I come to the question with an example.

Let us suppose two electrons are in space with initial velocity equal to zero.

Given the Coulomb force such electrons will be submitted to an equal and opposite accelerations (for the action reaction Newton law).

I expect that the complessive radiation emission at great distances will be null.

So the system will not loose energy.

But it is said that according to Maxwell theory this is not possible.

Where is the truth ?

I could give many other similar examples where, even if there are electric charges in accelerated motion, the system will not transfere electromagnetic energy to space.

Is really Maxwell's theory wrong at an atomic scale ?

Thanks for your considerations.