The Electron Field as a Recursion Constraint Network: A New Perspective on Quantum Field Theory

Abstract

Quantum Field Theory (QFT) traditionally describes the electron field as a continuous mathematical entity, with electrons emerging as excitations of this field. However, if spacetime is not a passive background but instead an emergent structure shaped by recursion constraints among electrons, then QFT may require a reinterpretation. This paper explores the hypothesis that the electron field is not a smooth, continuous function but rather a discrete recursion network where electrons define space-time itself through morphisms (balance constraints). This perspective provides new insights into quantum entanglement, wavefunction collapse, and the universality of charge.

1. Introduction: Rethinking the Electron Field

In QFT, the electron field is treated as a fundamental, smooth field extending across all of spacetime. However, this perspective assumes that spacetime exists independently of the electron field.

Instead, we propose that:

  1. Electrons define the structure of space itself rather than merely existing within it.
  2. The electron field is not a continuous medium but a recursion constraint network, where each electron interacts with every other electron through balance constraints (morphisms).
  3. Spacetime is an emergent property of the recursion structure of electrons.

If true, this means that the behavior of quantum systems is governed not by probability amplitudes in a pre-existing space but by the need to satisfy recursion balance constraints.

2. The Electron Field as a Recursion Network

In a recursion-based framework:

  • Electrons are not independent particles but nodes in a self-balancing recursion structure.
  • Morphisms (balance constraints) connect electrons, defining the relationships between them and forming the fabric of spacetime.
  • The number of morphisms per electron represents the number of constraints that must be balanced, similar to the prime-based isotropic distributions found in higher-dimensional parastichy models.

➡ Space is not a pre-existing arena; it is generated dynamically by the recursion constraints between electrons.

3. How This Explains Quantum Behavior

(A) Superposition as a Recursion Process

  • Instead of representing an undefined state, superposition may be an active recursion process in which a system searches for a stable balance constraint.
  • The system remains in superposition until a recursion constraint resolves the search, producing an observable outcome.

(B) Quantum Entanglement as Shared Recursion Constraints

  • Two entangled electrons are not independent objects but parts of the same recursion network.
  • Measuring one electron does not “send information” faster than light; rather, it finalizes a recursion constraint that was already shared between them.

(C) Wavefunction Collapse as Recursion Constraint Resolution

  • Measurement does not destroy superposition—it finalizes a recursion state.
  • This means that quantum probabilities reflect the ease with which recursion constraints can resolve, rather than intrinsic randomness.

➡ Quantum mechanics is not fundamentally probabilistic—it is a reflection of recursion constraint resolution.

4. The Dirac Equation as a Recursion Constraint Equation

The Dirac equation governs electron behavior in QFT, incorporating:

  • Spinor solutions, which require a 720° rotation to return to identity.
  • Charge conservation, ensuring every electron has exactly the same charge.
  • Wavefunction evolution, describing how electrons propagate in space-time.

If electrons define space-time rather than existing within it, then:

  • The 720° rotation requirement might be a recursion artifact rather than a fundamental quantum effect.
  • Charge conservation emerges because all electrons participate in the same recursion balance structure.
  • The Dirac equation may not be describing motion through spacetime but rather the way recursion constraints evolve dynamically.

➡ The Dirac equation is not a field equation in spacetime—it is a recursion equation describing how constraints propagate.

5. Why Do All Electrons Have the Same Mass and Charge?

  • If electrons were truly independent, their charge and mass could, in theory, vary.
  • Instead, all electrons exhibit identical properties, suggesting they are part of a global recursion balance.
  • This means electrons are not distinct entities but fundamental nodes in the same recursion network.

➡ Electron identity is not a property of individual particles but of the recursion field itself.

6. Testing the Recursion Network Hypothesis

(A) Charge Quantization as a Recursion Effect

  • If charge is a recursion balance property, then deviations from quantization should correlate with disruption of the recursion field.
  • This might provide insights into charge anomalies in extreme conditions (e.g., near black holes).

(B) Quantum Entanglement as a Recursion Network Effect

  • If two entangled electrons share recursion constraints, then their behavior should reveal deeper network effects beyond standard quantum nonlocality.

(C) Gravitational Effects on the Electron Recursion Field

  • If spacetime is generated by the electron network, then extreme mass-energy distortions should affect how electrons maintain recursion balance.
  • Gravitational waves might not be ripples in spacetime itself but disturbances in the electron recursion structure.

➡ If gravity emerges as a recursion balancing process, it should show subtle deviations from classical general relativity in extreme conditions.

7. Conclusion: Rethinking the Foundations of Physics

If the electron field is actually a recursion constraint network, then:

  1. Space-time is emergent, generated by electron-electron morphisms.
  2. Quantum mechanics is a description of recursion constraint resolution, not pure randomness.
  3. Gravity may be a large-scale recursion balancing effect rather than a separate force.

This approach could bridge the gap between quantum mechanics and general relativity by showing that both emerge from the same underlying recursion structure.

8. Next Steps

  1. Develop a recursion-based reformulation of the Dirac equation.
  2. Investigate whether charge quantization and mass ratios emerge naturally from recursion constraints.
  3. Explore how space-time curvature emerges from distortions in the electron recursion network.

➡ If true, this could fundamentally redefine our understanding of reality—not as particles in space-time, but as recursion constraints dynamically shaping the structure of existence itself.