Pushing an electric charge and pushing a mass - what is the difference in production of waves?

Pushing an electric charge

We have conjectured that the reason why a linearly accelerated electric charge radiates is that its electric field is a "flexible solid object", and the field carries a positive energy density E^2.

The pusher will feel that he is pushing a flexible object. If he wants to give 1 newton second of momentum to the charge, he has to push over a longer distance than he would need in the case of a totally rigid object. He has to do some extra work which does not go to the kinetic energy of the charge. This extra work is radiated away as electromagnetic radiation.

When studying electromagnetism, we can work in a Minkowski space with no gravity. We can assume that the metric stays the same, and we have an infinitely rigid rod with which to push. The extra energy cannot go to the deformation of the rod, as it is infinitely rigid.

The pusher concludes that some of the work he did was lost: it did not go to the kinetic energy and it did not go to the rod. It did not go to the static electromagnetic field of the charge. The energy had to go to the global electromagnetic field.

We have not yet calculated what kind of a flexible object the electric field has to be, to explain the radiative dissipation of energy. Can we assume that its energy density is E^2 and the flexibility comes from the retardation of the field? The energy of the field is infinite if integrated to r = 0. Should we stop at r = classic electron radius if the charge is one electron?

Pushing a mass

The energy content of a gravitational field is negative, if one tries to derive it from the same principles as in the case of an electric field. The concept of an object of mass m carrying a negative energy flexible field is perplexing. Would the inertial mass of the object first appear greater than m to the pusher? He would need to push a shorter distance to convey 1 newton second of momentum than in the case of a totally rigid object? We would have a perpetuum mobile, if the kinetic energy of the mass would increase more than the work done by the pusher.

A flexible positive energy field loses energy as radiation, if the object is pushed. A negative energy field would make the object to gain energy from empty space when pushed.

A negative energy field is a bad idea. Do the pseudotensors of Landau and Lifshitz and others make sense, as they seem to assign a negative energy to the field?

UPDATE May 29, 2019: a perfectly rigid rod seems to have a gravitational repulsion with the mass. We need to think again what actually happens if we try to push with a perfectly rigid rod. See our blog posts on May 28, 2019.

In the previous blog post we showed that if 3D space stretches to accommodate a longer rod when we do the pushing with a perfectly rigid rod, then the pusher does some extra work compared to the case of a fixed metric, and that energy might be the source of gravitational waves.

Does the Schwarzschild exterior metric carry positive energy?

If deformations of 3D space mean positive energy stored in space, one may ask if, for example, the 3D space deformation around a spherical mass carries positive energy.

The local observer finds the stress-energy tensor T zero around the spherical mass. He thinks that the energy content of space is zero there. But it is possible that a global observer would assign a positive energy content to space.

Then the far-away observer might see flexibility in the push from two sources: from the flexibility of the positive energy gravitational field, and the flexibility of 3D space under the infinitely rigid rod. We need to calculate what would be the contributions of these two effects.