Post on 03-Jan-2016
description
Cosmology 5022
Relativity
Length Contraction
S S’
event #1 0 0 0 0
event #2 0 L t’ L’
t x t’ x’
S’S#1 #2
v
rod is stationary in S’ frame
Want 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 #2
LT:
Simultaneous events
Time Dilation
S S’
tick #1 0 0 0 0
tick #2 dt x dt’ 0
t x t’ x’
S’S
v
clock is stationary in S’ frame
Want to measure dt, the time between ticks in S frame
In S frame the time between clock ticks is
LT applied to event #2
LT:
Time dilation has been verified experimentally
Basis and co-basis setsbasis set along coordinate axes
co-basis set
Parallel 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 enclosed
Newtonian Deviation Equation
Example:
particles approach each other in x1, x2 directions, separate along x3 direction
M
Note: in Eucledian space of Newtonian gravitycovariant = contravariant