Are momentum and energy together conserved?
Your question says that momentum and energy are together conserved.
The question does not specify if you are asking about a closed system's (like a galaxy cluster) total energy level or about micro interactions (particle) energy level as per QM.
- First, let's take the micro interactions as per QM:
This is only true for an elastic interaction, like elastic scattering. It is the typical case when a photon hits an atom and the photons energy is conserved, only its direction is changed. Rayleigh scattering is like that.
For an inelastic interaction, like inelastic scattering, Compton scattering, only momentum can be conserved, but energy not. When a photon hits an atom, and the photon gets inelastically scattered, its energy will change, but its momentum could be conserved.
Please see here:
- Now let's take a closed system's total energy level:
Though our universe is not closed, so its energy level is not conserved, we can select areas of space, like a galaxy cluster, which we can say is a local area as per GR, and so it's total energy level will be conserved.