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Energy in Special Relativity

  1. May 22, 2004 #1
    I'm reading Taylor and Wheeler's, Exploring Black Holes.

    I was doing okay until I reached their derivation of energy in Special Relativity.

    They arrived at this equation:

    [tex] \frac{t}{\tau} = \frac{E}{m} [/tex]

    Tau is proper time, t is the frame time, E is energy and m is mass.

    The authors used the Principle of Extremal Aging to derive the equation. How did they arrive at E/m as a constant of motion?
     
    Last edited: May 22, 2004
  2. jcsd
  3. May 22, 2004 #2

    robphy

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    t is the time-component of the position 4-vector with magnitude [tex]\tau [/tex].
    [tex]t=\gamma \tau [/tex]

    E is the time-component of the momentum 4-vector with magnitude [tex]m [/tex].
    [tex]E=\gamma m [/tex]
     
  4. May 23, 2004 #3
    :confused:

    I sort of understand the 4-vector part. How does that relate to "E/m"?
    I'm going to do some more reading check back with you later on in life.

    Could go into a litte more detail, maybe I'm missing something.
    Thanks for the response.
     
  5. May 23, 2004 #4

    robphy

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    Since [tex]t=\gamma \tau [/tex], we have [tex]\frac{t}{\tau}=\gamma[/tex].
    Since [tex]E=\gamma m [/tex], we have [tex]\frac{E}{m}=\gamma[/tex].

    Thus, [tex]\frac{t}{\tau}=\gamma=\frac{E}{m}[/tex].
     
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