This immediately removes the problem of electron self-energy giving an infinity in the energy of an electromagnetic field.
An electron particle does not naturally fit in to the theory: should a point charge see the effect of its own field?
They reconsider the fundamental problem of a collection of point charges, taking up a field-free action at a distance theory developed separately by Karl Schwarzschild,[2] Hugo Tetrode,[3] and Adriaan Fokker.
Wheeler and Feynman propose to develop these equations into a relativistically correct generalization of electromagnetism based on Newtonian mechanics.
[6]: 171 First, in a non-instantaneous action at a distance theory, the equal action-reaction of Newton's laws of motion conflicts with causality.
Wheeler and Feynman postulate the "universe" of all other electrons as an absorber of radiation to overcome these issues and extend the direct interaction theories.
They considered all the charged particles (emitters) present in our universe and assumed all of them to generate time-reversal symmetric waves.
Indeed, it is always possible to reverse the time direction by simply exchanging the labels emitter and absorber.
[7]: 52 Wheeler and Feynman claimed that thermodynamics picked the observed direction; cosmological selections have also been proposed.
is the speed of light), after the emission (retarded solution), and other waves, which will arrive at the same place at the instant
The sum of the two, however, results in causal waves, although the anti-causal (advanced) solutions are not discarded a priori.
Alternatively, the way that Wheeler/Feynman came up with the primary equation is: They assumed that their Lagrangian only interacted when and where the fields for the individual particles were separated by a proper time of zero.
So since only massless particles propagate from emission to detection with zero proper time separation, this Lagrangian automatically demands an electromagnetic like interaction.
One of the major results of the absorber theory is the elegant and clear interpretation of the electromagnetic radiation process.
A charged particle that experiences acceleration is known to emit electromagnetic waves, i.e., to lose energy.
This first interpretation, however, is not completely satisfactory, as it leads to divergences in the theory and needs some assumptions on the structure of charge distribution of the particle.
) is then If we sum the free-field term of this expression, we obtain and, thanks to Dirac's result, Thus, the damping force is obtained without the need for self-interaction, which is known to lead to divergences, and also giving a physical justification to the expression derived by Dirac.
This model still exists in spite of recent astronomical observations that have challenged the theory.
[11] Stephen Hawking had criticized the original Hoyle-Narlikar theory believing that the advanced waves going off to infinity would lead to a divergence, as indeed they would, if the universe were only expanding.
Again inspired by the Wheeler–Feynman absorber theory, the transactional interpretation of quantum mechanics (TIQM) first proposed in 1986 by John G. Cramer,[12][13] describes quantum interactions in terms of a standing wave formed by retarded (forward-in-time) and advanced (backward-in-time) waves.
is It was originally demonstrated with computer algebra[18] and then proven analytically[19] that is a total time derivative, i.e. a divergence in the calculus of variations, and thus it gives no contribution to the Euler–Lagrange equations.
Thanks to this result the advanced potentials can be eliminated; here the total derivative plays the same role as the free field.
[20][21][22] Also, this formulation recovers the Darwin Lagrangian, from which the Breit equation was originally derived, but without the dissipative terms.
[23] Furthermore, Moore showed that a model by Feynman and Albert Hibbs is amenable to the methods of higher than first-order Lagrangians and revealed chaotic-like solutions.
[24] Moore and Scott[16] showed that the radiation reaction can be alternatively derived using the notion that, on average, the net dipole moment is zero for a collection of charged particles, thereby avoiding the complications of the absorber theory.
[citation needed] As mentioned previously, a serious criticism against the absorber theory is that its Machian assumption that point particles do not act on themselves does not allow (infinite) self-energies and consequently an explanation for the Lamb shift according to quantum electrodynamics (QED).
Ed Jaynes proposed an alternate model where the Lamb-like shift is due instead to the interaction with other particles very much along the same notions of the Wheeler–Feynman absorber theory itself.
Jaynes has shown that it is easy to get both spontaneous emission and Lamb shift behavior in classical mechanics.
[26] This model leads to the same type of Bethe logarithm (an essential part of the Lamb shift calculation), vindicating Jaynes' claim that two different physical models can be mathematically isomorphic to each other and therefore yield the same results, a point also apparently made by Scott and Moore on the issue of causality.
[citation needed] In hindsight, the relationship between retarded and advanced potentials shown here is not so surprising in view of the fact that, in quantum field theory, the advanced propagator can be obtained from the retarded propagator by exchanging the roles of field source and test particle (usually within the kernel of a Green's function formalism).