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Comment by emucontusionswe | Hacker News Reader

These physicists observations won't achieve anything other than to corroborate the existing hypothesis. Proof requires a lot more than just observation.

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There are no physicists' observations here, as I get it, it is all theoretical work, which is essentially mathematics. It is not rigorous mathematics, otherwise we would actually have a proof, but just a proposed reasoning that in time might be made rigorous and become a real proof. Future will tell us.

It's not physics, it's just a reformulation of the problem into linear algebra with a new intuition about why it should be true, namely that if it were not true, then we'd be able to observe imaginary energy levels.

Does the intuition hold if violations are sufficiently rare, large, etc?

If the intuition you're referring to is the idea of finding a self-adjoint operator with eigenvalues exactly corresponding to the nontrivial zeroes, then yes. The existence of such an operator would guarantee that the zeroes are all on the critical line.

If you're referring to the heuristic arguments for why their proposed not-quite-self-adjoint operator should have only real eigenvalues, then no.

People really should try reading articles before commenting.

yeah, physics proofs (and the scientific method in general) rely on empirical data whereas mathematical proofs rely on deductive reasoning from existing proven statements. It's literally the opposite approach.

The article makes no mention of any proposed experiments. It sounds like the physicists are just using their understanding of the mathematics of quantum physics along with their intuition about such physical systems to guide the search for a rigorous proof. (cf. the article's discussion of PT-symmetric matrices)

good point, I just re-read the article and you're right. They must be approaching the problem from a theoretical basis.

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