Dear esteemed physicists :)(adsbygoogle = window.adsbygoogle || []).push({});

I've been trying to satisfy my own curiosity by proving relativistic Doppler using only Lorentz transforms between two inertial frames, one holding a source, the other the receiver.

I've managed to derive the correct expression [tex] \frac{\nu}{\nu_0} = \sqrt{\frac{c-v}{c+v}}[/tex]

for the redshift. But the blueshift still eludes me. I don't want to just switch the sign of v in the final expression, I want to be able to set up two inertial frames that are approaching each other and work through the transforms to get there for the blueshift. Preferably, it would be great if the source frame and the receiver frame are approaching (blueshift) then pass each other and then go into redshift as they recede from one another, and everything can be clearly seen from the equations. But I have no idea how to do this.

Any help please ? This is not homework. Thanks very much.

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# Proving relativistic blueshift with Lorentz transforms only

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