SR Doppler Effect: Differences in Wave VS Momentum Models

[Justintruth]

...model uses spherical Doppler wavefronts, why is this model inaccurate?

I don't know if its relevant to your problem but spherical wavefronts are impossible. To see why imagine the E or B vectors on a sphere. The Euler characteristic of a sphere is 2. Roughly the Euler characteristic can be seen to represent the minimum number of places where the wind speed must be zero. So if you imagine wind blowing on a sphere you will always have at least two places where the wind does not blow. On a torus you can have zero as the wind can blow up through the center around down and back in and up. The Euler characteristic is 0 for a Torus. So that means the curl of any vector field on a sphere must be 0 in at least two places. The E and B fields therefore must be zero. in fact this is true and all so called omni antennas have nulls.

 

[tade]

I don't know if its relevant to your problem but spherical wavefronts are impossible. To see why imagine the E or B vectors on a sphere. The Euler characteristic of a sphere is 2. Roughly the Euler characteristic can be seen to represent the minimum number of places where the wind speed must be zero. So if you imagine wind blowing on a sphere you will always have at least two places where the wind does not blow. On a torus you can have zero as the wind can blow up through the center around down and back in and up. The Euler characteristic is 0 for a Torus. So that means the curl of any vector field on a sphere must be 0 in at least two places. The E and B fields therefore must be zero. in fact this is true and all so called omni antennas have nulls.

I see, but I don't think it is that relevant.

What I said in #35, is it correct?