Cosmology 5022

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Cosmology 5022. Relativity. Length Contraction. Want to measure the length of the rod in S frame. S. S’. LT:. v. rod is stationary in S’ frame. #1. #2. LT applied to event #2. S’. S. t x t’ x’. - PowerPoint PPT Presentation

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Cosmology 5022

Cosmology 5022RelativityLength ContractionSSevent #1 0 0 0 0 event #2 0 L t L t x t x SS#1#2

vrod is stationary in S frameWant to measure the length of the rod in S frame

In S frame the length of the rod is

In S event #2 takes place before event #1

LT applied to event #2LT:Simultaneous eventsTime DilationSS tick #1 0 0 0 0 tick #2 dt x dt 0 t x t x SS

vclock is stationary in S frameWant to measure dt, the time between ticks in S frameIn S frame the time between clock ticks isLT applied to event #2LT:

Time dilation has been verified experimentallyBasis and co-basis sets

basis set along coordinate axes co-basis setParallel Transport

transport a vector without changing italong a closed loop

the transported vector is not the same as theoriginal one

the difference between the two depends on the path taken and the area enclosedNewtonian Deviation Equation


particles approach each other in x1, x2 directions, separate along x3 directionMNote: in Eucledian space of Newtonian gravitycovariant = contravariant