Fundamental Challenges:Circular Self-Referential in Quantum Field Theory

Title: Fundamental Challenges: Circular Self-Reference in Quantum Field Theory

Author: BÉO - Engineer, Independent Researcher

Publication Date: January 18, 2026

Introduction

This research analyzes the logical structure of Quantum Field Theory (QFT) and demonstrates the existence of circular self-reference A⊢B⊢A - a serious violation of the standards for valid deductive systems when QFT is claimed to be a "foundational theory".

Main Issue

QFT uses assumptions (such as vacuum stability, conservation laws) to derive conclusions, but then uses these very conclusions to validate the initial assumptions. This is the logical fallacy of "petitio principii" (begging the question) in formal logic.

Three Specific Points of Analysis

1. Vacuum Instability: Vacuum energy E → ∞ before renormalization, only becomes "stable" after technical correction

2. Acausality:QFT replaces actual causal mechanisms with probability amplitudes

3. Infinities from Point Definition: Particles defined as δ(x) generate divergences requiring treatment

Mathematical Analysis

Renormalization uses the expression m_physical = m_bare + δm where both terms diverge (∞-∞), violating standard rules of real analysis. The parameter m_bare is "backward defined" from the desired result rather than independently determined.

Case Study: Large Hadron Collider

Appendix B analyzes the circular structure in LHC experiments ($10+ billion): LHC Design → Measurement → Tuning 19+ free parameters → "Confirmation" of QFT. This is a closed loop where results are used to validate assumptions.

Conclusion

• QFT works excellently as a "tool" (accuracy 10⁻¹² in QED)
• - But lacks a solid "logical foundation" when claimed as foundational theory
• - Empirical success ≠ Logical validity
• - Need to distinguish "instrumental success" from "foundational validity"

Important Note

This research does NOT claim QFT is "wrong" or "useless". The purpose is to clarify logical boundaries and question foundational status, not to deny the instrumental value and scientific achievements of QFT.

Fields: Theoretical Physics, Formal Mathematics, Philosophy of Science

Level: Foundational

Status: Not peer-reviewed - Open for community review

License: CC BY 4.0

Contact: beo@beolabs.org

Reference DOIs:

- Section Zero Framework: 10.5281/zenodo.18063226

- Falsification of Acausality: 10.5281/zenodo.18150426

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