Lecture Five
Simultaneityand
Synchronization
Relativityof
Simultaneity
Synchronization
• Stationary observers
• Relatively moving observers
Synchronizationfor
Stationary Observers
Synchronizationfor
Relatively Moving Observers
Synchronizationfor
Relatively Rest Observers
Invarianceof
Interval
meter as unit of time• time for light to travel one meter
• 1 meter of light-travel time
• in conventional units:
c = 299,792,458 meters per second
• 1 meter of light-travel time = 1 meter/c
• 1 meter of time = (299792458)-1 sec
• 1 meter of time 3.3 nanoseconds
meter as unit of time
“ t = 1 meter (of time)” means
c t = 1 meter
geometrizationgeometrical units
natural units
1c
Invariance of Interval
•Event A: the emission of a flash of light
•Event B: the reception of this flash of light
Invariance of Interval
in rocket frame:•The reception occurs at the same place as the emission.
Invariance of Interval
in rocket frame:•The light flash travels a round-trip path of 2 meters.
Invariance of Interval
in rocket frame:x 'A = 0, t 'A = 0
x 'B = 0, t 'B = 2 meters
x ' = 0, c t ' = 2 meters
Invariance of Interval
in laboratory frame:light flash is received at the distance x to the right of the origin.
Invariance of Interval
in laboratory frame:The light flash travels the hypotenuse of two right triangles.
Invariance of Interval
in laboratory frame:x A = 0, t A = 0
x B = x , t B = t
c t = 2 [1+(x /2)2]1/2
Invariance of Intervalin rocket frame:
( x ' )2 = 0, ( c t ' )2 = 4
in laboratory frame:
(c t)2 = 4 [1+(x /2) 2]
= 4 + (x) 2
Invariance of Interval
4 = ( c t ' )2 - ( x ' )2
= (c t)2 - (x) 2
One epitome displays four great ideas
1. Invariance of perpendicular distance
2. Invariance of light speed
3. Dependence of space and time coordinates upon the reference frame
4. Invariance of the interval
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