What is energy?
I'm kind of struggling with the concept of energy. A particle in a conservative field has kinetic and potential energy (E=T+U), but I can always choose an inertial frame where the motion of the particle is zero, which means I can change the the particle's kinetic energy by just switching frames. I can Simultaneously change the zero point of the potential energy arbitrarily. So In one inertial frame the particle has E>0, in another E=0, and still E<0 elsewhere. I used to think that a negative total energy meant that the particle was in a bound state and vice versa, but now I'm not sure sure. Is it more of a bookeeping device for ultimately calculating the trajectory of the particle? Whats going on?