Rohrlich's derivation of E=mc2 wrong?

[Lamarr]

http://en.wikipedia.org/wiki/Mass–energy_equivalence#Alternative_versionAccording to Wikipedia,

"The velocity is small, so the right-moving light is blueshifted by ... Doppler shift factor $$1-\frac{v}{c}$$

But $$1-\frac{v}{c}$$ should not be applied under relativistic conditions.
The formula $$\frac{1}{1+\frac{v}{c}}$$ should be used instead.So wouldn't this invalidate Rohrlich's derivation?

 

[Lamarr]

The formula used by Rohrlich does not even fit into the relativistic doppler effect equation.

 

[bcrowell]

That's why they say, "The velocity is small,..." Taking units where c=1, the expressions 1-v, 1/(1+v), and $\sqrt{(1-v)/(1+v)}$ are all the same to first order in v.

 

[Lamarr]

but the relativistic doppler formula is derived by dividing the second equation by the lorentz factor.

So if time dilation is minimal, why use the first equation? He should've used the second one.

The first equation is for a detector approaching a stationary wave source, passing the wavefronts faster than their speed in a medium.

The second is for a wave source approaching a detector, and the position that each wavefront was generated changes.

The principles the first equation is based on seems to violate relativity, as one cannot approach light waves faster than their speed of propagation.

 

[Lamarr]

yes, it is true that both equations are similar at low velocities, but this a mathematical derivation of an equation and not a numerical approximation.

I plotted the graphs of both equations, and from what i can see, both show significant deviations at about 0.1c