bei48482_FM

6 Chapter One

Figure 1.4 shows the laboratory clock in operation. The time interval between ticks

is the proper time t 0 and the time needed for the light pulse to travel between the

mirrors at the speed of light cis t 0 2. Hence t 0  2 L 0 cand

t 0  (1.1)

Figure 1.5 shows the moving clock with its mirrors perpendicular to the direction

of motion relative to the ground. The time interval between ticks is t. Because the clock

is moving, the light pulse, as seen from the ground, follows a zigzag path. On its way

from the lower mirror to the upper one in the time t2, the pulse travels a horizontal

distance of (t2) and a total distance of c(t2). Since L 0 is the vertical distance between

the mirrors,



2

L^20 

2

(c^2 ^2 )L^20

t^2 

t (1.2)

But 2L 0 cis the time interval t 0 between ticks on the clock on the ground, as in

Eq. (1.1), and so

2 L 0 c



 1 ^2 c^2

(2L 0 )^2



c^2 (1^2 c^2 )

4 L^20



c^2 ^2

t^2



4

t



2

ct



2

2 L 0



c

0

t

t

2

Figure 1.4A light-pulse clock at

rest on the ground as seen by an

observer on the ground. The dial

represents a conventional clock on

the ground.

Meter stick

L 0

Mirror

Light pulse

Mirror

Photosensitive surface

Recording device

“Ticks”

Figure 1.3A simple clock. Each “tick” corresponds to a round trip of the light pulse from the lower

mirror to the upper one and back.

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