scaffolds

Percy Bridgman, in his 1922 Dimensional Analysis, articulated a profound but often-overlooked principle: dimensional formulas encode relationships between measurement operations, not properties of nature.

As Bridgman wrote:

"The dimensions of a physical quantity are not intrinsic to the thing measured, but are a consequence of the operations by which we measure."

This is the foundation of operationalism: what we call "physical quantities" are inseparable from the procedures used to measure them. A "length" is not a property an object has—it is the outcome of a measurement operation involving rulers, light signals, or interferometry.

The constants of physics arise precisely because we perform different measurement operations (laying rulers, timing oscillations, weighing objects) and then demand that the results be convertible into one another.

2.2 The Fragmentation of Measurement

To measure anything, we must project it onto conceptual axes. Physics has historically chosen three independent axes:

Length (meters)

Mass (kilograms)

Time (seconds)

These are not "natural kinds" discovered in nature—they are human cognitive structures imposed on experience to make it measurable. We could equally have chosen energy-frequency-momentum, or any other tripartite basis. The choice is arbitrary.

Einstein captured this epistemic status perfectly:

"Time and space are modes by which we think and not conditions in which we live."

The consequence of this arbitrariness: When we project a unified phenomenon onto separate axes, we create the need for conversion factors to translate between projections.

2.3 Constants as Conversion Factors Between Phenomena

The "fundamental constants" of physics (c, G, h) are precisely these conversion factors:

c: Converts between length-projections and time-projections (meters ↔ seconds)

h: Converts between energy-projections and frequency-projections (joules ↔ Hz) via E=hf

G: Converts between spacetime-curvature-projections and mass-energy-projections

Critical point: These constants do not appear in the physics itself. They appear in the translation between our phenomenal axes.

In Bridgman's terms: the constants are the calibration marks on the rulers we forgot we built.

2.4 The 2019 SI Redefinition: Making the Inversion Explicit

In 2019, the International System of Units was redefined. The constants are no longer measured—they are defined to have exact values, and our units are derived from them.

This inversion reveals the truth that was always present: constants are the anchors of our measurement map, not features of the territory being mapped.

3. The Planck Scale: The Natural Chart of Phenomena

3.1 Collapsing the Conceptual Axes

The Planck scale is derived purely from the operational constants (using Planck's original 1899 formulation with h, not the reduced ℏ):

 $l_{P} = \sqrt{\frac{h G}{c^{3}}}, m_{P} = \sqrt{\frac{h c}{G}}, t_{P} = \sqrt{\frac{h G}{c^{5}}}$

In these units, c=1, h=1, and G=1. The constants vanish because the conceptual separations they were created to bridge no longer exist.

In natural units:

A length IS a time (no conversion needed)

An energy IS a mass (no conversion needed)

A spacetime curvature IS a mass density (no conversion needed)

This is not a claim about the universe—it's a claim about what happens when we minimize the arbitrary projections in our measurement scheme.

3.2 Dimensionless Quantities: Approaching the Structural

Any physical quantity can be written as:

 $X_{SI} = X_{nat} \cdot X_{P}$

where:

 $X_{SI}$

is the measured quantity in our arbitrary units

 $X_{nat}$

is the dimensionless, measurement-independent quantity

 $X_{P}$

is the Planck-scale conversion factor

The dimensionless quantities are closer to the structure of the thing-itself. They don't depend on our choice of conceptual axes. They are invariants—not of coordinate transformations, but of measurement-scheme transformations. They remain unchanged when we rescale our rulers, clocks, or balances.

Example: The Fine Structure Constant

The fine structure constant is often written as:

 $α = \frac{e^{2}}{4 π ϵ_{0} ℏ c} \approx \frac{1}{137}$

A common objection: "Doesn't this depend on the elementary charge e, which is dimensional?"

The resolution: All the dimensional constants cancel, leaving only α. The invariant is α itself; e is merely a dimensional artifact of our choice to measure charge on a separate conceptual axis. The fine structure constant is not "about e" or "about c"—it is about the invariant coupling strength between electromagnetic interaction and quantum action. When we measure α ≈ 1/137, we're measuring a structural relationship that exists independently of whether we use coulombs or statcoulombs, joules or ergs.

This is precisely why dimensionless quantities are the proper focus of fundamental physics: they describe relationships that all measurement schemes agree on.

4. The Tautological Structure of Dimensional Laws

4.1 What E=mc² Actually Says

The common interpretation: "Energy equals mass times the speed of light squared—a property of the universe."

