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Four dimentional vector in special relativity

  1. Aug 1, 2012 #1
    About momentum-energy vector ,we have :

    [itex]\vec{P}[/itex]=([itex]\vec{p}[/itex],i[itex]\frac{E}{c}[/itex])

    and four dimentianal wave vector :

    [itex]\vec{K}[/itex]=([itex]\vec{k}[/itex],i[itex]\frac{\omega}{c}[/itex])

    They also satisfy the ralation :

    [itex]\vec{P}[/itex]=[itex]\frac{h}{2\pi}[/itex][itex]\vec{K}[/itex],

    because E=[itex]\frac{h}{2\pi}[/itex][itex]\omega[/itex].

    It is interesting.
     
    Last edited: Aug 1, 2012
  2. jcsd
  3. Aug 2, 2012 #2

    PAllen

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    FYI: very few people use the imaginary basis for time anymore, when speaking of 4-vectors. Instead of a (+,+,+,+) metric with one imaginary basis, a mixed signature metric is used.
     
  4. Aug 2, 2012 #3
    ds[itex]^{2}[/itex]=x[itex]^{2}[/itex]+y[itex]^{2}[/itex]+z[itex]^{2}[/itex]-c[itex]^{2}[/itex]t[itex]^{2}[/itex]

    In the four dimentional space-time vector,the concept of time has been bent,because time has the meaning of evolution and irreversibility.So it can't convert into space freely.
     
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