Mass-Energy Equivalence in the Presence of External Potentials

ABSTRACT

The notion of mass goes back to at least Newton, but its meaning and definition has changed over the centuries. Specifically, the theory of relativity drastically changed our perspective with mass-energy equivalence, and the mass of a composite particle on a geodesic trajectory is now generally understood to be the sum of the mass of the constituents and internal binding energies. It was proven only recently that this definition is consistent with the equivalence principle. However, in the presence of external potentials the notion of mass becomes more complicated. Does a trapped atom weigh more than a free atom? Can the act of pushing a particle change its inertia? In this talk I will answer these questions by constructing a general covariant framework based on reparameterization invariance, which allows us to study mass from a symmetry perspective. We distinguish between inertial mass and proper mass (the generator of proper time translations), and relate them via the four-dimensional Legendre transform, thus yielding a novel mathematical definition of both inertia and gravitational mass applicable even in the presence of external fields. It is found that only scalar field interactions contribute to the inertial (gravitational) mass. Our framework not only clarifies the role of mass in physics, but also provides a method to couple non-free particles to gravity which may be used to describe table-top experiments with the aim to probe gravity on the quantum scale.

BIOGRAPHY

Niklas E. Önne is a PhD student in the group of Sofia Qvarfort at Nordita and Stockholm University. His research focuses on probing the interface of gravity and quantum mechanics in the low-energy regime using quantum technologies such as optical cavities and atomic clocks. Niklas earned his Master's degree in Physics from Uppsala University in 2025. His thesis research on the nature of mass was conducted as a visiting scholar in the group of Igor Pikovski at Stevens.

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