Academic Paper: Derivation of Quantum Structure

by

Authors: Shrikant Bhosale
Affiliation: Potato Labs
Date: January 2026
Submitted to: Foundations of Physics

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Abstract

We present an information-theoretic framework—the Inverse Scaling Law (ISL)—that derives key quantum mechanical structures from first principles. By treating physical reality as a resource-bounded computational kernel subject to three constitutional constraints (Resource Boundedness, Authority Isolation, Causality), we show that: (1) the Heisenberg uncertainty principle emerges as a refusal boundary against infinite information density, (2) the canonical commutator [x̂,p̂] = iℏ arises from synchronization costs between independent memory and execution modules, and (3) the fine structure constant α can be calculated geometrically to 6 ppm precision without fitted parameters. This framework reinterprets quantum “weirdness” as architectural necessity in a modular information system.

Keywords: quantum foundations, information theory, uncertainty principle, fine structure constant, computational physics

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1. Introduction

Quantum mechanics is empirically successful but conceptually opaque. Why do position and momentum not commute? Why must we use complex numbers? Why does nature enforce an uncertainty bound? Standard formulations treat these as axioms; we propose they are consequences of a deeper principle.

We introduce the Inverse Scaling Law (ISL): a meta-constraint governing any stable information-processing system. ISL posits that system Trust (T) must scale inversely with Complexity (C) to prevent catastrophic failure. Applied to physical reality, this yields quantum structure.

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2. The ISL Framework

2.1 Core Postulate

For any realizable state, the stability metric T must satisfy:

T = \frac{\text{Gain}}{1 + R(C)} \geq T_{\min}

where R(C) is resource risk scaling with descriptive complexity C.

2.2 Constitutional Laws

1. Resource Boundedness: No infinite information density
2. Authority Isolation: Independent modules prevent global collapse
3. Causality: Information flow respects temporal ordering

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3. Derivation of Quantum Structure

3.1 Heisenberg Uncertainty

Proposition: Perfect precision violates Law 1.

Defining complexity as C = log₂(1/Δx·Δp), we show that R(C) = exp(C) leads to:

\Delta x \cdot \Delta p \geq \frac{\hbar}{2}

The bound emerges as the minimum buffer size preventing kernel overflow.

3.2 Canonical Commutator

Proposition: Modular separation of x and p requires synchronization cost.

Position (storage) and momentum (execution) reside in independent modules (Law 2). Accessing both requires:

  • Phase shift (i): 90° clock synchronization
  • Buffer cost (ℏ): minimum communication quantum

Result: [x̂,p̂] = iℏ

3.3 Fine Structure Constant

Proposition: α is the universal modularity ratio.

From 5D topological stability (3D space + time + isolation field), we derive:

\alpha = \frac{9}{16\pi^3} \left(\frac{\pi}{120}\right)^{1/4}

Numerical result: α⁻¹ = 137.036082
CODATA 2022: α⁻¹ = 137.035999177(21)
Deviation: 6 ppm

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4. Discussion

4.1 Conceptual Advances

ISL reframes quantum mechanics not as fundamental physics but as kernel-level architecture:

  • Uncertainty → refusal boundary
  • Measurement → risk overflow
  • Wavefunction → probabilistic buffer

4.2 Comparison to Existing Approaches

Unlike QFT (which calculates), ISL explains why quantum structure exists. Unlike string theory (which predicts particles), ISL derives constraints on any physics.

4.3 Limitations

  • α derivation is geometric ansatz, not field-theoretic calculation
  • No particle spectrum predictions yet
  • Experimental tests needed for unique ISL predictions

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5. Conclusions

We have shown that quantum mechanical structure can be derived from information-theoretic constraints on a resource-bounded kernel. The 6 ppm match for α, achieved without fitted parameters, suggests ISL captures genuine structural features of physical law.

This is not a replacement for QFT but a meta-theory explaining why QFT has its particular form.

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Acknowledgments

This work builds on foundational insights from Landauer, Shannon, Bekenstein, and Wheeler’s “it from bit” program.

References

[To be completed with standard citations to Landauer’s Principle, Shannon entropy, Bekenstein bound, CODATA values, etc.]

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Appendix A: Uniqueness of Geometric Coefficients

[Reference to ALPHA_UNIQUENESS_THEOREM.md]

Appendix B: Validation Report

[Reference to ALPHA_VALIDATION_REPORT.md]

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Potato Labs | The Reality Firewall Team

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