Tuesday, 15 April 2008

Relativity Confusion

I've just been working through some relativity questions, and most of the stuff I can just about manage, when prompted by the solutions. Indeed, figuring out which Lorentz transformation to use, and the rough procedure to solve a problem, aren't actually too bad, but today I'm having problems with basic mathematics.

The solutions given are in quite a brief format, where huge swathes of steps have been missed out. Often, it's just a few lines of algebra which is fairly straightforward, but today I don't seem to be able to "see" these, and have to work through them, blind.

One particular bit, which I've tried for the best part of 15 minutes, and have now given up on temporarily, is convincing myself that

\frac{1-v/c}{\sqrt{1-v^2/c^2}} = \sqrt{\frac{1-v/c}{1+v/c}}

This is a fairly fundamental step in calculating Relativistic Doppler shifts, since:

\nu^\prime = \nu\sqrt{\frac{1-v/c}{1+v/c}}

If anyone can tell me how those two things are equal, I'd love to know! Of course, maybe tomorrow it'll be clear. Today is not a good day to revise, but I have to do it anyway.

1 comment:

  1. (1-v/c)/sqrt(1-v^2/c^2)=(1-v/c)/sqrt((1-v/c)(1+v/c))=(1-v/c)^(1-1/2)/sqrt(1+v/c)=sqrt((1-v/c)/(1+v/c))
    Where the identity 1-x^2=(1-x)(1+x) has been used ;)