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

How to derive t1 in terms of t and t in terms of t1

  1. Jul 30, 2012 #1
    1. (x=X1+vt1, x1=x-vt )

    2.(t=t1+vx1/c2, t1=t-vx/c2 )


    I know that 1. is x in terms x1 and x1 in terms of x.
    I understand it very well, the adding and substracting of
    velocity.

    But i am unable to understand the 2.how these equation are
    derived and what does they mean.

    The mane problem is how they are derived.

    Please help me.
     
  2. jcsd
  3. Jul 30, 2012 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    c2 means c^2 (c squared)?
    This looks like a classical formula, as time passes at the same rate for t and t1. They are just shifted by a constant value, which is meaningless in physics (there is no absolute time in physical equations, just time differences).

    Edit: Ah, those are the moving x1, x? Sorry, I am confused by your equations. Can you provide the source, or at least write them in a clean way (with [tex] tag would be perfect, together with an explanation what the parameters are)?
     
  4. Jul 30, 2012 #3

    PeterDonis

    User Avatar
    2016 Award

    Staff: Mentor

  5. Aug 4, 2012 #4
    x=stationary observer
    x1=moving observer
    c2= c squared
    v= velocity
     
  6. Aug 4, 2012 #5

    DrGreg

    User Avatar
    Science Advisor
    Gold Member

    That still doesn't answer the question. I assume x is supposed to be a distance (not an observer) so you have to specify between what and what and measured by who. Similarly for the other terms.

    The Lorentz transform is usually expressed in a form something like[tex]
    \begin{align}
    t_1 &= \frac{t - vx/c^2}{\sqrt{1-v^2/c^2}} \\
    x_1 &= \frac{x - vt}{\sqrt{1-v^2/c^2}} \\
    t &= \frac{t_1 + vx_1/c^2}{\sqrt{1-v^2/c^2}} \\
    x &= \frac{x_1 + vt_1}{\sqrt{1-v^2/c^2}}
    \end{align}
    [/tex]
    where

    t = time between event O and event E as measured by observer A
    x = distance between event O and event E as measured by observer A
    t1 = time between event O and event E as measured by observer B
    x1 = distance between event O and event E as measured by observer B
    v = velocity of observer B relative to observer A

    My equations look rather different to yours, so did you really mean what you wrote? And if you did, what do the letters mean (they can't be the same as the meanings I gave).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to derive t1 in terms of t and t in terms of t1
  1. Terms explanation (Replies: 14)

Loading...