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It's a tad difficult following this last post. Are you saying time is something to do with the observer? I mean I do agree. The theory of relativity is an observer-dependent theory. Another issue, is whether time can be made into an operator. There is an invariant time operator of the form R/c however, it might be argued this is trivial. There's also the unitary operator of time evolution, but again, is this a non-trivial operator?
I did at one time explore a line element in which you treat time as an operator along with the usual space dimensions. But that would be for extended discussion outside the scope of this post. The real thing I want to explore is whether curvature manifests time in a natural way to be itself observable. We can see curvature, and certainly GR uses time in a clever way to manifest curvature as a warping of space.
One issue quantum mechanics has is that while space is an observable, time isn't. I'd like to challenge this if we can.