From Special Relativity French As the text points out an obs

From Special Relativity, French

As the text points out, an observer does not have a complete view of what is happening everywhere in his reference frame at a given instant; he is aware only of what is happening at his location at that instant. Suppose a meter stick pointing in the x direction moves along the x-axis with a speed 0.8c, with its midpoint passing through the origin at t=0. Assume the observer is situated at the point x = 0m and y = 1m.

a) Where in the observer\'s frame is the midpoint of the meter stick at t=o?

b)When does the observer see the midpoint pass through the origin?

c) Where do the endpoints appear to be at this time?

Solution

Where in the observer\'s frame is the midpoint of the meter stick at t=o?

light reaching from any point on the stick takes 1/c seconds to reach the observer’s eye.

within this interval any point on the stick would move 1/c*0.8c = 0.8 m.

at t=0 the midpoint of the stick is at origin but observer’s eye will receive light from the point (-0.8,0). Observer at rest will see the midpoint at 0.8,0

When does the observer see the midpoint pass through the origin?

observer will see the midpoint passing through the origin at 3.0e-8 seconds.

C) Where do the endpoints appear to be at this time?

length of the stick from observer’s point = 1*(1-(0.8c)²/c²)^1/2

                                                          = 0.6 m

midpoint is at origin          ,

endpoints are at (-0.3,0) and (+0.3,0)