What the mathematics actually says:

The measurement-independent physics is the dimensionless identity:

 $E_{nat} = m_{nat}$

This is the claim about reality: the phenomenon we project as "energy" and the phenomenon we project as "mass" are the same aspect of the noumenon, viewed along different conceptual axes.

To express this in SI units, we must account for our arbitrary choice of separate axes:

 $E_{nat} \cdot E_{P} = m_{nat} \cdot m_{P}$

Rearranging:

 $E_{SI} = m_{SI} \cdot \frac{E_{P}}{m_{P}}$

The ratio

 $E_{P} / m_{P}$

is, by the definitions of our measurement scheme, numerically and dimensionally equal to c².

Therefore: E=mc² is not a statement about the universe. It is a statement about the relationship between two phenomenal projections (energy and mass) that we have chosen to measure on separate scales. The equation is a dimensional tautology—it must be true given our choice of units, regardless of what the underlying reality is.

The physics: Energy and mass are the same.
The unit conversion: They differ by c² in our measurement scheme.

4.2 What Newton's Law Actually Says

The common interpretation: "Gravity is a force proportional to mass and inversely proportional to distance squared—a law of nature."

What the mathematics actually says:

The measurement-independent physics of a weak gravitational field is captured by the dimensionless potential:

 $τ = \frac{G m}{c^{2} r} = \frac{m_{nat}}{r_{nat}}$

In natural units, gravitational potential is simply a mass-to-distance ratio—a pure geometric statement.

The gravitational interaction between two objects is described by the dimensionless quantity

 $τ_{1} τ_{2}$

—the product of their potentials. This is the physics.

To convert this dimensionless interaction into our SI unit of force (Newtons), we must scale by the natural unit of force, the Planck Force

 $F_{P} = c^{4} / G$

 $F_{SI} = (τ_{1} τ_{2}) \cdot F_{P} = (\frac{G m_{1}}{c^{2} r}) (\frac{G m_{2}}{c^{2} r}) (\frac{c^{4}}{G})$

Algebraic cancellation yields:

 $F_{SI} = G \frac{m_{1} m_{2}}{r^{2}}$

Therefore: Newton's law is not a discovery about nature. It is the inevitable result of projecting the dimensionless geometric relationship

 $τ_{1} τ_{2}$

onto our SI measurement grid.

The physics: Gravitational interaction is proportional to the product of dimensionless potentials.
The unit conversion: This becomes

 $G m_{1} m_{2} / r^{2}$

in SI units.

5. The Epistemological Claim Encoded in General Relativity

5.1 A Worked Example: Sitting in a Chair

Consider a person sitting in a chair on Earth. The standard Newtonian description invokes two forces: gravity pulling down, the chair pushing up. We will show that General Relativity's mathematical structure reveals a different picture—one with no forces at all, only geometric necessity in the space of phenomena.

5.2 The Time-Field as a Phenomenal Structure

Both Earth and the person are manifestations of the unified process (the noumenon). What we measure are their projections:

Earth's time-field at your location:

 $τ_{Earth} = \frac{G M_{Earth}}{c^{2} r} \approx 7 \times 10^{- 10}$

This is the dimensionless measure of how much slower time runs for you (phenomenon: time-projection) compared to an observer at infinity.

Your own time-field:

 $τ_{you} = \frac{G m_{you}}{c^{2} r_{you}} \approx 10^{- 23}$

These τ values are not separate "fields" acting on spacetime—they are the local structure of the time-phenomenon.

5.3 The Geometry of Phenomenal Spacetime

The metric describing spacetime near Earth (weak-field approximation) is:

 $d s^{2} = - (1 - 2 τ) c^{2} d t^{2} + (1 + 2 τ) d r^{2} + r^{2} d Ω^{2}$

The critical feature is the time component:

 $- (1 - 2 τ) c^{2} d t^{2}$

. This shows that τ is not an external field—it is the texture of the time-phenomenon itself.

Because τ is larger closer to Earth and smaller farther away, there exists a gradient

 $\nabla τ$

pointing radially inward. The time-phenomenon has geometric structure.

5.4 Motion as Geodesic Necessity

What we call "motion" is the path traced by an object through phenomenal spacetime. In the absence of non-gravitational forces, objects follow geodesics—the straightest possible paths through the curved geometry of phenomena.

For an object starting at rest, the geodesic equation reduces to:

 $\frac{d^{2} r}{d t^{2}} = - c^{2} \nabla τ$

Substituting

 $τ = G M / (c^{2} r)$

 $\frac{d^{2} r}{d t^{2}} = - c^{2} \nabla (\frac{G M}{c^{2} r}) = - \frac{G M}{r^{2}} \hat{r}$

This is Newton's law of gravity—but derived not from a concept of "force," but from the geometric requirement that an object follow a straight line through phenomenal spacetime that has a time-gradient.

