Constants as Dual-Role Operators: Encoding Input and Output Processing in Physics

J. Rogers, SE Ohio, 08 Jun 2025, 0043

Abstract

Fundamental physical constants such as h, G, and c are traditionally viewed as conversion factors between units or as proportionality constants in physical laws. This paper proposes a radical computational perspective: these constants encode both input and output processing, acting as bidirectional operators that map quantities into and out of natural (Planck-scale) unit systems where the actual physics computation occurs. This dual role is analogous to encoding and decoding in computation theory, revealing that what we call "fundamental constants" are actually computational pipelines that translate between our arbitrary measurement conventions and the natural scale where physics operates. Recognizing this structure clarifies the deep unity underlying physical law and measurement, suggesting that all physical calculations are actually performed at the Planck scale with constants serving as translation interfaces.

1. Introduction

Physical constants are the backbone of quantitative science, appearing in the most fundamental equations and setting the scales for measurement. Yet their true computational role has been systematically misunderstood. Historically, constants like ℏ, G, and c have been treated as static conversion factors, bridging disparate axes of measurement (mass, length, time, frequency, energy). This view, while mathematically functional, obscures their deeper role as computational operators.

This paper advances the thesis that fundamental constants are computational morphisms—each encodes both an input transformation (mapping quantities to normalized Planck-scale units where computation occurs) and an output transformation (projecting results back to target unit systems). This dual-processing role reveals that all physics calculations actually happen at the Planck scale, with constants serving as the translation machinery between our macroscopic measurement conventions and the fundamental computational substrate of reality.

The implications are profound: rather than mysterious cosmic parameters, constants emerge as necessary computational infrastructure for translating between arbitrary human measurement scales and the natural units where physics fundamentally operates.

2. The Universal State and Measurement Architecture

2.1 The Universal State Framework

All physical quantities can be understood as different projections of a single, dimensionless universal state S_u. This state represents the underlying "amount" or "intensity" of a physical system, independent of how we choose to measure it. Any measurable quantity Q is related to this universal state by:

        Q = S_u × Unit_Scale_Q

Where Unit_Scale_Q is the scaling factor that converts the dimensionless universal state to our chosen measurement units for quantity Q.

You can find S_u by dividing any property by the scaling factor for that axis of measurement:

         S_u =  Q / Unit_Scale_Q

2.2 Natural Units as Computational Substrate

Natural (Planck) units reveal the scale where the universal state operates directly, without scaling artifacts. In these units, fundamental relationships reduce to their essential form:

• Length ≡ Time (c = 1)
• Energy ≡ Frequency (h = 1)
• Mass ≡ Length (G = 1)

These equivalences aren't mathematical conveniences—they reveal that at the Planck scale, these different "types" of measurement are actually identical projections of S_u.

Forcing constants to 1 is the traditional incorrect way to view constants.  It is not about forcing constants to 1.  It is about harmonizing our units of measure to the natural L~T and m~f and so on equivalences. 

3. Constants as Computational Morphisms

3.1 The Dual-Processing Architecture

Physical constants function as computational pipelines with two distinct stages:

Input Processing (Encoding): Convert macroscopic quantities to their Planck-scale equivalents, removing arbitrary scaling factors to reveal the underlying universal state relationships.

The physics happens at these natural ratios.

Output Processing (Decoding): Project the Planck-scale computation result back to the desired measurement axis and unit system.

This architecture explains why constants have complex dimensional structures—they're not simple ratios but complete computational workflows.

3.2 Detailed Analysis: Planck's Constant (ℏ)

Traditional view: h converts between energy and frequency via E = hf

Dual-processing analysis:

• Input stage: Frequency f is converted to its mass equivalent via the Hz/kg relationship inherent at Planck scale
• Computation stage: Physics operates on this mass-equivalent at the natural scale where mass ≡ energy
• Output stage: Result is projected to the energy axis using c² scaling

h encapsulates this entire three-stage pipeline: frequency → mass → energy, not merely "energy = constant × frequency."

3.3 Detailed Analysis: Gravitational Constant (G)

Traditional view: G is the proportionality constant in Newton's law

Dual-processing analysis:

• Input stage: SI masses m₁, m₂ and distance r are normalized to dimensionless Planck ratios: (m₁m₂/m_P²) and (l_P²/r²)
• Computation stage: Force calculation occurs at Planck scale using these dimensionless ratios
• Output stage: Planck force result is scaled to SI Newtons via F_P

The gravitational "law" F = Gm₁m₂/r² is actually: F = (m₁m₂/m_P²) × (l_P²/r²) × F_P

G = (l_P²/m_P²) × F_P is the computational pipeline that handles this translation.

3.4 Detailed Analysis: Speed of Light (c)

Rather than a velocity limit, c² emerges as the scaling factor between mass and energy projections of the same universal state.

Dual-processing analysis:

• Input stage: Mass is recognized as compressed spatial extension (gravitational radius scaling)
• Computation stage: At Planck scale, mass ≡ energy directly
• Output stage: c² provides the scaling to project this relationship to our energy units

This explains why c appears squared in E = mc²—it's not about velocity but about the dimensional scaling required for mass→energy projection.

