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Homework Help: A question about 4-velocity vector in relativity

  1. Jul 10, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello ,
    I have the book (An introduction to tensor calculus , relativity and cosmology) , this book defined the 4-velocity vector as :-

    070810110726mkyfk8arz.jpg
    And this book stated that :-

    070910090736sah8o1wcrk1i.jpg
    How could we obtain (17.4) from (15.6) ???
    Please I need help .


    Thanks ……..



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 10, 2010 #2

    kuruman

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    Calculate the magnitude squared of the four-vector on the right side of 15.6. What do you get?
     
  4. Jul 10, 2010 #3
    i do that but i don't obtain the result (-c^2)
    i still need help .
     
  5. Jul 10, 2010 #4

    kuruman

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    Show exactly what you did. You probably made a mistake somewhere.
     
  6. Jul 10, 2010 #5
    let (1-[v^2]/[c^2])^-1/2 = y
    therefore ?:-
    V = y (v,ic)
    V^2 = (y^2) ([v^2] + [ic]^2)
    then V^2 = [y^2] ([v^2]-c^2)
    that's all.



    i still need help , please .
     
  7. Jul 10, 2010 #6

    kuruman

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    You should have left the denominator alone instead of replacing it by 1/γ. All you need to do is simplify

    [tex]\frac{v^2-c^2}{1-\frac{v^2}{c^2}}[/tex]
     
  8. Jul 15, 2010 #7
    i understand the idea , thank you veryyyyyyyy much .
     
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