1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Length Contraction

  1. Jan 9, 2008 #1
    A rod of length 2l is at rest in frame O' with co-ords (x',y',z')=(±l,λ,0)

    Observer O moves at speed u along the x axis.

    The first part of the question is just to derive the length contraction - fine, O measures the length as 2l / γ

    The next part has me stuck:

    "Show that, at t = 0, the observer O sees the light rays from the two ends of the rod
    coming in at angles that lead to an apparent length of 2lγ (making the assumption
    that the rod is oriented parallel to the x-axis with a y separation of λ from the origin).
    Comment briefly on the discrepancy between the two results. "

    I've tried drawing space-time diagrams, and just got in a bit of a mess. I can work out equations for the worldlines of the front and back of the pole (e.g. for one end (ct,x,y,z) = (ct'γ - lγ u/c, γ t'-lγ ,λ,0) etc), but setting t=0 for front and back just gives the 2l / γ. result
     
  2. jcsd
  3. Jan 10, 2008 #2
    The light rays are sent in the same time at the rod system or in the same time at the observer's system. In the first case, the ray sent from the begining of the rod will be advanced in time gamma*l*u^2 seconds and the ray sent from the end will be delayed the same quantity.

    The result will be that it looks like the rays have been sent from a distance that looks (gamma*l). You can also transform the vector 2*l x+0 t from the Rod system to the observer system, it will become 2*l*gamma.
     
  4. Jan 10, 2008 #3
    The light rays are sent in the same time at the rod system or in the same time at the observer's system. In the first case, the ray sent from the begining of the rod will be advanced in time gamma*l*u^2 seconds and the ray sent from the end will be delayed the same quantity.

    The result will be that it looks like the rays have been sent from a distance that looks (gamma*l). You can also transform the vector 2*l x+0 t from the Rod system to the observer system, it will become 2*l*gamma.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Length Contraction
  1. Length Contraction (Replies: 5)

  2. Length Contraction (Replies: 6)

Loading...