Why is energy not conserved in this situation Suppose there are three masses that are still relative to each other in space. They are positioned in an equilateral triangle. Let's accelerate one mass towards the other two with a force. The energy added to this system should be $F\cdot{ds}$. However, according to the particle that has been accelerated, the work done is double this amount assuming that the three particles are of the same mass. I don't think that I fully understand how does the conservation of energy really works.
 A: Conservation of energy occurs within a given reference frame.  If you change reference frames, you cannot use those rules.
A clear example of this occurs if you consider the energy of the system when considering the Earth and an airplane flying through the air.  From the perspective of an observer on the ground, the airplane has kinetic energy of $\frac{1}{2}m_{plane}v^2$, and the earth has 0 kinetic energy.  From the perspective of an observer on the plane, it is the plane that has 0 kinetic energy, and the earth has kinetic energy to the tune of $\frac{1}{2}m_{earth}v^2$.  Needless to say, given that $m_{earth}\gt\gt m_{plane}$, the two observers will disagree greatly on the numeric value for the system's kinetic energy.  However, if we consider changes in kinetic energy, both systems will find that energy is conserved (from their own perspective).
A: Ok I think there are 2 distinct problems here. firstly it is that I cannot apply the same equations for energy in an accelerating coordinate system. It only works for inertial reference frames. Secondly it is that even under galilean transformations work done is not (and doesn't need to be) invariant which is what was addressed
