The Perception of Time

To understand time I have to understand my own perception of it first. 

The perception of time does not start with the clock. Firstly I am aware of myself, secondly I am aware of the immediate environment, then I perceive a change through senses. The change comes to my attention by becoming aware of a difference between the current sensation and the memory of this sensation being absent or by remembering other characteristics of it (No pain then pain, or less pain, more pain). In the normal state of mind I distinguish between current and not current, so the primary perception of time is Now and the Past. There is no immediate need to realise the Future. The sense of the future comes late in brain development and according to evidence available to G.J Whitrow[1], animals do not perceive the future. Contemporary adult human has a well developed concept of Now, the Past and the Future, and can cognitively time travel back and forth. Significant part of awareness can be a-temporal, such as a mental process elaborating some logical problems related to coexisting concepts, for example while performing an arithmetical operation in memory.

Apart from the ability of remembering facts and things, human memory is also capable of recording the order of events. Events are sensed changes of state in memory believed to be the representation of some real world changes of a state. The necessary ingredients in the perception of time are:

1. A perceiving process in human brain or in a computer.
2. State memory being continuously updated from sensor sources by the perceiving process.
3. Algorithms ordering and retrieving information from sensors and long term memory.
4. Ability to see different states in memory and ordering them  successively as they appear.

Ingredients 1-3 are natural properties of human mind or a computer system, ingredient 4 is the ability which equates to an elementary perception of time in terms of "before" and "after". The ordering and memory allow counting reoccurring events which can be a measure of duration, which is one of the faces of time.  Apart from immediate real time sensation of events appearing in order, the stored information allows off-line reasoning about the order of events and hence about the passage of time.
What it has been said above is nothing new. Aristotle in his Physics[2]  (350 BC) says:

• But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed [...] On the other hand, when we do perceive a ‘before’ and an ‘after’, then we say that there is time. For time is just this — number of motion in respect of ‘before’ and ‘after’.

Physically significant are events pertaining to physical objects coming to existence or becoming present in my field of observation. A glass mirror broken brings to existence a number of irregular pieces and such sequence perceived by me is a physically significant and unique change that can be said to occur in time in a particular order. The memory of the real change is retained even if some subsequent process disintegrates glass pieces into dust. We should examine later if such apparently unique order can be linked to the concept of time used in theory of relativity, and would it be relative to any observer to a degree that it can even be reversed.

At this point I conclude that my innate perception of time gives me the capability of ordering events in terms of "before" and "after" as well as enables primitive measure of duration by counting reoccurring events recorded in memory. In that context it appears that those two capabilities can be related to time defined either by Newton or the theory of relativity and there is nothing subjective or mystical in those capabilities. There is limited precision problem but it can be eliminated with adequate choice of time scales used in experiments with reality. Therefore I believe that this common sense perception of time can be validly used in reasoning in the context of relativity and time reversal discussions.

Having said that I immediately recall inspirational thoughts on time written by Ernst Mach in 1883 in his book "The Science of Mechanics"[3]

• When we say a thing A changes with the time, we mean simply that the conditions that determine a thing A depend on the conditions that determine another thing B, The vibrations of a pendulum take place in time when its excursion depends on the position of the earth. Since, however, in the observation of the pendulum, we are not under the necessity of taking into account its dependence on the position of the earth, but may compare it with any other thing (the conditions of which of course also depend on the position of the earth), the illusory notion easily arises that all the things with which we compare it are unessential. Nay, we may, in attending to the motion of a pendulum, neglect entirely other external things, and find that for every position of it our thoughts and sensations are different. 
• Time, accordingly, appears to be some particular and independent thing, on the progress of which the position of the pendulum depends, while the things that we resort to for comparison and choose at random appear to play a wholly collateral part. But we must not forget that all things in the world are connected with one another and depend on one another, and that we ourselves and all our thoughts are also a part of the nature. It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things ; made because we are not restricted to any one definite measure, all being interconnected.[...]
• We arrive at the idea of time, — to express it briefly and popularly, — by the connection of that which contained in the province of our memory with that which is contained in the province of our sense-perception. When we say that time flows on in a definite direction or sense, we mean that physical events generally (and therefore also physiological events) take place only in a definite sense.

[1]Whitrow G.G, Time In HistoryOxford University Press 1989
[2]Aristotle, Physics, Grece 350 BC
[3]Mach E. The Science of Mechanics Chicago The Open Court Publishing Company London 1901
     http://ia600406.us.archive.org/35/items/sciencemechanic00machgoog/sciencemechanic00machgoog.pdf