Arguments against the idea that Time has an ending
Firstly, reasons why I am not convinced that Time can have had a beginning or will have an end:
a) It seems to me that Time is a prerequisite for anything to begin or end, even time itself. A beginning is an occurrance/change/event. Without time occurances/changes/ events cannot happen. If time did not exist prior to the beginning of time then how, within that timelessness, could the occurrance/change/event of Time's beginning happen.
b) It is sensible to enquire, "At what time did time begin?" because if you say "Time began at no time" then this is the same as saying Time did not begin. If you say "There was no time before time" then this is just the same as saying, "Time did not have a beginning".
c) Furthermore, if you say that, after the last tick of time, time will end, then how long will that last tick of time last, since there would be no time after it, there would be no time for it to end within thus the end of time would be endless which is the same as saying Time will not have an end.
Secondly, if I accept that Stephen Hawkings is right that time will end.
But say that I accept Stephen Hawkings statement that time will end when the universe ends.
So the universe ends.
And then just as the big bang happened, another big bang happens.
If there was no time between them, then the second big bang would happen instantaneously after the end of the universe; there would be no gap of time between them thus it would be as if a big bang happened just as the universe had ended.
And since there would be no gap between the end of time and the rebeginning of time, it would be as if time was without end.
Or to put it another way
If there is no elapse of time between the end of time and the rebegining of time then the progression from one to the other would be seamless; so seamless, infact that one could argue Time did not end at all.
Lastly, an assumption without proof made by Stephen Hawkings
Lastly, if he is saying that Time will end when the universe ends, Stephens Hawkings must assume that Time or "Spacetime" does not exist beyond our universe but no scientist, as yet, has any proof of what exists beyond our universe. There are some physicists who think that our universe might be infinite and there are other physicists who believe that there may be many universes outside our universe. If Time does exist beyond our universe then that must surely mean Time exists without our universe; that Time would continue to exist even if the universe ceased to exist.