Lecture Five

Simultaneity and Synchronization

Relativity of Simultaneity

Synchronization Stationary observers Relatively moving observers

Synchronization for Stationary Observers

Synchronization for Relatively Moving Observers

Synchronization for Relatively Rest Observers

Invariance of 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 = ( ) -1 sec 1 meter of time  3.3 nanoseconds

meter as unit of time “  t = 1 meter (of time)” means c  t = 1 meter

geometrization geometrical units natural units

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 Interval in 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