Relationships, Laws, and Reasons Why

I'm a big Vsauce fan (who isn't?)  In his recent video, Laws & Causes, Michael Stevens engages in his trademark smart and entertaining intellectual meanderings.  I really liked his bit about how just knowing about the relationships between variables doesn't actual explain the cause of the relationship itself.  However, I feel he really missed a golden opportunity in this video in his explaining of the "cause" of angular momentum.

True, simply labelling a phenomenon as "angular momentum" and understanding the relationship between the variables involved in not the same as understanding the cause of the conservation law.  But when he unpacks conservation of angular momentum in terms of forces and inertia (which he does a nice job of!), he actually took the explanatory arrow in the wrong direction!

It turns out conservation of angular momentum is not caused by torques, inertia, and forces as he implies.  It's actually the other way around!  All of Newton's Laws are simply manifestations of the existence of a couple of conservation laws (specifically Conservation of Linear and Angular Momenta).

Emmy Noether, 1882-1935

So, Vsauce, you should have taken that big brain of yours over to Emmy Noether who actually explained to us where conservations laws come from!  Turns out that although you can explain conservation of angular momentum in terms of forces, torques, and inertia, it really is the angular momentum that is the transcendent quantity that nature cares about.  So why does conservation of angular momentum exist?  Symmetry.



If you want a universe where the laws of nature are the same no matter which direction you face, then there must be a corresponding conservation law: angular momentum (thank you Noether's Theorem!).