Dear Professor Annila,
A most interesting and enjoyable essay on time!
It is definitely one of my favourite topics.
Early on you state: "We readily use notions of time: just in time; time flies; only time will tell. Yet we have a devil of a time to define time itself. We use time to relate events to one another, but we are not quite able to relate the concept itself to anything. Why is time instinctively felt on the one hand, but beyond our ken on the other? I have managed to produce a non self-referential definition of time using the Planck-Einstein equation and a better understanding of what is meant by a 'clock'. The definition then removes all time paradoxes and makes the understanding of the flow of time easy to grasp.
However the arrow of time is a much more difficult concept, which I discuss briefly in my essay "Wandering towards a 'Theory of Everything' and how I was stopped from achieving my goal by Nature", where when I look at Loschmidt's paradox, and the philosophy of presentism.
My TOE brings up the notion of absolute time as the iteration of a computational TOE, and I eventually get to a position where I dispense with time altogether from my ontological framework, although it (time) is quite handy when dealing with mathematical algorithms.
In your conclusion you say: "Time occupied the minds of both Newton and Einstein. Now the issue is neither about absolute nor relative time but about tangible time - the quantum is the matter of time." I agree with this entirely, based on what I perceive the 'quantum' to be. In my case the quantum is the energy embodied in a defined volume of space.
Best wishes on your interesting essay.
Lockie Cresswell