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Homework Help: Four Vectors

  1. Apr 25, 2010 #1
    Im having some four-vector definition issues. I have a relativity exam coming up and they quite often ask about 4-vectors.

    1) Does this definition sound ok?
    'A four-vector is 4 numbers, say X=(X0, X1, X2, X3), used to describe an event in minkowski space. The 'zeroth' is the time component, while the other 3 components are the spatial components of a 3-vector. A four-vector differs from a 3-dimensional vector in that it can undergo a lorentz transformation and remain a four-vector. '
    2) How do i show that a vector is actually a four vector?
    Do i just show that it remains a valid four vector under a lorentz transformation?

    Any help is greatly appreciated
    thanks
     
  2. jcsd
  3. Apr 26, 2010 #2
    Hi, the best way to define 4 vectors are by their transformation properties, which is essentially what you have said. In equation form it is

    [tex]\widehat{x}^{\mu}=\Lambda^{\mu}_{\nu}x^{\nu}[/tex]

    Here Lambda is the mu, nu component of the lorentz matrix, and the einstein summation convention is used.
     
  4. Apr 26, 2010 #3

    diazona

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    Homework Helper

    Yep, that works. I think it's also possible to show that it's a four-vector by demonstrating that if you contract it with another four-vector, the result is Lorentz-invariant (i.e. is a scalar). Sometimes that might be easier.
     
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