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