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If the fine-structure constant alpha changes as the universe expands, the simplest description lets it follow a power of the scale factor, and the present drift rate is then the power index times the Hubble rate. Atomic-clock comparisons limit the drift to 6.20e-17 per year at two standard deviations (Rosenband et al. 2008). Converting with a Hubble rate of 7.16e-11 per year bounds the power index to 8.66e-07, and the same law then permits at most 6.06e-06 of fractional change in alpha between recombination and today, and at most 1.12e-07 across the 1.8 billion years since the Oklo natural reactors operated. These are computed bounds from stated assumptions, not measurements; the study is simulated in the sense that the frame prediction is evaluated arithmetically against published experimental limits.
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William Alexander Aldred (2026) studied this question.
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