The Fine-Structure Constant as a Scaled Quantity

TL;DR

This paper reinterprets the fine-structure constant alpha as a scale-dependent structural ratio emerging from the intersection of classical electromagnetism, quantum mechanics, and relativity, rather than a fundamental constant.

Contribution

It offers a new perspective on alpha as a contingent structural ratio, emphasizing its dependence on the intersection of multiple physical scales and correcting its traditional view as a fundamental constant.

Findings

Alpha arises at the intersection of classical, quantum, and relativistic scales.

Expressing laws in canonical form clarifies alpha's scale-dependent nature.

The running of alpha in QED supports its status as a scale-dependent coupling.

Abstract

The fine-structure constant alpha approximately 1/137 is traditionally regarded as a fundamental dimensionless parameter. I argue instead that alpha is a scaled quantity that arises only where the structural scales contributed by classical electromagnetism (e), quantum mechanics (h-bar), and special relativity (c) intersect. None of these theories, taken individually, supplies the independent scales required to define alpha. The constant first appears when relativistic corrections are added to the Schrodinger-Bohr description of hydrogen (Sommerfeld), and it becomes the structural coupling in quantum electrodynamics, where quantum and relativistic effects modify the classical electromagnetic interaction. Expressing the governing laws in canonical form reveals this dependence and eliminates representational artifacts that make alpha appear fundamental. The running of alpha in QED further demonstrates its status as a scale-dependent coupling rather than a universal constant. I conclude that alpha is a domain-specific structural ratio reflecting contingent relationships among independent physical scales.