Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Lorentz Transformations - 2 formulas for "t"

  1. Aug 20, 2014 #1


    User Avatar

    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]
    [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


    User Avatar
    Science Advisor
    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


    User Avatar

    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook