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In the experiments below, {{math|Δ''α''}} represents the change in {{mvar|α}} over time, which can be computed by {{mvar|α}}<sub>prev</sub> − {{mvar|α}}<sub>now</sub> . If the fine-structure constant really is a constant, then any experiment should show that
<math display="block">\frac{\ \Delta \alpha\ }{\alpha} ~~ \overset{\underset{\mathsf{~def~}}{}}{=} ~~ \frac{\ \alpha _\mathrm{prev}-\alpha _\mathrm{now}\ }{\alpha_\mathrm{now}} ~~=~~ 0 ~,</math>
or as close to zero as experiment can measure. Any value far away from zero would indicate that {{mvar|α}} does change over time. So far, most experimental data
These experimental results fit into a first-order nonlinear quantum theory that predicts the numerical value of the fine-structure constant with an accuracy of 5/10000 and that leads indeed to the invariance of <math>\alpha</math>.<ref>
{{cite journal
|last1=Reinisch |first1=G. |last2=Gazeau |first2=M.
|date=2016
|title=Role of nonlinearity in non-Hermitian quantum mechanics: Description of linear quantum electrodynamics from the nonlinear Schrödinger-Poisson equation
|journal=[[European Physical Journal Plus]]
|volume=131 |pages=16220
|doi=10.1140/epjp/i2016-16220-6}}</ref><ref>
{{cite journal
|last=Reinisch |first=G.
|year=2024
|title=Quantum-dot helium: An artificial atom with stunning nonlinear properties
|journal=[[Physics Letters A]]
|volume=498 |pages=129347
|doi=10.1016/j.physleta.2024.129347}}</ref><ref>
{{cite journal
|last=Reinisch |first=G.
|year=2024
|title=Mathematical definition of the fine-structure constant: A clue for fundamental couplings in astrophysics
|journal=[[APL Quantum]]
|volume=1 |pages=016111
|doi=10.1063/5.0200259}}</ref>
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