Wheeler–Feynman absorber theory

Definition

Consider a system of point charges $q_1, \dots, q_N$ moving in Minkowski space. For each $j$ let $F_j^{\mathrm{ret}}$ and $F_j^{\mathrm{adv}}$ be the retarded and advanced Liénard–Wiechert fields of charge $j$, written as electromagnetic tensors. They come from the retarded potential and its time-reversed counterpart. In Wheeler–Feynman absorber theory:

1. the field acting on charge $i$ is $\displaystyle F^{(i)} = \sum_{j \neq i} \tfrac{1}{2}\left( F_j^{\mathrm{ret}} + F_j^{\mathrm{adv}} \right)$, with no self-interaction;
2. each charge obeys the Lorentz force law $m_i \dfrac{du_i^\mu}{d\tau} = q_i F^{(i)\mu}{}_{\nu} u_i^\nu$ with this field;
3. the system is a complete absorber: $\displaystyle \sum_{j=1}^{N} \left( F_j^{\mathrm{ret}} - F_j^{\mathrm{adv}} \right) = 0$ everywhere outside the absorbing matter.