Transcript Length Contraction

Length Contraction
Relative Space
 An observer at rest measures a proper time for a clock in
the same frame of reference.
 An object also has a proper length when measured by
an observer in the same frame of reference.
 If other observers are moving the apparent length will
change in the direction of motion.
Contraction
 Light traveling the
length of B’s ruler
takes less time as
A sees B.
• Time dilation
• Constant light
speed
L
L
c

t t 
Gamma Again
 Each observer sees the other stick contracted.
2
L
v
L  1    L 

c
Distant Star
 A starship cruises at
0.999c towards a star
that is 200. ly away.
 What is the apparent
distance to a traveler
on the ship?
 The speed given is in
units of c so
v/c=0.999.
 For the moving
observer,
L  L  L 1 0.999
2
 So, L’ = 8.94 ly.
Doppler Shift
 The classical Doppler
shift for sound is due
to relative motion
between source and
observer.
• Depend on specific
motion
cs  vo
f f
cs  vs
 Relativity changes
this for light.
• Constant speed of
light
• Only relative velocity
Relativistic Shift
 The relativistic
Doppler shift uses
length contraction (or
time dilation).
 Both the wavelength
and frequency are
shifted.
  c/ f
1 v / c
  
1 v / c
1 v / c
f f
1 v / c
Redshift
 Objects that move
rapidly away have
wavelengths shifted
longer.
 Visible light shifts
towards the red, and
the effect is the
redshift.
next