clock speed of light event proper time interval
Fig. 4-3B illustrates these same two events from the standpoint of observer B, who is parked by the tracks as the train goes by at a speed of 



v
.


{\displaystyle v.}

 Instead of making straight up-and-down motions, observer B sees the pulses moving along a zig-zag line. However, because of the postulate of the constancy of the speed of light, the speed of the pulses along these diagonal lines is the same 



c


{\displaystyle c}

 that observer A saw for her up-and-down pulses. B measures the speed of the vertical component of these pulses as 



±



c

2


−

v

2




,


{\displaystyle \pm {\sqrt {c^{2}-v^{2}}},}

 so that the total round-trip time of the pulses is 




t

B


=
2
L

/




c

2


−

v

2







{\displaystyle t_{B}=2L/{\sqrt {c^{2}-v^{2}}}\,}

 



=

t

A



/



1
−

v

2



/


c

2




.


{\displaystyle =t_{A}/{\sqrt {1-v^{2}/c^{2}}}.}

 Note that for observer B, the emission and receipt of the light pulse occurred at different places, and he measured the interval using two stationary and synchronized clocks located at two different positions in his reference frame. The interval that B measured was therefore not a proper time interval because he did not measure it with a single resting clock.
