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Lorentz Transformations - 2 formulas for "t"

  1. Aug 20, 2014 #1

    len

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    Depending on where I go to get a good understanding of the Lorentz transformations, I run into two formulas for time (t):

    [tex]T=T_0 * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } }[/tex]
    and
    [tex]t=\left( t' + \frac{vx'}{c^2} \right) * \frac{1}{ \sqrt{ 1-\frac{v^2}{c^2} } }[/tex]

    What is the explanation for having these two different formulas for time? If there was only one or the other, it would make sense to me but I can't understand how there can be two.
     
  2. jcsd
  3. Aug 20, 2014 #2

    ghwellsjr

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    Gold Member

    The first one is what you get when x'=0, in other words, for an object that is at rest at x'=0.
     
  4. Aug 21, 2014 #3

    Nugatory

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    Staff: Mentor

    The second formula is the Lorentz transformation for the ##t## coordinate. It tells you how to calculate what time will appear on a clock in the unprimed frame when a clock in the primed frame reads a particular value.

    The first formula is not a Lorentz transformation at all. It's the timedilation formula that tells you how how much time will have passed in the moving frame if a given amount of time has passed in the non-moving frame.
     
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