You aren't being very consistent your proton which you are happy to say exists can only be defined by a wave. I assume you aren't going to try and cling to the classical rubbish. So if your proton can only be described by a wave then time must exist for the wave to exist (wave = movement in time BY DEFINITION).
Same logic as you applied to the proton it doesn't matter whether you measured it or not, it has to exist to the same level the proton does.
So either both exist or neither exist and that is reality .... QED.
Given release of direct detection of gravity waves today we can even say that anywhere gravity exists then time must exist ... GR demands it !!
So this idea is now up against GR and QM which both say no
For science time exists from the moment of the big bang, it isn't up for conjecture to laymen. Personally I find the whole idea of playing with the concept naive and foolish. A related question would be does the universe exist if Bill S wasn't born, how would he know.
