What question did this study set out to answer?

The aim is to evaluate an algebraic equation that predicts the fine structure constant, α⁻¹, without empirical references.

March 18, 2026Open Access

An Algebraic Value of α⁻¹ Indistinguishable from the Most Precise Measurement in Physics

Key Points

The aim is to evaluate an algebraic equation that predicts the fine structure constant, α⁻¹, without empirical references.
Developed an algebraic equation using π, factorials, and integers.
Compared the algebraic prediction to recent empirical measurements from Harvard's electron g-2 experiment.
Analyzed implications of the predicted value on the muon g-2 anomaly.
The predicted value of α⁻¹ = 137.035999177 is very close to the most precise measurement available.
The difference is just 11 parts per billion, indicating high precision.
The muon g-2 anomaly is not significantly affected by variations in α.

Abstract

A single algebraic equation containing no empirical inputs — only π, factorials, and the structural integer 4 — produces α⁻¹ = 137.035999177. This value falls 11 parts per billion (0.3σ) from the most recent and most precise determination of the fine structure constant: the Harvard electron g-2 extraction of Fan et al. (2023). At current experimental precision, the algebraic value and the measured value are indistinguishable. The muon g-2 anomaly is shown to be insensitive to α at the required level. The paper locates the algebraic prediction within the five competing experimental determinations and identifies the next-generation experiments that will confirm or falsify it.

An Algebraic Value of α⁻¹ Indistinguishable from the Most Precise Measurement in Physics

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Abstract

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