Develop a theoretical description of particle–field interactions

Develop a set of governing equations that describe the mechanical–electromagnetic interaction between charged particles and the electromagnetic field, namely the coupled process of particle motion and electromagnetic field propagation, to replace non-relativistic instantaneous action-at-a-distance models in microscopic thermodynamic analyses.

Background

The paper argues that standard mechanical and electromagnetic formulations describe only actions under prescribed conditions (particles moving in a given field, or fields radiated by a given particle motion), not true interactions where particle dynamics and field evolution are coupled.

The author emphasizes that instantaneous action-at-a-distance potentials used in Hamiltonian mechanics are non-relativistic and inadequate, and highlights unresolved issues such as radiation reaction and the Lorentz–Dirac equation as reflections of the missing interaction framework.

References

The trouble is that at present we have no description of particle-field interactions.

— On the origin of irreversibility  (2509.20117 - Matolcsi, 24 Sep 2025) in Section 2 (Action and interaction), end of item 4

although Tumulka claims that satisfactory equations for photon trajectories have not been found yet.

— Hidden Variables in Quantum Mechanics: A Journey Into de Broglie-Bohm Pilot-Wave Theory  (2608.18829 - Oldofredi, 19 Aug 2026) in Section 7.1, “Stochastic Models: Bell-type Quantum Field Theory and Recent Advancements”