4. Unifying Framework: Constants as Translation Infrastructure

4.1 The Computational Model

All physics calculations follow this pattern:

1. Encode macroscopic quantities to Planck scale using input processing
2. Compute relationships directly at the universal state level
3. Decode results to desired measurement axis using output processing

Constants are the computational infrastructure that makes this translation possible. They're not describing physical relationships—they're enabling the computation of universal state relationships within our measurement frameworks.

4.2 Why This Was Overlooked

The dual-processing nature of constants has been historically invisible because:

1. Compound operations: Each constant performs multiple transformations that appear as single operations
2. Focus on proportionality: Traditional physics emphasizes the proportional relationships constants enable, not their computational structure
3. Unit system dependence: The processing becomes apparent only when explicitly considering the translation between natural and conventional units

4.3 Implications for Physical Understanding

Demystification: Constants aren't mysterious cosmic parameters but necessary computational tools for measurement translation.

Unification: All fundamental relationships reduce to universal state equivalences at the Planck scale, with constants providing the measurement interface.

Simplification: Complex equations often simplify dramatically when viewed as universal state computations with scaling interfaces.

5. Applications and Examples

5.1 Blackbody Radiation

Stefan-Boltzmann Law: Traditional: σ = 2π⁵k⁴/(15c²h³)
Dual-processing view: σ = K_Hz⁴ × Hz_kg × (2π⁵/15)

The complex constant structure encodes: temperature⁴ → frequency⁴ → mass → intensity scaling.

Planck's Law: Traditional: B(f,T) = 2f³h/c²(e^(hf/kT) - 1)
Dual-processing view: B(f,T) = 2f³ × Hz_kg/(e^(f/(T×K_Hz)) - 1)

The constants encode frequency→mass conversion (numerator) and frequency/temperature ratio (exponential).

5.2 Hawking Temperature

Traditional: T_H = ℏc³/(8πGM k_B)
Dual-processing view: T_H = mass_Freq × Hz_K

A black hole's mass directly determines its characteristic frequency, which directly corresponds to its temperature. The traditional formula obscures this simple relationship under layers of unit conversion.

5.3 Gravitational Physics

Every gravitational calculation actually performs the computation at Planck scale:

• Convert masses to Planck mass ratios
• Convert distances to Planck length ratios
• Compute force relationships with these dimensionless quantities
• Scale result back to desired units

G is the complete computational pipeline for this process, not a fundamental "strength" of gravity.

6. Broader Implications

6.1 Categorical Structure of Physics

This framework suggests that physics has a categorical structure where:

• Objects are projections of the universal state onto measurement axes
• Morphisms are the fundamental relationships between these projections
• Constants are the functors that translate between measurement categories

6.2 Relationship to Established Mathematical Frameworks

Lie Group Theory: Captures the continuous symmetries between measurement axes, but doesn't reveal the underlying universal state structure.

Buckingham π Theorem: Identifies dimensionless combinations that eliminate scaling artifacts, revealing universal state relationships, but doesn't explain why this works.

Category Theory: Provides the complete mathematical foundation for understanding measurement as projection and scaling of universal states.

6.3 Pedagogical Revolution

Teaching physics with this perspective would:

• Eliminate the mystery surrounding fundamental constants
• Reveal the deep unity underlying apparently different physical phenomena
• Provide intuitive understanding of complex relationships
• Connect physics to information theory and computation

7. Conclusion

Fundamental constants are not mysterious cosmic parameters but computational interfaces that enable translation between our arbitrary measurement conventions and the Planck scale where physics actually operates. Each constant encodes both input processing (encoding quantities to natural units) and output processing (decoding results to measurement axes).

This perspective reveals that:

1. All physics calculations occur at the universal state level using either natural scales involving time or Planck-scale relationships
2. Constants provide the computational infrastructure for measurement translation
3. Physical "laws" are actually measurement relationships made possible by these translation interfaces
4. The apparent complexity of physics often masks underlying simplicity at the universal state level

Recognizing constants as dual-role computational operators opens new avenues for understanding the fundamental unity of physics and suggests that what we call "fundamental physics" is really the study of measurement translation between human conventions and natural computational substrates.

The implications extend beyond physics to information theory, computation, and our understanding of measurement itself. If physical reality operates computationally at the Planck scale, then constants represent the API through which macroscopic measurement systems interface with this computational substrate.

References

1. NIST CODATA values and fundamental constants documentation
2. Planck, M. (1899). "Zur Theorie des Gesetzes der Energieverteilung im Normalspektrum"
3. Wheeler, J.A. & Zurek, W.H. (1983). "Quantum Theory and Measurement"
4. Baez, J. & Stay, M. (2011). "Physics, Topology, Logic and Computation: A Rosetta Stone"
5. Computational analogies in biological information processing systems

Keywords: fundamental constants, computational physics, universal state, Planck units, measurement theory, categorical physics, input-output processing, encoding-decoding, morphisms, dimensional analysis