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arXiv · 2609.32368

From Mass to Energy-Momentum: The Field-Theoretic Perspective on the Energy-Mass Relation

Patrick M. Duerr·J. Brian Pitts
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Abstract

The paper examines the energy-mass relation of Special Relativity (SR), its status and interpretation, through the lens of classical/non-quantum relativistic field theory. The latter arguably constitutes the fullest embodiment of SR as what Einstein labelled a "principle theory". It forms, we propose, the most appropriate perspective also for understanding the energy-mass relation. In a field-theoretic setting, the key notion is a system's energy-momentum (in local/differential or global/integral form, defined via a suitable energy-stress complex). The energy-mass relation then expresses the role that a system's _rest_-energy (provided it exists) plays as the functional counterpart of mass: thanks to important theorems, rest-energy qualifies as its field-theoretic generalisation or successor term. That is, while mass is dispensed with as a fundamental notion, rest-energy retains some---but not all---of its salient functional roles; for special cases, it turns out to be directly correlated with mass. In field theory as a general framework for more specific relativistic theories, energy-momentum replaces mass as the essential notion---a profound, yet often overlooked revision in basic physical concepts. Conservation in particular is guaranteed only for energy-momentum, but no longer for mass. In several regards, energy-momentum fuses energy, momentum and mass, with novel connections amongst them and concomitant physical effects. Situating the energy-mass relation within field theory is a surprisingly neglected, but deeply insightful vista for clarifying and philosophically reflecting on SR's foundations. The field-theoretic interpretation achieves a compelling inner coherence and unifying power, and ties it to the rich heuristic resources of field theory, crucial for post-1905 developments in physics.

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BibTeXRIS

Patrick M. Duerr, J. Brian Pitts. 2026-09-26. From Mass to Energy-Momentum: The Field-Theoretic Perspective on the Energy-Mass Relation. https://arxiv.org/abs/2609.32368

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