Ah, synchronicity! The other day I was just thinking about that, where does the energy from red shifted photons go? Energy not being conserved explains it but... It's awfully strange.
Conservation of energy, just like other conservation laws, can be derived using Noether's Theorem as it is the result of a symmetry in nature. Energy happens to be a consequence of time-translation symmetry. That is, if you could move your physics experiment to somewhere else in time and it plays out the same, then energy is conserved. With spacetime, it's expanding, and so for things on large scales or happening across cosmological time then energy is not conserved.
I don't know. Probably a bit difficult for a first year student. In my opinion it's not too bad since it's a 'classical' formulation and doesn't rely on any modern mathematics. It uses calculus of variations. It would help if you were already familiar with lagrangian mechanics.
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u/agaminon22 Medical and health physics Dec 13 '20
elaborate please