Mass-energy equivalence and the gravitational redshift: Does energy always have mass?

TL;DR

This paper challenges the common interpretation that all forms of energy have mass, using thought experiments to show exceptions like electric potential energy in capacitors, aligning with electromagnetic phenomena like light.

Contribution

It demonstrates that not all energy types, such as electric potential energy, contribute to gravitational mass, refining the understanding of mass-energy equivalence.

Findings

Electric potential energy does not contribute to gravitational mass.

Light has momentum but no rest mass.

Energy's contribution to mass depends on its nature and context.

Abstract

One of the most widespread interpretations of the mass-energy equivalence establishes that not only can mass be transformed into energy (e.g., through nuclear fission, fusion, or annihilation) but that every type of energy also has mass (via the mass-energy equivalence formula). Here, we show that this is not always the case. With the help a few thought experiments, we show that, for instance, the electric potential energy of a charged capacitor should not contribute to the capacitor's gravitational rest mass (while still contributing to its linear momentum). That result is in agreement with the fact that light (ultimately, an electromagnetic phenomenon) has momentum but not rest mass.