cosmology 5022
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 PresentationTRANSCRIPT
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Cosmology 5022
Relativity
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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
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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
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Basis and co-basis setsbasis set along coordinate axes
co-basis set
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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
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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