About 5 years ago, while reading the chapter on optics in Feynman’s lectures, I started to wonder why the principle of least time is called a “principle” and not a “law” like Newton’s laws of motion. For a very long time I convinced myself that it has to do with the origins of the statement. If the statement/theory comes from observations about nature, we call it a law, like the law of gravity. Instead, if it starts out completely theoretically then we tend to call them a principle like the principle of least action. While I still believe in this explanation, I started to appreciate a new perspective that I’ve heard in this lecture (the following video starts at the relevant time stamp):
A principle is a universal law about universal laws. - David Deutsch
It makes a lot of sense! You can derive all the laws of ray optics from the principle of least time. Or in general, you can derive equations of motions (and Newton’s laws) from the principle of least action.
PS: If you have time, check out the entire video (at 1.5x atleast). David Deutsch talks about steady-state model of cosmology; the importance of discovering principles (with the example of the principle of conservation on energy); and about his constructor theory.