Why a periodic motion creates electromagnetic waves but a linear motion does not?

We need a classical mechanics analogue for the electromagnetic field, to have a better intuitive understanding of it.

A possible analogue is a tight drum skin whose mass is zero. The skin can still store energy because it stretches and energy is stored in the deformation.

                  finger
                   | |
   _____       U     ______ drum skin
             \______/

Let us press the skin with a finger. What happens if we move the finger at a constant speed along the drum skin?

The valley which the finger creates in the skin moves. If the skin would have mass, then the upward movement of the skin behind the finger would probably create waves. If a mass starts moving up, it is out of its equilibrium position, and the inertia of the mass will keep it oscillating. Waves are born.

But if the mass-energy of the skin is solely in the stretching of the skin, then it might be that no oscillation will happen? When the finger has moved far away, the mass-energy of the skin is very small and there is not much inertia any more.

Note that if the skin has a positive mass, then the speed of waves in it has a preferred coordinate system: the inertial coordinates determined by the drum. The waves cannot be Lorentz-covariant then.

If we accelerate the finger in a linear fashion on the skin, then the big picture does not change very much from the movement at a constant speed. Only close to the finger there is considerable mass-energy which could sustain waves with its inertia.

But if we let the finger do a periodic motion on the skin, then deformation of the skin will spread to all directions as waves. The deformation carries mass-energy, and that mass-energy has inertia, which will sustain waves.

To exist, waves require inertia. And the waves themselves can carry the required inertia with them because they deform the skin and thus carry mass-energy.

We have presented this idea in our blog also before. We should calculate the wave equation for a massless drum skin, and calculate also the solution for a linearly accelerated finger.

There is at least one obvious problem: if we let a finger pump mass-energy to the skin, then that mass-energy defines a preferred coordinate system. That would be against Lorentz-covariance. However, the existence of photons somewhere does necessarily define a preferred coordinate system. Does our model break Lorentz-covariance or not?