Eli5: Please explain the Stationary-action principle
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You’re essentially trying to find the shortest between between two points on a curved surface. A simple analogy is “how do I know I’m at the top of a (smooth) hill?” If you’re at the top, short steps are just about flat, but if you’re on the side of the hill, a short step might take you either uphill or downhill. Stationary action extends this to paths between two points, where the distance you have to travel is like the height of the hill. If your path is the shortest path, small deviations (short steps) won’t affect the distance (height) very much, but if your path isn’t the shortest path, small deviations will change the distance. Mathematically, it’s easier to figure out the path that doesn’t change lengths than the shortest path. The stationary action principle says those two paths are the same, so you might as well do it the easy way.
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