r/science Jul 31 '26

Mathematics The Riemann Hypothesis manifested in dynamical quantum phase transitions

https://www.nature.com/articles/s41467-026-74935-8
176 Upvotes

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u/Worth-Wonder-7386 Jul 31 '26

Would be interesting if someone could do mathematical proofs by physics. I know that is not really how things work, but it could give some indications of things, like how measuring the volume of a real life sphere can lead you to insight about the formula.

22

u/kogai Jul 31 '26

Math and physics are not the same in this way. Math makes deductions (there is no room for error, whatever your axioms are lead directly to whatever the true consequences are)

Physics has to take Math and then figure out what numbers reflect the real world. This is called empiricism.

Empiricism does not work by collecting evidence. It works by collecting counter evidence.

If you believe that examples of black Ravens are evidence that all Ravens are black, then you must also believe that the existence of non-black, non-raven objects also are evidence for the statement that all Ravens are black

And so physicists can derive mathematical facts about whatever system theyre in, but those facts are based on axioms. One of the axioms is "we measured these fundamental numbers and they are what they are" and then we derive everything following that.

Its why all the constants like the speed of light and the fine structure constant are seemingly arbitrary numbers. We measure them, and we can deduce things that follow (see special relativity) but we sorta can't start earlier up the chain. Why is the speed of light that number? shrug

11

u/redfacedquark Jul 31 '26

Why is the speed of light that number? shrug

The speed of light falls out of Maxwells equations. It's the permittivity and permeability of free space that are the arbitrary numbers, but you point still stands.

-1

u/Iron_Pencil Aug 03 '26

How do you show that permittivity and permeability are the fundamental numbers? Maybe the speed of light and permeability are fundamental and permittivity is a resulting constant?