Brian,
Thank you for your comments on my essay. I will respond to them there.
I see space (or at least distance) as an equal partner when considering time and change because without it, I cannot visualize how it is possible for change to occur. In other words, the consideration of a "before" and "after" requires in my view a locational background through which these notions become meaningful, but I think I am becoming a bit philosophical.
I am taking thermodynamics/statistical mechanics this term and I think I tend to agree that combinatorics can be a useful tool in physics (although I have not taken a course on this).
When it comes to receiving constructive criticism you are fortunate to possess the wisdom that eludes many people who are much older than you.
wrt to my question, I was not referring to anything as sophisticated as the quantum zeno effect. Let me give a simple example to illustrate what I mean:
Consider the muon. As far as we know, it is a fundamental particle and therefore, by your idea, it can experience time only by means of its interactions outside of itself. Here I will consider interactions with an electric field, since the muon carries a non-zero electric charge. It is also unstable, and therefore the decay time (when considering a large sample of muons) can act as a clock.
Scenario 1:
Consider a muon that travels through a field set up by two identical electric charges q1 and q2. For simplicity assume the charges are equidistant from the Muon. There are two arrangements associated with the electric field sources(q1,q2) and (q2,q1) which are derangements of each other.
Scenario 2:
Consider a muon that travels through a field set up by three identical electric charges q1, q2 and q3. For simplicity, again assume the charges are equidistant from the muon (they would have to be in a plane perpendicular to the muon's direction of motion). There are six arrangements associated with the electric field sources (q1,q2, q3) (q1,q3,q2) (q2,q1,q3) (q2,q3,q1) (q3,q1,q2) (q3,q2,q1) which can be divided into three deranged pairs.
There are more derangements associated with the second scenario. Here each individual combination has only one derangement but with n(q)>3 it can have more than one.Would it therefore not be expected that the average decay time of a large sample of muons passing through a field created by more source charges i.e. a stronger field be shorter than that of one passing through a weaker one?
Armin