1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: 4-vectors scalar product

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    If a and b are 4-vectors give the definition of the scalar product a.b and demonstrate its Lorentz invariance

    2. Relevant equations

    3. The attempt at a solution
    So (with 4-vectors double underlined!)
    a.b = a0b0-a1b1-a2b2-a3b3

    a' = (a0*gamma - beta*gamma a1 , -ao*beta*gamma + a1* gamma, a2 , a3)
    b' = (bo*gamma - beta*gamma b1, -bo*beta*gamma + b1* gamma, b2 , b3)

    a'.b' = two brackets above multiplied together
    =(aobo*gamma^2+a1b1*beta^2*gamma^2 -aob1*beta*gamma^2 - a1bo*gamma^2*beta)-(aobo*beta^2*gamma^2 - aob1*beta*gamma^2 - a1bo*beta*gamma^2 +a1b1*gamma^2) -a2b2-a3b3

    =a0b0(gamma^2-beta^2*gamma^2) + a1b1(beta^2*gamma^2-gamma^2) - a^2b^2-a^3b^3
    substituting gamma=(1-beta^2)^-0.5 gives

    which doesn't equal a.b.!!!
    Could someone please tell where I am going wrong. I am really confused
  2. jcsd
  3. May 3, 2009 #2


    User Avatar
    Homework Helper
    Gold Member

    Hi CaptainJack,

    Your error seems to be in making the above substitution... remember to take care of the negative sign in the exponent:

    [tex]\gamma=(1-\beta^2)^{-0.5} \implies \gamma^2=\frac{1}{1-\beta^2}\neq1-\beta^2[/tex]

  4. May 3, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper

    Hi captainjack2000! :smile:

    This is your second post that I have found virtually unreadable …

    can you please try to use β and γ, and the X2 and X2 tags just above the Reply box? :smile:
  5. May 3, 2009 #4
    Oh thanks you..its just me being stupid!

    Really sorry about that didn't notice them..will definitely use them next time!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook