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I where does the line element of Minkowiski space come from?

  1. Jul 26, 2017 #1
    How is it derived?
    ds^2 =-cdt^2+dx^2+dy^2+dz^2
     
  2. jcsd
  3. Jul 26, 2017 #2
    Had this been ds^2 =+cdt^2+dx^2+dy^2+dz^2 it would've been the Pythagorean Theorem.
     
  4. Jul 26, 2017 #3
    If it was ecludian space
     
  5. Jul 26, 2017 #4

    George Jones

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    I would say that it is not derived (except maybe as an approximation to more general spacetimes), i.e., it is arrived at by induction, not by deduction.
     
  6. Jul 28, 2017 #5

    PAllen

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    Well, it can derived depending on what your assumptions are. If you assume the Lorentz transform, then the Minkowski line element follows as the only possible metric that is invariant under Lorentz transforms. Similarly, if you assume the Minkowski metric, you can derive the Lorentz transform.
     
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