Question

3) Two events are perceived by inertial observer A as being
separated by distance x and time t.
a) What is the time between the events perceived by inertial
observer B who is at both events, and is that more or less than
t?  (One way is to find an invariant.)
b) Does B reckon that A's clock is ticking slowly or quickly,
and by what factor, in terms of the above givens?
c) How does B resolve the apparent contradiction between the
answers to parts (a) and (b) here?   

Answer 1

a)

The time interval between the two events measured by B will be smaller as compared to the t ( the time measured by the observer A) because the time measured by B is the proper time as the two events occur at same place in the frame of B. For the two events to occur at same place in frame B, it should be moving with a velocity

v = x/t

w.r.t. frame A.

So time measured by observer B is

b)

B will reckon that A's clocks are ticking slowly as A is moving w.r.t. B with velocity V' = -v i.e.,

V' = -x/t.

Of course, moving clock ticks slower by the factor

c)

From frame B, the clocks of A are not synchronizerd. So, the time measured by A is erroneous for B.