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Special Relativity question

  1. Oct 6, 2013 #1
    Question
    Suppose an inertial frame of reference S’ moves at a constant velocity v in the
    positive x-direction with respect to a second inertial frame S. The Lorentz
    transformation from S to S’ for the x coordinate of displacement is given by:
    x′ =γ (x − vt)
    Write down a corresponding expression for the inverse transformation, i.e. from
    S’ to S, giving x in terms of x’ and t’.
    Use these two expressions to derive the Lorentz transformation equation for time:

    t'=γ(t-vx/c^2)


    I think I have the first part, I answered x =γ (x' + vt). But the second part I have no idea I have been looking online and even watching lectures on youtube.
    Thanks in advance.
     
  2. jcsd
  3. Oct 6, 2013 #2

    Ibix

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    vt? Are you sure?
     
  4. Oct 6, 2013 #3
    Sorry vt'

    Do you know the second part or even where I should start?
     
  5. Oct 6, 2013 #4

    Ibix

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    You've got x' in terms of x and t, and x in terms of x' and t'. Which variable don't you want to appear in the final expression?
     
  6. Oct 6, 2013 #5
    X' I think. Sorry if I sound a bit stupid. I'm in my first year and this is only my second question.
     
  7. Oct 6, 2013 #6

    phyzguy

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    Take your answer for the first part, substitute in for x' in terms of x and t, then solve for t' in terms of x and t.
     
  8. Oct 6, 2013 #7
    Ok I've done what you have said and got-

    t'=(x+γ(γx-γvt))/γv

    Now I am competent lost
     
  9. Oct 6, 2013 #8
    Completely*
     
  10. Oct 6, 2013 #9

    phyzguy

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    This is correct, you just need to simplify it. What is γ equal to?
     
  11. Oct 6, 2013 #10

    Ibix

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    Expand the Lorentz gammas and collect terms. Courage! This one always looks a mess to me until it all clicks into place at the end.
     
  12. Oct 6, 2013 #11
    Can anyone actually show me this step as I am completely thrown. I just can't make sense of it.
     
  13. Oct 6, 2013 #12

    Ibix

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    You have a sign wrong in your expression for t', I just noticed. That might be your problem.
     
  14. Oct 6, 2013 #13
    Yeah I found that when I started from scratch. But I'm still at a loss. It just looks a mess. Do you expand all the gammas?
     
  15. Oct 6, 2013 #14

    Ibix

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    Collect your x and t terms. The t term should fall out straight away. That leaves the x term. I'd suggest that if in doubt, expand, is a good rule of thumb here. You might want to use [itex]\beta=v/c[/itex] to save ink.
     
  16. Oct 6, 2013 #15
    Ok. Well just got into bed so I will give it a go before I go to university tomrrow. Thanks for your help guys.
     
  17. Oct 7, 2013 #16
    When you studied algebra, did they teach you how to solve 2 linear algebraic equations in two unknowns?
     
  18. Oct 7, 2013 #17
    Yeah as far as I'm aware no hate when algebra is explained in words. But yeah I think I did.
     
  19. Oct 7, 2013 #18
    If that is the case, that's all you have to do in this problem. Your two unknowns are x and t. Solve for 'em.

    Chet
     
  20. Oct 7, 2013 #19
    Thank you
     
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