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Scalar Product of displacement four vector

  1. Jun 25, 2015 #1
    1. The problem statement, all variables and given/known data
    How does the scalar product of displacement four vector with itself give the square of the distance between them?

    2. Relevant equations

    (Δs)2= Δx.Δx ( s∈ distance, x∈ displacement four vector)
    or how
    ds2αβdxαdxβ
    3. The attempt at a solution
    Clearly I am completely new to the subject, thus I have no idea about it.
     
  2. jcsd
  3. Jun 25, 2015 #2
    The flat space-time metric tensor (I love this sentence) ηαβ is a bunch of zero except when α = β so clearly we can reduce ds2 to some simpler formula, Cheers !
     
    Last edited: Jun 25, 2015
  4. Jun 25, 2015 #3
    What actually do want to say? My question is how does the scalar product of 2 displacement four vectors gives the distance between them. I can not figure out the answer from your reply..:oldconfused::oldconfused::oldconfused:
     
  5. Jun 26, 2015 #4
    I mean that ηαβdxαdxβ = ηααdxαdxα summation over α,
    [EDIT: In case I'm not clear enough η11 = 1, η22 = η33 = η44 = -1]
     
    Last edited: Jun 26, 2015
  6. Jun 29, 2015 #5
    I get the whole point. Thanks for all replies.
     
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