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!

Lorentz Transformation

  1. Jan 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Two events occur at the same place in an inertial reference fram S, but are separated in time by 3 seconds. In a different frame S', they are separated in time by 4 seconds.

    (a) What is the distance between the two events as measured in S'?
    (b) What is the speed of S relative to S'?

    2. Relevant equations

    I'm presuming:

    t' = gamma*(t-ux/c^2)

    3. The attempt at a solution

    I have the answer, and a hint saying to use the interval S^2, but I have no idea what that means, and where I start. When I look and the relevant Lorentz equations, they involve velocity, and I do not have a velocity here.

    Could you please point me in the right direction?

    Thank you in advance.
  2. jcsd
  3. Jan 22, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    The hint is implying that you use the invariant space-time interval to solve this problem. The following quantity is called the space time interval:

    [tex](\Delta s)^2= (\Delta x)^2 + (\Delta y)^2 + (\Delta z^2) - (c\Delta t)^2[/tex]

    This quantity is a Lorentz scalar and is thus invariant over Lorentz transformations (it is the same in all inertial frames). So, in one dimension this means:

    [tex](\Delta x)^2- (c\Delta t)^2=(\Delta x')^2- (c\Delta t')^2[/tex]

    Can you use this the solve the problem?
  4. Jan 22, 2009 #3
    Do I find [tex](\Delta t)[/tex] by doing SQRT[(4^2)-(3^2)] = ROOT 7

    Then at they are both at the same coordinates in the inertial reference frame, we can ignore x , y and z. Therefor S equals the root of (c^2)*(ROOT 7) = 7.9x10^8m

    Is this correct?
  5. Jan 22, 2009 #4


    User Avatar
    Homework Helper
    Gold Member

    You should only have one factor of c in your final line, since you take the square root of c^2 when solving for the answer.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Lorentz Transformation
  1. Lorentz Transformations (Replies: 11)

  2. Lorentz transformation (Replies: 1)

  3. Lorentz Transformations (Replies: 29)