- #1
Biest
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So I have been trying to wrap my head around time dilation and length contraction... It is all good until i come to the point to derive length contraction from time dilation...
So we have
[tex] \gamma \Delta \tau = \Delta t [/tex]
[tex] \gamma L = L_0[/tex]
So now from my lecture notes i have an observer Ha riding a broom at speed v, and a stationary observer He (so yeah if anybody has the book it is Hartle's Gravity book chapter 4 problem 19). In Ha's frame [itex] L_0 = v \Delta \tau [/itex] and in He's frame [itex] L = v \Delta t [/itex], so now when i substitute that into the equation for time dilation I will not get the result for length contraction. Am I misinterpreting the question or something... Ironically, the gravitational red-shift seems a easier from Hartle's explanation... Maybe I am just missing a [itex] \gamma [/itex] somwhere.
Thanks for any help.
Cheers,
Biest
So we have
[tex] \gamma \Delta \tau = \Delta t [/tex]
[tex] \gamma L = L_0[/tex]
So now from my lecture notes i have an observer Ha riding a broom at speed v, and a stationary observer He (so yeah if anybody has the book it is Hartle's Gravity book chapter 4 problem 19). In Ha's frame [itex] L_0 = v \Delta \tau [/itex] and in He's frame [itex] L = v \Delta t [/itex], so now when i substitute that into the equation for time dilation I will not get the result for length contraction. Am I misinterpreting the question or something... Ironically, the gravitational red-shift seems a easier from Hartle's explanation... Maybe I am just missing a [itex] \gamma [/itex] somwhere.
Thanks for any help.
Cheers,
Biest