Figure it out with a Lorentz contraction...
Time in the moving system will be observed by a stationary observer to be running slower by the factor:

v2 / c2 = 1, 1-1 = 0, sqrt of 0 = 0, 1/0 is infinite, t'=t/0, t'=infinite, time will move infinitely slower on the lightbeam as time for a stationary observer, hence time does not pass on the lightbeam.