The power output of an oscillating charge in the rubber plate model agrees with Larmor formula

UPDATE March 16, 2021: there are calculation errors in this blog post. See the March 15, 2021 post for a correct calculation of the lagging mass.

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Let us finally calculate a value for the power output, if we assume that the mass of the far electric field of an electron is lagging behind in the oscillation, and causing a drag on the oscillation.

This is the rubber plate model. The "plate" is the static electric field of the electron. The inertia of the plate is caused by the mass of the field.

Let us calculate a concrete example. Let an electron orbit a proton at a distance r = 0.5 * 10^-10 m. The speed of the electron is

       v = c / 137 = 2 * 10^6 m/s.

The acceleration of the electron is

       a = v^2 / r = 10^23 m/s^2.

The electron makes 10^16 cycles per second.

The Larmor formula gives as the power output

        P = 5 * 10^-8 W.

That is 3 * 10^-5 eV per cycle. An aside: a 10 eV state transition in a hydrogen atom may require a million cycles of the electron.

The mass of the electric field of the electron outside the distance 1/4 * 3 * 10^8 m / 10^16 = 15 nm is

       m = 2 * 10^-7 m_e.

The field may cause a dragging force of 

       F = m a = 2 * 10^-14 N

on the electron.

We get a power drain of

       P = F v = 4 * 10^-8 W

on the electron. Quite a good agreement with the Larmor formula.

If we double the speed of the electron, the acceleration (a = v^2 / r) is 4-fold. The Larmor formula says that the power is then 16-fold.

In our own calculation, the mass of the field dragging on the electron is double, the acceleration 4-fold, and the speed double. The power is thus 16-fold. We get an agreement with the Larmor formula.

Conclusion. We can explain the Larmor formula with a model where the mass of the far field of the electron lags behind the movement of the electron and uses its inertia to drain the maximum possible power from the movement of the electron.