On the Mass of (Gravitational) Potential Energy

Abstract

In classical mechanics, when a body freely moves or is externally forced to move in a conservative force field, such as a planet moving away from a star or a weight lifted from the floor, its kinetic energy or the work done on it is converted and stored as potential energy. The concept of potential energy was developed to uphold the fundamental principle of conservation of energy. According to the widely accepted interpretation of mass-energy equivalence, every form of energy has mass. This leads to the natural questions: does potential energy have mass? And if so, where is that mass located? We will start by briefly reviewing the issue through an examination of some key literature on the topic. The current consensus is that potential energy gets stored in the field energy of the interacting system. As a result of mass-energy equivalence, the equivalent mass is distributed throughout the entire space in some manner. However, this presents some difficulties. Here, like some other scholars in the past, we show that it contradicts the principles of special relativity and argue that potential energy does increase the mass of the bodies composing the system. We present an accessible thought experiment that heuristically corroborates that view specifically for the gravitational potential energy. We finally speculate on how that mass increase is distributed among the interacting bodies.