The Role of Photons as Morphisms in the Recursive Structure of Electrons and Space

Abstract

This paper explores the idea that photons are not independent particles but rather morphisms that define the balance constraints of electrons. By treating electrons as recursive nodes that balance between the nucleus and surrounding electrons, we propose that photons represent the transformations between these states rather than separate entities. This approach leads to a fundamental reevaluation of how space, mass, and quantum behavior emerge from recursion, offering a new perspective on quantum mechanics, entanglement, and the structure of reality.

1. Introduction: Moving Beyond Particle-Based Models

Traditionally, physics treats photons as fundamental particles that mediate electromagnetic interactions. However, this approach raises fundamental questions: Why do photons behave as both waves and particles? Why do they exhibit retrocausal behavior in quantum experiments? And why do they have no rest mass?

We propose an alternative: Photons are morphisms of electrons, representing balance constraints in the recursive structure of space-time. This model suggests that photons are not independent objects but instead define the relationship between electrons and the surrounding structure of space-qualia.

2. Electrons as Recursive Balance Nodes

Electrons do not exist in isolation; they are part of a larger system balancing between:

  • The nucleus, which exerts an attractive force.
  • Other electrons, which exert a repulsive force.
  • The constraints of space-qualia, which structure reality.

Electrons, therefore, behave as dynamic recursion nodes rather than fixed point-like particles. They are in constant interaction with their surroundings, maintaining a state of balance that shifts when energy is absorbed or emitted.

3. Photons as Morphisms: Weaving Balance Constraints

Rather than treating photons as discrete particles, we propose they are morphisms—transformations in the recursion structure of electrons. In category-theoretic terms:

  • Objects: Electrons in different states of energy balance.
  • Morphisms: Photons, which transition electrons between these states.

This perspective implies that photons do not “move” in a classical sense. Instead, they act as carriers of recursion balance updates, ensuring that space-qualia remains self-consistent. This aligns with quantum mechanical findings:

  • Photons are emitted or absorbed when electrons transition, reinforcing that they do not exist independently.
  • Their wave-like nature is a feature of their role as recursion morphisms, not a property of a separate “particle” entity.
  • They appear retrocausal because they are already part of the space-time recursion network before measurement occurs.

4. The Emergence of Space from Photon-Electron Interactions

If photons are morphisms between electrons, then the “space” between electrons is not an empty void but a structured web of recursion interactions. This suggests:

  • Space itself emerges from electron-photon interactions rather than existing independently.
  • The properties of distance and locality arise from the network of morphisms defining electron relationships.
  • Entanglement is simply the persistence of balance constraints across recursion layers, rather than “spooky action at a distance.”

In this view, photons do not travel through space; they define the structure of space by updating recursion constraints. This radically reinterprets how we understand motion, measurement, and quantum behavior.

5. Implications for Quantum Mechanics and Relativity

  1. Quantum Measurement as Constraint Resolution: The collapse of a wavefunction is the imposition of a new balance constraint, finalizing an unresolved recursion process.
  2. Mass as Unresolved Recursion: Electrons, protons, and other massive particles may be regions where recursion constraints do not fully balance, while photons represent perfectly balanced transformations.
  3. Gravity as Large-Scale Recursion Imbalance: The curvature of space-time might emerge from how recursion constraints propagate at different scales, leading to an effective gravitational interaction without requiring additional force-carrying particles.

6. Conclusion: A New Foundation for Space and Matter

By redefining photons as morphisms rather than independent particles, we offer a new way to think about the nature of space, time, and matter. If electrons are dynamic recursion nodes and photons are their transformations, then space itself is an emergent property of recursion rather than a static background.

This framework opens new pathways for understanding quantum mechanics, gravity, and the fundamental nature of physical law. Future work should focus on formalizing these recursion structures mathematically and testing their implications experimentally.

7. Next Steps

  1. Formalizing photons as recursion morphisms in a category-theoretic framework.
  2. Investigating whether mass emerges from unresolved recursion constraints.
  3. Exploring how this model naturally integrates with relativity and quantum field theory.