In which field of physics can I find a solution to this question:
What is energy, and why and when is it conserved?
When I asked a similar question to my professors and peers, they said, 'We discovered the conservation law through experimentation.' (In the first place, they don't even provide a proper definition of energy.)
My thoughts are like, 'Really? How did scientists conduct experiments to confirm that this strange formula (1/2 * m * v^2 for kinetic energy and the concept of potential energy, assuming that all mechanical energy is either kinetic or potential) actually conserves? How did they even come up with this formula and assert that it’s conserved?'
I have a similar doubt about momentum and angular momentum.