The mathematical claim: "Gravity" is not a force causing motion. It is the statement that what we project as 'straight-line motion' through the unified process appears as curved motion when viewed in the fragmented space of our phenomenal projections.

5.5 The Role of the Chair

The chair exerts a non-gravitational force that prevents you from following the geodesic. It must provide a proper acceleration:

 $a_{chair} = + c^{2} \nabla τ = \frac{G M}{r^{2}}$

This acceleration continuously deflects your worldline away from the geodesic path. This deflection is what you experience as weight.

Clarification on "non-gravitational": What does "real" mean in the Kantian framework? Non-gravitational forces are phenomenal manifestations of interactions between other projections—in this case, electromagnetic repulsion between atoms in the chair and atoms in your body. They are "real" in the sense that they correspond to invariant structural relationships in the noumenon—but they are still phenomena, not direct access to the noumenon.

The Equivalence Principle Resolved:

The equivalence of gravitational mass and inertial mass—tested to 1 part in 10¹⁵—has been a foundational mystery since Newton and a postulate of General Relativity since Einstein. In this framework, it is not a mystery or a postulate—it is a tautology.

Both gravitational mass (your contribution to time-field depth) and inertial mass (your coupling to the summed cosmic time-field) are projections of the same underlying structure onto our measurement axes. Their numerical equality in any measurement scheme is inevitable, not coincidental. The equivalence principle is thus revealed as an artifact of the unified nature of the noumenon—when viewed through our phenomenal projections, the same depth appears whether we measure it gravitationally or inertially.

Summary of the epistemological structure:

Concept	Newtonian (Phenomenal) View	Kantian (Structural) View
Gravity	A force pulling you down	The geodesic structure of phenomenal spacetime with time-gradient
Weight	The reaction force balancing gravity	The proper acceleration deflecting you from geodesic motion
Free fall	Zero net force	Following the geometric necessity of the phenomenal structure
Motion	Change in position caused by forces	Geometric flow through the projection-space

6. The Unified Process: The Necessary Noumenon

6.1 Why It Cannot Be Defined

The paper repeatedly refers to a "unified process" underlying mass, energy, space, time, and gravity. Readers might expect this process to be defined—to be given equations, dynamics, or structure.

But this expectation misunderstands the argument.

The unified process is the thing-itself, the noumenon. Kant's fundamental epistemological claim is that we cannot know the thing-itself directly. We can only know phenomena—the appearances of things as filtered through our forms of intuition and categories of understanding.

To define the unified process would be to claim direct access to the noumenon—which is precisely what the analysis shows is impossible.

Why this limitation is necessary: Kant argued that concepts without intuition are empty. All our scientific concepts are tied to our a priori forms of intuition (space and time) and the empirical measurements we make within them. We cannot form a concept of the noumenon because we have no intuition—no measurement axis—to apply to it. We can know that it exists (something must ground the phenomena), and we can study the structural relationships between its phenomenal projections, but we cannot know what it is in itself.

This is not a failure of current physics—it is a fundamental limit on what measurement-based inquiry can achieve.

6.2 Mach's Principle and the Sum of Time-Fields

There is, however, suggestive structure that hints at the relational nature of the noumenon. Ernst Mach proposed that inertia is not an intrinsic property of objects, but emerges from their relationship to all other matter in the universe.

In our framework, we can express something similar: the local rate of proper time τ_local may be determined by the sum of all gravitational potentials from all masses in the universe:

 $τ_{local} = \sum_{i} \frac{m_{nat, i}}{r_{nat, i}}$

This suggests that what we experience as "the flow of time" at a given location is the integrated projection of all mass-energy distributions in the cosmos. Time is not a background stage—it is a relational phenomenon emerging from the global distribution of the unified process.

This resonates with Mach's insight while remaining agnostic about the noumenon itself. We're describing the phenomenal structure (how time-fields sum) without claiming to know what produces them.

6.3 What We Can Know

We can know:

That it exists: Our measurements are measurements of something

That it has structure: Our phenomena exhibit consistent, lawful relationships

What it is not: It is not mass, not energy, not space, not time—these are projections

We can study:

The geometry of phenomenal space (how projections relate to each other)

The invariants under measurement-scheme changes (dimensionless quantities)

The minimal projection structures (natural units, geometric formulations)

But we cannot "see" the unified process directly, any more than Plato's cave-dwellers can turn around and see the fire. We are constitutionally limited to studying shadows.

