Forgive me if the title sounds ignorant, but I’m genuinely trying to understand this concept. Everything I’ve read about Noether’s theorem says basically the following: If a system remains the same (in some way) after a transformation, then there must be type of quantity or property in the system that remains constant.
But isn’t that just common sense, or already implied by the premise? As I understand it, it basically states that “If something is the same, then something about it has not changed”.
In: Physics
One thing you are missing is that the *way* the system is supposed to be symmetric (unchanged) may not have an obvious connection to the numerical quantity that stays constant (is conserved).
Example: that the laws describing a physical system are preserved by a change in time leads to the conservation of energy. I don’t think this link is obvious at all: if you told someone learning physics that conservation of energy is due to the physics of the system being the same at all times, that person is unlikely to say “yeah, that’s obvious”.
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