Can someone show me where I'm going wrong in the following?(adsbygoogle = window.adsbygoogle || []).push({});

From Rindler's Relativity book, page 103, the wave 4-vector is defined as L = f (n/w, 1/c ) where f is the frequency andnthe unit vector parallel to the velocity of propagation of a plane wave, w.

To get a feel for how it transforms, I'm starting with the y, z components since they should remain unchanged for a frame s' travelling along the x-axis of the stationary frame with velocity v:

f n_y/w = f' n'_y'/w' - (1)

Where cos theta is the direction cosine of the velocity of propagation, it is easily shown that:

f' = gamma (1 - v/w cos theta ) - (2)

n'_y' is parallel to w'_y' and so:

n'_y' = w'_y'/w' - (3)

So, substituting for f' and n'_y' in (1) should = f n_y hence verifying that the y and z components transform as the components of a 4 vector:

f' n'_y'/w'

= gamma (1 - v/w cos theta ) w'_y'/w'^2

= gamma (1 - v/w cos theta ) (u_y/gamma(1 - vw_x/c^2) ) / w'^2

But w'^2 = ( gamma^2 (w_x - v)^2 + w_y^2 + w_z^2)/ gamma^2(1 - vw_x/c^2)^2

So, it looks as if it won't simplify the way I want to show (1)

Thanks for your comments in advance.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Question concerning wave 4-vector

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Question concerning wave | Date |
---|---|

A question of history concerning Rindler Coordinates | Dec 18, 2014 |

Question concerning speed of light in reference frames | Oct 9, 2014 |

Questions concerning GPS Navigation! | Jun 8, 2013 |

Questions concerning Cosmological Constant | Jul 21, 2012 |

Several Questions Concerning Mass-Energy | Jun 17, 2012 |

**Physics Forums - The Fusion of Science and Community**