# Does gravitational radiation have a formalism similar to Wheeler-Feynman electrodynamics?

Binary systems radiate energy away in gravitational waves as the orbits of the two masses spiral in towards each other. My understanding of gravity is that we think of it as a mediator of particle-particle interactions. If we expect there to be a massless force carrying boson for gravity, then we expect gravity mediates interactions between masses. However, if one considers a binary system assuming no other masses in the system, general relativity still predicts gravitational waves.

In comparison electrodynamics has a similar case when modeling a particle in the presence of the purely retarded field of another particle. One must include the radiation reaction self-force in order to get the correct equations of motion as we observe. However Wheeler-Feynman electrodynamics allow us to think of this model not as a general model for two interacting particles but a model in which two particles interact in the presence of fixed charges (absorbers) stationed an infinite distance away in all directions. In this way the field only mediates interactions between charges, the "field" itself cannot carry energy off to infinity if there are no charges at infinity.

I realize Wheeler-Feynman still has some issues when quantization as there is no mass normalization which is required for the lamb shift. I've read there are corrections/tricks to make it work though. I'm not concerned with quantization as much as I am with a classical picture in which an interaction is mediated by a field or in this case a metric. It seems problematic that gravity can carry radiation off to infinity with no matter capable of absorbing it at infinity. The traditional approach to Maxwell's laws is equivalent to the stipulation in Wheeler-Feynman electrodynamics that all "free" radiation is absorbed by matter not explicitly included in the model. It seems to me gravity should have such a formulation if we believe it to mediate interactions between particles. I realize that relativity implies a mass energy equivalence and the solution might be that spacetime itself can contain the energy with no contradiction. I would like to see an argument for this if this is indeed the case.

Since gravity doesn't have a superposition principle like E&M, I don't get how one would construct such a theory. Does this mean a Wheeler-Feynman formulation of gravity is not possible?

• "It seems problematic that gravity can carry radiation off to infinity with no matter capable of absorbing it at infinity." Why does that seem problematic? If the waves move with finite velocity, they will never get infinitely far from source. This is the same as in EM theory - fluctuations of star light move out to the surrounding space and this goes on indefinitely. – Ján Lalinský Jun 21 '16 at 20:50
• There exists a view of electromagnetism where the waves do not carry energy away from the system and only transport energy from one particle (or charge element in a distribution) to the next. You can reinterpret my question as asking if such a view exists and is consistent for gravity. – Daniel Kerr Jun 21 '16 at 21:08
• Such a view of electromagnetism is not well backed by experience, because we do not know of any wall far away that would stop radiation from going further out. Even if such wall was there, it is not clear how it could be consistent with currently known physics, since there is no medium that stops EM field from propagation exactly. Even if we enclose a system of charges in a cavity made of perfect conductor, this will only make field vanish in the conductor, not outside it. – Ján Lalinský Jun 22 '16 at 19:25
• I was not aware of any problems with this interpretation with classical physics. The ansatz is that every charge in the universe absorbs and emits all of the radiation present in it. In practice one cannot conduct an experiment where all charges in the experiment fulfill this requirement since they cannot be completely isolated from external charges. However the universe as a whole would have no "free" radiation. The experiment would be best modeled with purely retarded fields and a self-force term. My question isn't one of practicality just perspective. – Daniel Kerr Jun 23 '16 at 2:53
• You mention lots of concepts but it is not clear how you imagine the hypothetical universe. If you're thinking of the Feynman-Wheeler absorber hypothesis, this is not "the traditional approach to Maxwell's laws". Nothing is known about what happens to fields far away; the simplest picture is that they extend to infinity. The idea of perfect absorber seems very artificial to me, like an idea that our universe is a region of space in which no matter which direction one goes, it ends with impenetrable walls. – Ján Lalinský Jun 24 '16 at 0:43