Over hundreds of years the conservation of energy and momentum in a closed System was proven. 100 years ago, Emmy Noether showed that these fundamental laws arise from the following facts and vice versa: - Homogenity in time (i.e. physical laws will be the same independent of the time where physics take place) leads to energy conservation - Homogenity in space leads to momentum conservation
Now I have heard that quantum field theory in curved spacetime does not contain energy and momentum conservation (Why?). Also in the theory of Phonons I have seen that there are existing single interactions with no momentum or energy conservation.
But almost every physical Research states that energy and momentum is conserved; even in single quantum mechanical interactions like electron + positron -> photon.
Can it be that there might be interactions on Quantum Level where energy and momentum is not conserved?