I understand the iron fillings become little magnets all pointing in the same north south direction similar to the spin aligned electrons in the permanent magnet.
Similarly, a compass near a wire traces out the magnetic field lines ie North/South.
My question is how do I reconcile the fact that...
I know that the Action has units Energy·time or Momentum·position. A second fact is that the derivative of the action with respect to time is Energy and similar with momentum-position, consistent with a units ie. dimensions check.Is it a coincidence that both are Noether conserved quantities...