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S.R Question.

  1. Sep 10, 2007 #1
    Can anyone explain to me why Pythagoras' Theorem governs the rate of change, of mass, length and time within accelertated bodies?
    It's a simple theorem learnt by most children by the age of eleven, so one would expect the answer to this question to be quite simple as well.
     
  2. jcsd
  3. Sep 10, 2007 #2

    Ich

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    It's actually not the well-known theorem of Euclidean space, but a different version belonging to Minkowski space, where the length of a vector (e.g. a time interval) is calculated from its components using
    s² = t² - x² - y² - z². (or -t² + x² + y² + z² as a matter of convention)
    In one spatial dimension, this becomes
    s² ("true" elapsed time) = t² - x² = t²*(1-v²) (less than elapsed coordinate time).
    The same logic gives relativistic mass: it is the "time component" of a vector (Energy-Momentum vector) which has a length equal to the rest mass. Modern usage is to call the time component energy, not relativistic mass.
    It's a different situation for length contraction: what we define as "length" is actually not a component of a vector, but a one-dimensional slice of a two-dimensional entity, the measuring rod, which extends both in space and in time. Therefore the different result.
     
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