Ask Ethan: Where Is The Line Between Mathematics And Physics?
“Where does one draw the line between abstract mathematics and physics? Is Noether’s Theorem part of the scientific corpus of knowledge, or the mathematical? What about Maldacena’s conjecture?”
We all know that one of the reasons physics is such a powerful science is because of its predictive power. If you give a physicist the equations governing your system, and the right initial conditions, they can tell you exactly how it will evolve arbitrarily far into the future, limited only by the uncertainty built into the equations themselves. But not everything is purely determined by the math of the equations. You don’t have to go to a super-advanced example to see that, either. Give me a projectile in motion, tell me its position and velocity, and the equations you get from Newton’s laws give you two possible answers for where-and-when it will hit the ground. But only one of those answers is correct! How can you tell? It requires more than just mathematics on its own; it requires you to know something about your Universe.