Cosmology 5022

download Cosmology 5022

of 6

  • date post

    03-Jan-2016
  • Category

    Documents

  • view

    29
  • download

    0

Embed Size (px)

description

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

Transcript of Cosmology 5022

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

Example:

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