Hi JCNS,
I really enjoyed your post. It is one of the most lucid treatment of the problem of defining time that I have read. The exposition was clear and the reasoning easy to follow.
The only shortcoming that I can see is that, though you explain that time corresponds to the sequential rearrangement of the components of reality, in essence, that the accepted notion of time is an illusion, you insist that we can still retain the operational notion of time and theories such as special relativity.
Special relativity needs time to be a physical aspect of reality. If it is not, then time cannot be unified with space. And space-time, doesn't not exist. You can't unify a concept, which corresponds to no physical aspect of reality with space, which is an aspect of physical reality. Special relativity can't exist without time being physical. Physical time is required for the effect of time dilatation to exist. Without time dilatation, there is no special relativity. Without time, there is no time dilatation.
I think the essay contrives its conclusion into agreeing with accepted theories. But you can't have it both ways. If time is not physical, then you must reevaluate, even reject many of the dominant theories.
That said I agree with you as far as how time is defined in terms of rearrangements or, in my terms, according to the principle of strict causality.
In regards to time, you might find my answer to the FQXi article titled "Killing Time"
"note: This is from a article I posted on my blog in 2010, which, coincidentally, is also titled "Killing Time."
The greatest problem with current physics theories is that they consider time as if it were a property of physical reality.
Time is a relational concept which is made to allow us to compare events with periodic and cyclic systems; in other words, clocks. But time has no more effect on reality than the clocks that are used to measure it? The fact, when you think of it, clocks don't really measure time.
Take an event consisting of the fall of an object from a point to "a" to a point "b". When we say we measured the time it took for that event to happen, what we actually did is count the number of cycles (seconds, or fraction of seconds for instance) from when the object was dropped from "a" and stopped the count when it reaches point "b". So we don't actually measure time. What we do is simply count the number of cycles the clock's mechanisms go through over the course of the event.
There is no reason why time should be anything more than a relational concept, a useful relational concept I admit, but only a concept. Yet time, physicists will argue, is necessary to the study of nature.
Every process, every event, transformation or phenomenon appears to happen in time. Without time, it is believed, the Universe would be static. Worse, there would be no Universe at all. What we fail to understand is that affirming the necessity of time is like saying that the atoms in the Universe could not exists without the number systems we use to count them. The argument is akin to the solipsistic argument that reality cannot exist without an observer (which is something many quantum-physicists actually try convince us of).
So let's make things clear for a start. Planet Earth, the solar system, our galaxy, our Universe existed before there were people to observe them and before the concept of time, which is a construct of the observers, was invented.
So what does it mean that time is really a relational concept? What it essentially means is that there are no physical interaction between a phenomenon and the number of cycles of the periodic system we may compare it to.
You'll notice that I didn't say there is no interaction between the phenomenon and the periodic mechanism. What I said is that there is no interaction between the phenomenon and the abstraction that is a number. That said, there is a very simple test to determine if a notion is a property of physical reality or if it's merely a concept. The test is one of necessity.
For the sake of argumentation, let's assume that time is a fundamental property of physical reality. If time is a fundamental physical property of reality, then the existence of time must be an axiom essential to any theory of physical reality. What this implies is that it should be impossible to describe any physical phenomenon without the use of time. Impossible! Are you sure?
A principle of strict causality which describes physical phenomena as sequences of events related through causality doesn't require the concept of time. Even concepts such as motion and speed can be described without ever using concept of time.
In fact, the only indication that time may be physical is the effect of time dilation. Time dilation is the inevitable consequence of two axioms: the constancy of the speed of light and the continuity of space. But it can be shown that if space is discrete,then there is no need to resort to the concept of time dilation to explain the constancy of the speed of light.
Then, if time is not an essential axiom, it follows that time is not a fundamental property of physical reality. As a consequence, time is nothing more than a relational concept.
In my opinion, we need to make a distinction between reality and representations of reality by models or concepts. I think we're confusing the two when it comes to time."
On that, congratulations on what, in my opinion, is a well written and lucid exposition of the problems relevant to the definition of time.