jwatersphd

I have some specific questions - as you remark, "Time translation symmetry gives conservation of energy. Space translation symmetry gives conservation of momentum. Rotation symmetry gives conservation of angular momentum." What I do not understand is why each of these is the case. Does it have to do with the nature of the equations for kinetic energy and/or E=M(c*c), where E and M are essentially equivalent, and the other variable, velocity, involves time? And velocity is the first differential of the function for displacement over time. But, were that the case, why would not displacement symmetry - change in position - likewise give conservation of energy? I'm just not following why these specific conservations arise paired with their symmetries. Thanks - jwatersphd