Reduction in gravity from photon exchange Let's say you have two bodies at are held at rest relative to each other exchanging (real, not virtual) photons back and forth.  Then we let them go (maybe push them apart slightly), so they will begin to move apart at some velocity.  Now, if they have a relative velocity between them, the photons absorbed will be of longer wavelength and therefore lower energy than when the photons were emitted.  This will result in a net energy decrease of the system.  Would this energy decrease reduce the gravitational attraction between the particles, causing an increasing separation acceleration as long as there is an exchange of photons?
 A: Let's break this down a bit.
What would happen if we had a flashlight on a body moving away with some velocity? The emitted photons "lose energy" here as well.
Firstly, energy is relative. The energy from one frame need not be the same as that from another frame of reference. From the body frame, there is no change in wavelength thus no change in energy. Fro the ground frame, it seems to be emitted at its "new" wavelength, so there is no change in energy. Whether or not the two energies match is irrelevant.
OK, now let's look at this: two bodies, with equal masses and velocities, being hit by photons of equal energy, one head on and one from behind.
In the moving frame, the initial energies are the same but the final energies are not. However, they turn out to be equal in the ground frame. 
This is due to energy-momentum mixing. Look more closely in the ground frame. One  of the two slows down (by momentum conservationp, and one speeds up. For the one that slows down, more energy is transferred to the rest energy for the body, and less for the one that speeds up. Which makes it okay for the two to have differing momenta and energies in the moving frame.

These two together solve the paradox. See, when a moving body emits and absorbs a photon in the same direction, its rest energy is not unchanged. The absorbed photon speeds it up and gives it less rest energy than an emitted photon of the same energy in the ground frame(choosing a ground frame where the photon is emitted opposite to the motion of the body).
So, from the ground frame, both moving bodies speed up, but lose rest mass. Which is OK, conservation law-wise. The same happens in a moving frame, andthe photon redshift enables it to happen. So, there is no loss of energy.
Of course, there is a separation deceleration if we add gravity. But no acceleration, as energy isn't changing; only rest energy is.