6.4 The Role of Dimensionless Physics

Dimensionless quantities are significant because they are invariant under changes in our measurement scheme. They don't depend on whether we use meters or feet, kilograms or pounds, seconds or years.

They are still phenomena—they are still projections, not the thing-itself. But they are projections that multiple measurement schemes agree on. They are closer to structural properties of the noumenon.

Examples:

The fine structure constant:

 $α \approx 1 / 137$

Mass ratios:

 $m_{e} / m_{p} \approx 1 / 1836$

The dimensionless form of gravity:

 $τ = m_{nat} / r_{nat}$

These are the quantities that future physical theories should focus on, because they minimize the arbitrary elements of our measurement apparatus.

7. Implications for the Future of Physics

7.1 The Mistake of Reifying Constants

Modern physics has committed a category error: treating features of our measurement apparatus as if they were properties of nature.

We ask questions like:

"Why does the speed of light have the value it does?"

"Why is the gravitational constant so small?"

"Why is Planck's constant non-zero?"

These are malformed questions. They are asking for explanations of our choice of rulers.

A concrete example of this error: Anthropic principle arguments often treat constants like G or the cosmological constant Λ as "parameters of the universe" that could have been different, and then marvel that they happen to allow life. This framework shows these arguments are confused—they are asking why our rulers have the length they do, not why the universe has the structure it does. The dimensionless ratios (like the ratio of electromagnetic to gravitational coupling strength, ~10³⁶) are the proper subject of such inquiry, not the dimensional constants themselves.

The proper questions are:

"What is the dimensionless structure of electromagnetic propagation?" (not "why c?")

"What is the dimensionless coupling strength of gravity relative to other interactions?" (not "why G?")

"What is the scale of quantum action relative to classical observables?" (not "why ℏ?")

"What is the dimensionless value Λl²_P of the cosmological constant in Planck units?" (not "why Λ = 10⁻⁵² m⁻²?")

7.2 The Path Forward: Mathematics of Minimal Projection

The future of fundamental physics lies in developing mathematical languages that:

Minimize arbitrary projections: Use geometric, topological, or information-theoretic structures that don't presuppose separation into mass/length/time

Describe invariants: Focus on dimensionless quantities and relationships that all measurement schemes agree on

Respect epistemological limits: Acknowledge that we're describing phenomenal structure, not noumenal reality

Candidates include:

Topological field theory: Describes physical systems via properties invariant under continuous deformation

Information theory: Quantifies physical systems by entropy, mutual information, and other dimensionless measures

Category theory: Describes structure through relationships and transformations rather than objects with properties

Geometric algebra: Unifies spatial, temporal, and dynamical concepts in a single mathematical framework

7.3 Unification as Recognition, Not Discovery

The standard approach to unification seeks a single force or field from which all others emerge. This presumes that:

Forces/fields are the fundamental ontology

They are currently separate

Physics must discover how they combine

The Kantian analysis suggests a different picture:

The unified process already exists—it is the noumenon. Mass, energy, space, time, electromagnetism, gravity—these are already unified at the noumenal level. They appear separate only because we have projected them onto separate phenomenal axes.

Unification is not about discovering new physics that combines separate entities. It is about developing mathematical frameworks that require fewer arbitrary projections, bringing our phenomenal descriptions closer to the structure of the noumenon.

8. Conclusion: The Epistemology in the Equations

"E = mc² is not a discovery; it's a unit conversion between two projections of a single phenomenon."

This paper has argued that the mathematical formalism of modern physics—when read carefully—encodes a Kantian epistemological framework:

8.1 Summary of Claims

Constants are artifacts of measurement, not properties of reality

They are conversion factors between arbitrary phenomenal projections

Their numerical values reflect our choice of units, not features of nature

Dimensional equations are tautologies, not physical laws

They relate phenomena to phenomena, not phenomena to reality

They must be true given our measurement scheme, regardless of the underlying physics

Dimensionless relationships are the physics

They are invariant under measurement-scheme changes

They approach (but never reach) structural properties of the noumenon

The unified process is unknowable directly

Mass, energy, space, time are phenomenal projections, not noumenal entities

We can study the geometry of phenomenal space, but not the thing-itself

Gravity is geometric necessity

The geodesic equation describes motion without invoking force

What appears as "gravitational attraction" is straight-line motion through curved phenomenal spacetime

8.2 What This Means for Physics

This is not a new theory of nature. It is a meta-theoretical analysis revealing what our current theories already say about the limits of physical knowledge.

