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

Lorentz transformations (2nd year relativity)

  1. Oct 11, 2010 #1
    1. The problem statement, all variables and given/known data

    A light signal is sent from the origin of a system K at t = 0 to the point x = 1 m, y = 8 m, z = 13 m. a) At what time t is the signal received?
    b) Find ( x', y', z', t' ) for the receipt of the signal in a frame K' that is moving along the x axis of K at a speed of 0.6c.

    2. Relevant equations

    The lorentz transformations:

    x' = [tex]\gamma * (x - vt)[/tex]
    y' = y
    z' = z

    3. The attempt at a solution

    Part a was easy. I got the right answer. I just took the length of the vector given by the co-ordinates and divided by the speed of light. The answer is [tex] 5 * 10^8 [/tex] I am having trouble with part b.

    Ofcourse, y' and z' were easy to get. t' (i had 3 tries, and i used them all) so I lost a mark there. I have one try left on x'.

    Using the equation, we first have to solve for [tex]\gamma[/tex]. Plugging the numbers into the equation for gamma:
    [tex] \frac{1}{\sqrt{1-(v/c)^2}}\; \text{yields} \; 1.25[/tex]

    Then using the lorentz transformation I have the following eqn:
    x' = [tex]\gamma[/tex] (x - vt) . Plugging in the numbers yeilds
    x' = 1.25(1 - 0.6 * c *(5E-8))

    I get 10 as the answer. It is wrong. I also thought t = 0 could work since thats when the event happened. But the answer 1.25 is also wrong.

    My third attempt yielded 11.25m however, I am scared to submit it. If anyone can please verify my number for me.
  2. jcsd
  3. Oct 11, 2010 #2


    User Avatar
    Homework Helper

    The Lorentz transformations are more accurately written
    [tex]\Delta t' = \gamma(\Delta t - v\Delta x/c^2)[/tex]
    [tex]\Delta x' = \gamma(\Delta x - v\Delta t)[/tex]
    The [itex]\Delta[/itex] indicates that the numbers to be plugged in should be the difference between two spacetime events. So putting in t=0 is a mistake that you should not make again.

    Can you show your calculations for the other two attempts?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook