Understanding Relativity and Cosmology Concepts in Length Contraction and Time Dilation

1. Cosmology 5022 Relativity

2. 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’ event #1 0 0 0 0 In S frame the length of the rod is In S’ event #2 takes place before event #1 event #2 0 L t’ L’ Simultaneous events

3. Time Dilation Want to measure dt, the time between ticks in S frame S S’ LT: v clock is stationary in S’ frame LT applied to event #2 S’ S t x t’ x’ tick #1 0 0 0 0 In S frame the time between clock ticks is tick #2 dt x dt’ 0 Time dilation has been verified experimentally

4. Basis and co-basis sets basis set along coordinate axes co-basis set

5. Parallel Transport transport a vector without changing it along a closed loop the transported vector is not the same as the original one the difference between the two depends on thepath taken and the area enclosed

6. Newtonian Deviation Equation Note: in Eucledian space of Newtonian gravity covariant = contravariant Example: M particles approach each otherin x1, x2 directions, separate along x3 direction