The implications are:

Stop reifying constants and asking why they have particular values

Focus on dimensionless structure as closer to noumenal invariants

Develop mathematical languages that minimize arbitrary phenomenal projections

Recognize that "unification" means reducing projections, not discovering new entities

8.3 The Prison We Built

"Physical law is not a window to reality, but a mirror reflecting our measurement habits."

Modern physics has extraordinary calculational power. We can predict the magnetic moment of the electron to twelve decimal places. We can model the collision of black holes a billion light-years away.

But we have traded philosophical clarity for technical prowess. We have forgotten that our equations describe our measurements, not the thing being measured.

We are like Plato's cave-dwellers who have become so skilled at predicting shadow-movements that we have forgotten the shadows are not the reality. We have built an elaborate mathematical apparatus that relates shadow to shadow, projection to projection.

The constants are the chains on our wrists. They are reminders that we are measuring with arbitrary rulers, projecting onto arbitrary axes, converting between arbitrary units.

This paper has argued for a paradigm shift—not in physics, but in how we interpret what our physics is telling us. The mathematics itself encodes the message: you are measuring phenomena, not noumena. Your laws are relationships between projections. The thing-itself remains beyond your grasp.

The future lies not in tighter chains, but in recognizing them for what they are—and perhaps, in developing new mathematical languages that require fewer chains at all.

Acknowledgments

This work synthesizes insights from dimensional analysis (Bridgman, 1922), natural units (Planck, 1899), the geometric interpretation of General Relativity (Einstein, 1915; Misner, Thorne, Wheeler, 1973), and Kantian epistemology (Kant, 1781). The contribution is not in the technical content—which is standard—but in the meta-theoretical interpretation: recognizing that these mathematical structures encode claims about the limits of physical knowledge.

References

Bridgman, P. W. (1922). Dimensional Analysis. Yale University Press.

Einstein, A. (1915). Die Feldgleichungen der Gravitation. Sitzungsberichte der Preussischen Akademie der Wissenschaften.

Einstein, A. (1920). Relativity: The Special and General Theory. [Quote: "Time and space are modes by which we think..."]

Frieden, B. R. (1998). Physics from Fisher Information. Cambridge University Press.

Jaynes, E. T. (2003). Probability Theory: The Logic of Science. Cambridge University Press.

Kant, I. (1781/1787). Kritik der reinen Vernunft.

Mach, E. (1883). Die Mechanik in ihrer Entwicklung. [On relational nature of inertia]

Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. W. H. Freeman.

Penrose, R. (1967). "Twistor algebra." Journal of Mathematical Physics 8(2): 345-366.

Planck, M. (1899). Über irreversible Strahlungsvorgänge. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin. [Original formulation using h, c, G]

Rovelli, C. (1996). "Relational quantum mechanics." International Journal of Theoretical Physics 35(8): 1637-1678.

Susskind, L. (1995). "The world as a hologram." Journal of Mathematical Physics 36(11): 6377-6396.

Note on Planck Units

This paper uses Planck's original 1899 formulation with the non-reduced constant h (where E=hf), rather than the later convention using ℏ=h/2π. Using ℏ introduces a geometric convention (radians, the factor 2π) into what should be purely physical definitions. This is a category error: we should not mix geometric conventions with fundamental physical scales. Planck's original formulation with h, c, and G is conceptually prior and avoids this conflation.

Addressing Common Objections

Objection 1: "If constants are just artifacts, why are they constant over time?"

Answer: We define them to be constant. The 2019 SI redefinition fixes their values exactly—so if we ever observed data that seemed to show a change in c, we would not conclude c had changed; we would conclude that our measurement of one axis (e.g., length or time) had drifted relative to the others. Constants are constant because our measurement scheme holds them constant. Any "variation" would manifest as changes in dimensionless quantities, which would indicate actual structural changes in the noumenon's projections.

Objection 2: "What about the cosmological constant Λ? Is that an artifact too?"

Answer: The cosmological constant has both aspects. If measured as a dimensional quantity (Λ ≈ 10⁻⁵² m⁻²), it is an artifact of our choice to measure length on the meter axis. If measured as a dimensionless quantity (Λl²_P in Planck units, where l_P is the Planck length), it becomes an invariant structural parameter—currently ~10⁻¹²². This dimensionless value is the proper mystery: why is the vacuum energy density so small compared to the Planck scale? The dimensional value 10⁻⁵² m⁻² tells us nothing; the dimensionless ratio 10⁻¹²² demands explanation.