- #1

yuiop

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I have re-written this as as I accidently deleted my original post. I was wondering if the relativistic Doppler shift of a reflection from a mirror moving away from the observer was the same as the Newtonian equation in the special case that the mirror is orthogonal to the direction of motion.

I referred to equation (13) in this paper http://arxiv.org/ftp/physics/papers/0409/0409014.pdf and set theta to zero for this special case.

I now think I have figured out the answer to my own question.

The equation I gave in my my first post:

[tex] f = f_0 \frac{1-2v/c+v^2/c^2}{1-v^2/c^2} [/tex]

Can be re-arranged:

[tex] f = f_0 \frac{(1-v/c)(1-v/c)}{(1-v/c)(1+v/c)} [/tex]

and simplified:

[tex] f = f_0 \frac{(1-v/c)}{(1+v/c)} [/tex]

and this is exactly the same as the none relativistic equation for Doppler radar.

Length contraction and time dilation is not involved in this special case of reflection in a moving mirror.

I referred to equation (13) in this paper http://arxiv.org/ftp/physics/papers/0409/0409014.pdf and set theta to zero for this special case.

I now think I have figured out the answer to my own question.

The equation I gave in my my first post:

[tex] f = f_0 \frac{1-2v/c+v^2/c^2}{1-v^2/c^2} [/tex]

Can be re-arranged:

[tex] f = f_0 \frac{(1-v/c)(1-v/c)}{(1-v/c)(1+v/c)} [/tex]

and simplified:

[tex] f = f_0 \frac{(1-v/c)}{(1+v/c)} [/tex]

and this is exactly the same as the none relativistic equation for Doppler radar.

Length contraction and time dilation is not involved in this special case of reflection in a moving mirror.

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