Testing My Theories

Read my article: The Search for FieldX – an update from May 9th, 2025, explaining the problem with the g-factor

Introduction

This article documents an attempt to calculate the electron and muon anomalous magnetic moments (commonly expressed as the \( g \)-factor) using two speculative theoretical frameworks I have been developing: Tugboat Theory and Nested Field Theory. These models propose, respectively, that inertia and relativistic effects arise from a delayed synchronization of field interactions (Tugboat), and that particles are not point-like but composed of self-nested, interacting field structures (Nested Fields). The calculations were carried out in collaboration with ChatGPT-4 to test whether these theories could offer an alternative explanation for the well-known discrepancies between Standard Model predictions and experimental measurements of the \( g \)-factor.

The result was clear: neither theory, in their current form, produced corrections of the right magnitude or sign to explain the anomalies. Both models, when applied to one-loop quantum electrodynamics (QED) corrections, resulted in deviations far too large to match the observed data — even with finely tuned parameters. These outcomes suggest that the present mathematical formulations of the theories are inadequate for this application.

However, the process itself has been valuable. By directly confronting a precise, measurable physical quantity, the theories were subjected to a real test — not just philosophical speculation. The fact that they failed in this context is not a final dismissal, but rather a signal that their mathematical foundations may require deeper refinement. With expert guidance — particularly in field theory, renormalization, and effective Lagrangian modeling — it may still be possible to reformulate these ideas in a way that yields subtle, testable effects without contradicting established results.

This is not a breakthrough, but it is a step forward: a narrowing of possibilities, a clarification of limits, and a sharpening of focus. This is how science proceeds.

Results and Evaluation

To assess whether Tugboat Theory or Nested Field Theory could explain the observed discrepancies in the electron and muon \( g \)-factors, I implemented numerical simulations based on one-loop quantum electrodynamics (QED) vertex corrections. In standard QED, the anomalous magnetic moment \( a = (g - 2)/2 \) arises from virtual photon and particle-antiparticle loop interactions. These corrections are precisely calculated and tightly constrained by both theory and experiment.

Multiple parameter sweeps were conducted for each theory, both independently and in combination. The results were consistent and conclusive: in all tested cases, the theoretical modifications introduced effects that were several orders of magnitude too large. While the experimental anomalies in the \( g \)-factor are on the order of \( 10^{-9} \) (muon) and \( 10^{-13} \) (electron), the calculated deviations due to the theories were on the order of \( 10^{-4} \) — a difference of at least five to nine orders of magnitude.

In short, the models not only failed to explain the anomalies but significantly overshot the required precision. Even in highly fine-grained simulations, neither theory was able to produce small enough corrections to match observed values without simultaneously breaking consistency with QED’s successful predictions.

Discussion and Future Directions

The main issue appears to lie in scale and sensitivity. The \( g \)-factor anomalies are among the most precisely measured quantities in all of physics. Any viable explanation must deliver corrections with accuracy better than one part in a billion, while simultaneously preserving the success of standard QED. The modifications proposed in this study — field delays and nesting-based form factors — introduce deviations that are far too large and insufficiently constrained by established principles like gauge invariance, renormalizability, or effective coupling limits.

Nevertheless, this failure does not preclude their relevance elsewhere. There are three areas where the core ideas of these theories may still offer valuable insights:

1. Inertia and Relativistic Effects: Tugboat Theory proposes that inertia arises from time-delayed field synchronization. This may have explanatory power in regimes such as rapidly accelerating systems or quantum gravity transitions.
2. Photon Propagation and Vacuum Structure: Nested Field Theory could be relevant in phenomena where vacuum texture affects particle behavior, such as Casimir effects or tired light models.
3. Modified Field Theories and Nonlocal Dynamics: These theories may be reworked into nonlocal or memory-dependent Lagrangians to uncover new predictions in less tightly constrained domains.

With expert collaboration in quantum field theory and Lagrangian modeling, it may still be possible to formalize these ideas into consistent, predictive frameworks.

Conclusion

This study was an exercise in scientific accountability: to test new theoretical ideas not just for novelty or coherence, but for predictive power. Tugboat Theory and Nested Field Theory did not survive the test of explaining the \( g \)-factor anomalies — and that is a result worth publishing. Negative results are part of the scientific process, and in this case, they serve as signposts pointing toward the limitations of current formulations and the need for deeper, more precise models.

The door is not closed. These ideas may yet find life in other domains — or they may inspire new concepts better equipped to bridge the gap between known physics and the unknowns that remain.

For now, the result is clear: these theories do not explain the \( g \)-factor. But the journey of theory testing has yielded insight, discipline, and a sharper sense of direction. And that, too, is progress.