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Is the fine-structure constant rational, or irrational? I have asked this question on the physics stack exchange, but I want to get some mathematicians' perspectives as well.

user107952
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    It is absurd to speak in these terms about experimental physics constants. – Lucian Sep 10 '14 at 02:00
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    Indeed: we don't know any physical constant exactly, only to several decimal places. And any rounded-off number's several decimal places is consistent with being rational or irrational. It's not even clear it's consistent to talk about the exact value of a physical constant even in theory. – Greg Martin Sep 10 '14 at 02:03

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There is no generally accepted mathematical formula for the fine structure constant. It may not even be a constant: see e.g. work of J.K. Webb et al.

Robert Israel
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