Last month I ran across an alleged quantum-gravitational bound on the fine structure constant (proposed by Shahar Hod) that is remarkably close to the actual value. I am somewhat surprised that it has received almost no public attention, but there are many examples of neglected ideas and observations, inside and outside physics.
The actual "bound" is ln(3)/(48pi). As I describe in the linked post, this work is descended from an episode in black hole physics from over twenty years ago, in which the quantity ln(3) showed up in the "quasinormal" resonant modes of charged near-extremal black holes. (Carl Brannen says the quasinormal modes are associated with excited unbound states, which makes sense since they describe Hawking radiation, i.e. a quantum escaping from the black hole.)
Today Scott Aaronson mentioned some results on how to efficiently distinguish three states of a qubit. I mused that maybe the current generation of "qubitzers" could take another look at the ln(3) mysteries, using tools from those results. (I spoke of "qutritzers", but I think technically this is not about qutrits, just about three states of a qubit.)
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