The Fine-Structure Constant as a Projective Invariant: Lamb Shift and Schwinger Effect in a Pre-Geometric Framework

The Lamb shift and the Schwinger effect are among the most precise and conceptually challenging predictions of quantum electrodynamics. They are conventionally interpreted as consequences of vacuum fluctuations, radiative corrections, and non-perturbative instabilities of a dynamical quantum vacuum. While this interpretation achieves remarkable quantitative success, it leaves open fundamental questions regarding the ontological status of the vacuum and the origin of renormalization procedures.

In this work, we propose a unified reinterpretation of these phenomena within a relational pre-geometric description, in which all effective physical observables emerge from a non-injective projection of an underlying relational substrate. From this perspective, vacuum-related effects do not arise from physical excitations of an underlying field-theoretic vacuum, but from intrinsic limitations of the projection mapping relational configurations to effective spacetime descriptions.

  We show that the Lamb shift can be understood as projective spectral noise, reflecting the finite resolvability of highly localized interactions and the coarse-grained influence of unresolved relational modes. Similarly, the Schwinger effect is reinterpreted as a saturation phenomenon associated with the bounded capacity of the projection to transport relational flux under extreme field conditions, leading to a breakdown of injectivity and the emergence of new effective degrees of freedom.

A central result of this analysis is a unified structural interpretation of the fine-structure constant. Rather than appearing as an unexplained fundamental parameter, it emerges as an invariant ratio between projective resolution and relational flux capacity, governing both atomic-scale spectral corrections and strong-field instabilities.

This reinterpretation preserves the quantitative predictions of quantum electrodynamics while providing a coherent ontological account of its most subtle effects. It demonstrates that precision QED phenomena can be consistently embedded within a pre-geometric relational description, supporting the view that quantum field theories operate as effective descriptions of deeper projective constraints rather than as fundamental theories of the vacuum.