As an ex-physicist this is confusing, just because it seems like a profound challenge to Samuelson, Afriat, and the rest of revealed preferences, but pulls back at the last minute to preserve GARP by rationalizing these changes back into a preferences-oriented utility function. 

 So, why not just keep it as a potential energy term, and proceed the way physicists do, which is to use observations of outcomes to conjecture modifications and develop the theory? Doing so is also more amenable to accounting for sequencing, probabilistic outcomes, etc.