Why the Concept of Potential Energy Must Be Frame Invariant

In recent years, there have been a number of articles published concerning whether or not potential energy (PE) as defined in mechanics is invariant under Galilean transformation. This essay addresses that issue in a different, more fundamental and elegant way than has been done thus far. It recognizes that a considerable change in the concept of PE has occurred over the last century, mostly as a result of both the special and general theories of relativity. We will show, by simple argument, that PE is Lorentz invariant, even if it is not a rigorously proper relativistic quantity. Although PE is an extremely important classical (i.e., pre-relativistic) theoretical device, it depends on the positions of the interacting bodies at any and every moment. Simply put, if the relative position of any constituent changes, the corresponding interactions must change instantly, and that violates special relativity. In general relativity, PE is not even a well-defined concept.