Re:What Makes the Hardest Equations in Physics So Difficult?
by whatshisface on Tuesday January 16, 2018 @04:31PM
(#16162837)
One reason to think the physics would be interesting: it isn't every day that we can arrange macroscopic systems in ways where their small-scale behavior gets amplified enough for us to measure. Arranging a blowup in the Navier-Stokes equations would be a way to study atomic-scale physics on human scales - and, likewise, arranging a blowup (if one exists) in the QCD quark-gluon plasma equations would allow us to get unexpectedly sensitive measurements of particle-scale physics.
Re:What Makes the Hardest Equations in Physics So Difficult?
by pixelpoet on Tuesday January 16, 2018 @08:07PM
(#16164577)
A nice example of such a practical tool for microscopic analysis is X-ray crystallography, once you have the theory of Fourier transforms and lattices.
Re:What Makes the Hardest Equations in Physics So Difficult?
by Someone on Wednesday January 17, 2018 @02:41AM
(#16166185)
Your repeated use of the word ‘blowup’ makes me think of the way we get small-scale behavior amplified enough for us to see, hear, and feel: in atomic weapons.
There is a chance that understanding how quarks interact will give us even more powerful weapons (which might at one time be useful to blow up large incoming space rocks) or give us clean energy. How large that chance is is anybody’s guess.
Re:What Makes the Hardest Equations in Physics So Difficult?
by andrewflnr on Tuesday January 16, 2018 @08:21PM
(#16164656)
I guess if you're looking for pure mathematical abstraction, Navier-Stokes doesn't seem like the most interesting without the physics connection. But that's just me.
Re:What Makes the Hardest Equations in Physics So Difficult?
by adrianratnapala on Tuesday January 16, 2018 @09:57PM
(#16165114)
I suppose what is interesting is the very difficulties we have deciding if there are smooth solutions. It would be interesting if there are whole class of PDEs which are difficult in this way. And if there isn't, then what is special about the NS? That too, is interesting.
Re:What Makes the Hardest Equations in Physics So Difficult?
by andrewflnr on Friday January 19, 2018 @07:21PM
(#16191174)
Fair point, there.
What you are missing is that mathematicians are concerned about Navier-Stokes itself, as an independent entity in pure mathematics, not related to its physics correspondence.
I think it would be safe to say that everybody believes that even if Navier-Stokes does have a singularity in it, that there won't be any way to manifest that singularity in the real universe with our discrete atoms. But that still leaves the math question, and the possibility that even approximating the singularity may produce interesting physics.