Imagine an event where, for example, two equal mass but oppositely charged objects approached each other from rest under the influence of the electrical force of attraction between them. In terms of energy we can say that the loss of electrical potential energy is equal to the gain of kinetic energy. Now imagine this event being observed by two observers one at the centre of mass frame, the second in the non inertial frame of one of the accelerating particles. For simplicity let all velocities be low enough to be considered as non relativistic. Now consider one point in the approach, where from the centre of mass frame each object has velocity v. From this frame the total KE of the system would be calculated as MV2, where M equals mass of each object. From the non inertial frame the speed of approach of the second object would be seen as 2v and the KE calculated as 2Mv2 In other words the observed KE depends on the frame of the observer But shouldn't both observers agree about the change of PE? If so from energy conservation this implies the gain of KE should be the same for all observers. Obviously I'm overlooking something here? Any suggestions please?