Wheeler–Feynman absorber theory

Wheeler–Feynman absorber theory. It is a classical electrodynamics theory proposed in the 1940s that reformulates Maxwell's equations using only direct particle interactions, eliminating the concept of a free electromagnetic field. The theory posits that the radiation reaction force on an accelerating electric charge arises from the advanced waves emitted by all other charges in the future universe, acting as a perfect absorber. This time-symmetric framework aimed to resolve foundational issues like the Abraham–Lorentz force and influenced the development of quantum electrodynamics.

Overview and motivation

The theory was developed by John Archibald Wheeler and his student Richard Feynman as an attempt to construct a more satisfactory foundation for electrodynamics. It was motivated by long-standing paradoxes in classical theory, particularly the problematic nature of the radiation reaction and the infinite self-energy of a point charge. Wheeler and Feynman were inspired by earlier ideas from Ernst Mach and the work of Hugo Tetrode and Adriaan Fokker, who explored direct action at a distance theories. The central postulate is that an accelerating charge interacts directly with all other charges in the universe, with the combined response of those charges—acting as a perfect absorber—providing the damping force. This approach eliminates the independent electromagnetic field as a dynamical entity, making the theory explicitly time-symmetric by incorporating both retarded and advanced solutions to Maxwell's equations.

Mathematical formulation

The formulation begins with the Liénard–Wiechert potential for a collection of point charges. The total potential at a particle is taken as half the sum of the retarded and advanced contributions from all other particles. The key equation for the force on the *i*-th particle involves summing over all other particles *j*. A critical mathematical step is the derivation of the absorber condition, which states that the total advanced field from all particles in the future universe perfectly cancels the free advanced field of the source, leaving only the familiar retarded radiation. This condition relies on the assumption that the universe is a perfect absorber, meaning all radiation is eventually absorbed. The analysis uses Green's function methods and relies on specific cosmological assumptions about the distribution of matter in the universe.

Key results and implications

A primary result is the derivation of the Abraham–Lorentz–Dirac force from purely time-symmetric interactions, thereby explaining radiation damping without self-interaction. The theory provided a novel interpretation of temporal asymmetry, suggesting the observed dominance of retarded radiation is not a fundamental law but a statistical consequence of the absorber condition. It directly influenced Feynman's later work on the path integral formulation of quantum mechanics and his diagrammatic approach to quantum electrodynamics. The concept of using both advanced and retarded solutions also found applications in the study of black holes and gravitational waves within general relativity.

Relation to other theories

The theory is a direct descendant of earlier action at a distance proposals by Carl Friedrich Gauss, Bernhard Riemann, and Hendrik Lorentz. It shares philosophical similarities with Mach's principle in its relational view of inertia. In quantum field theory, it connects to the Feynman propagator, which also incorporates both advanced and retarded components. The absorber idea was later revisited in the transactional interpretation of quantum mechanics proposed by John G. Cramer. It also relates to modern research on precognition in theoretical physics and studies of cosmological horizons.

Criticisms and challenges

The most significant criticism concerns the absorber condition, which requires specific, arguably *ad hoc*, assumptions about the universe, such as perfect absorption and a particular distribution of matter. Critics like Paul Dirac and Albert Einstein questioned its physical plausibility. The theory also struggles to account for a non-absorbing universe or one with significant amounts of dark energy. Furthermore, its extension to quantum electrodynamics was largely superseded by the more successful and standard renormalization techniques developed by Julian Schwinger, Sin-Itiro Tomonaga, and Freeman Dyson. Despite its elegance, it remains a minority interpretation due to these conceptual and practical difficulties.

Category:Theoretical physics Category:Electromagnetism Category:Physics theories