Relativity & Dipole Radiation: Reconciling Perspectives

[Frank Peters]

Consider a dipole antenna that is radiating at it's resonant frequency F.

Consider an observer approaching this dipole antenna, in a direction perpendicular to the axis of the dipole, at velocity 0.6c.

According to the relativistic doppler shift, the frequency perceived by the moving observer will be 2F.

However, since the axis of the dipole is perpendicular to the motion it will not be Lorentz contracted. The moving observer will be able to measure (in principle) the unchanged antenna length and thereby deduce that the radiation frequency should be F.

How are these two perspectives reconciled? Does the moving observer conclude that the antenna is not resonant? If so, the antenna pattern in the rest frame would be that of an ideal dipole but in the moving frame the antenna pattern would be different.

All the equations I have seen that deal with this topic indicate that a distortion of the ideal resonant dipole pattern occurs in the moving frame. But since the moving frame will perceive a non-resonant dipole antenna, a distortion of the resonant pattern would not seem likely.

 

[Vanadium 50]

In one case you have a stationary antenna and the radiation is purely electric dipole. In the other you have a moving antenna and the radiation is a mix of electric and magnetic dipoles.

 

[Dale]

If so, the antenna pattern in the rest frame would be that of an ideal dipole but in the moving frame the antenna pattern would be different.

This is what I would expect. After all, even monopole fields lose their spherical symmetry when boosted.