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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
  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


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


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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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