Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick question about relative velocity in Lorentz Transform

  1. May 9, 2015 #1
    Do two inertial observers in relative motion agree on their relative velocity? Velocity is distance per unit time and they don’t agree on the distance or the elapsed time. If the apparent distance in the prime system is shorter and the elapsed time is longer, then it seems that the apparent relative velocity in the prime system must be smaller. The inverse transform gets a little strange if one can’t assume the exact same relative velocity.
     
  2. jcsd
  3. May 9, 2015 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Why don't you check this yourself? By definition, the Lorentz transform is constructed so that the world line with ##x' = 0## has ##x = vt##. Can you figure out how to measure the velocity of the spatial origin of the unprimed frame in the primed one?
     
  4. May 9, 2015 #3

    PeroK

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Suppose two inertial observers are in relative motion. If they don't measure the same relative velocity, then which one measures the greater velocity? The one moving left? Or the one moving right? Or, the one you choose to call O'? Of the one you choose to call O (without a prime)?

    Is it the one whose clock is running slow? But, to each, it's the other's clock that is running slow and whose lengths are contracted.
     
  5. May 9, 2015 #4

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Of course, ultimately, you do not need to know this to derive the inverse formula. Just solve for ##x## and ##t## in terms of ##x'## and ##t'##. It is simply taking the inverse of a 2x2 matrix.
     
  6. May 9, 2015 #5

    A.T.

    User Avatar
    Science Advisor
    Gold Member

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quick question about relative velocity in Lorentz Transform
Loading...