Someone stopped me in the street..
"D'you know what time is mate?"
The structure of matter affects space-time so, in theory, as you
approach the singularity of the big bang the curvature of space- time becomes infinite - so how can either exist before that point? But if the big bang turns out to be a recurring phenomenon and there were other big bangs prior to ours, what happens to the time that measures the time between one big bang and the next? Why should time not exist then?
Then, if the 'many worlds' theory of quantum mechanics is correct, (the Everett interpretation), then there may be multiple space times; so there may be no such thing as time itself, but merely spatial relationships between energy states occurring in quantum fields in multiple universes.
But space might not exist either!! What we ordinarily mean by space could turn out to be just changes in the relative position between things to which we've ascribed a separate identity for reasons such as that's just how we experience things. So, could time exist without events occuring on which to hang measuring instruments with which to measure its passing?
Wait...it's lunchtime!!
Dammit! Lunchtime is an illusion too..srsly.
Shumacher's thought experiment might be relevant.
Suppose you have a universe divided into regions A B and C. In region A time proceeds normally for ten years but it freezes during the eleventh. In region B time is normal for thirteen years then freezes for a year. In region C the same thing but on a seventeen year cycle. Region B and C will observe region A freeze and region C will observe regions A and B freeze in turn and then unfreeze. Every 2210yrs, or whatever it is, time will freeze in all three regions. But time still exists during this frozen time, right? Because after a year they all unfreeze again. Curious, no?