Prime Numbers, Isotropy, and Quantum Measurement: A Recursion-Based Perspective

Abstract

This paper explores the idea that quantum superposition is not merely an undetermined state but a recursive process searching for a prime-based isotropic distribution. Measurement, in this view, is an external constraint that collapses this recursion early, forcing a simpler resolution that satisfies local balance constraints rather than achieving an optimal isotropic state. By examining the role of prime numbers in wave interference, space-time recursion, and particle stability, we propose a novel framework for understanding quantum mechanics, measurement, and the fundamental structure of space-time.

1. Introduction: The Hidden Role of Prime Numbers in Physics

Prime numbers appear in wave interference, diffraction patterns, and self-organizing systems to approximate isotropy in higher dimensions. If space-time and quantum mechanics are fundamentally recursive structures, prime distributions may underlie the formation of stable quantum states.

A radical hypothesis emerges: Quantum superposition is a recursion process searching for an isotropic prime distribution, and measurement is the external constraint that collapses this search prematurely. This could provide a deeper explanation for quantum wavefunction collapse, probability distributions, and even the emergence of time.

2. Prime Numbers and Isotropic Distribution in Recursion Constraints

(A) Prime Numbers in Wave Interference and Diffraction

  • Prime-number-based spacings in diffraction and interference patterns lead to more uniform, non-repeating distributions.
  • Quasicrystals use prime-based lattice structures to form non-periodic but highly ordered diffraction patterns, maximizing isotropy.
  • Electron orbitals and quantum energy levels exhibit structures that resemble prime gaps, suggesting a fundamental connection between prime sequences and quantum stability.

(B) The Role of Primes in Recursive Balance Constraints

  • Recursive structures tend toward prime-distributed configurations to achieve maximum isotropy.
  • Stable fundamental particles may emerge from prime-based recursion constraints—unstable particles fail to find a prime-aligned balance and decay.
  • Quantum superposition may be a system dynamically searching for a prime-distributed recursion constraint before resolving.

➡ Prime numbers may encode fundamental recursion constraints that define quantum stability and space-time balance.

3. Quantum Superposition as a Recursive Search for Prime-Isotropic Constraints

(A) The Traditional View of Superposition

  • In standard quantum mechanics, superposition represents an unresolved quantum state existing in multiple configurations.
  • Measurement forces a system to collapse into a single definite state, seemingly at random.

(B) The Prime-Isotropy Hypothesis

  • What if superposition is actually a recursive search for a prime-based balance constraint?
  • Instead of randomly existing in multiple states, the system is actively resolving itself toward an isotropic configuration.
  • Prime-based recursion naturally minimizes interference and optimizes stability—making it a preferred end state.

➡ Quantum states may not be random superpositions but actively evolving recursion searches for prime-based isotropy.

4. Measurement as the Collapse of Recursion into a Simpler Constraint

  • Measurement introduces an external balance constraint, forcing the system into a locally stable but suboptimal state.
  • Instead of allowing recursion to resolve fully into an isotropic distribution, measurement collapses the system prematurely.
  • This explains why quantum probability distributions appear biased—certain states are more likely because they provide simpler local recursion balance.

➡ Measurement is a shortcut that locks a system into an easily satisfied constraint rather than allowing full recursion resolution.

5. Implications for Space-Time, Quantum Mechanics, and Particle Stability

  1. Fundamental particles may be stable because they align with prime-based recursion constraints.
  2. Quantum probabilities might reflect recursion constraint biases rather than pure randomness.
  3. Time may emerge as a recursion process seeking isotropic equilibrium.

6. Conclusion: A New View on Quantum Mechanics and Recursion

This framework suggests that quantum mechanics is not a fundamental theory but an emergent recursion process, where superposition represents an ongoing search for isotropic balance constraints. Measurement, instead of being a mysterious wavefunction collapse, is simply the imposition of a simpler, non-optimal recursion constraint.

By examining the role of prime distributions in recursion and isotropy, we may unlock new insights into the nature of quantum measurement, space-time emergence, and the fundamental structure of reality.

7. Next Steps

  1. Develop a mathematical framework for prime-based recursion constraints in quantum systems.
  2. Investigate whether mass and spin quantization follow prime-distributed recursion rules.
  3. Analyze how time emerges as a recursion search for prime-isotropic balance.

➡ If true, this could mean that reality itself is structured around prime-distributed recursion constraints! What should we explore next?