Delta² said:
First all i am greek myself ) some of it sounded not greek but chinese i would say (hehe both greek and chinese are civilizations with big history anyway). I still don't see it as a problem of consistency/inconsistency/partial or limited inconsistency, rather i see it as a problem to express something which seems to be elementary in other more trully elementary concepts.
1 and 2 are very mathematical ways of looking at time, it might be convenient to look it that way for QM or GR . However how can we say that the two directions in time ( i suppose u mean backward and forward) are identical since entropy increases as time increases and if we could go backwards in time we could have a decrease in total entropy.
Well Yahsu! Or Nee Hao Ma!
Yes, so we have an apparent elementary quality and maybe there is something more elementary we can use to define/characterize/address it. Maybe.
Here was my approach: First, tease out all the features that bundled together with what we mean by time. There are quite a few... for example,
1. There are several structural layers. It is one dimensional or two (noting complex case in QT). It has a metric, a topology, etc. etc. Ultimately, all of these structural features boil down to a set theoretic expression defining:
i. a set
ii. with a topology
iii. with a metric
iv. asymmetrical structure
and so on. Doing this actually helps to clarify the rather significant differences evident in different physcial characterizations of time. Okay, this was the 'easy' part of the problem. Now to the hard part...
i. it has direction
ii. it has 'flow'
iii. it has a magical locus called a 'now'
There are two ways to go. Either we say all this other stuff is 'psychological' and leave it to the psychologists to sort out (personally, not an approach I recommend!) or we rethink what we mean by physical properties.
If we go the second way, it may well be that there are more 'fundamental' ways to speak about time - in fact, that is my own personal 'religious' intuition on the issue - but whatever the 'truth' of the matter may be, we need to find a way to even speak about it.
In this sense, we need to be able to speak about something like 'change' or 'now' or 'direction' or 'flow' (as a 'quale' or phenomenological qualityity) in terms that a hard nosed physicist can actually smell it so to speak. That is not easy in some cases.
Sure, we can define 'now' as a perspective - that is relatively unproblematic. But direction has no meaning in the physical lingo nor does flow or change...
So without this, how can we ever hope to find the real elementary parts upon which what we called time is built/structured/made? For even if we epiphony our way to an answer, we still do not have the language or semantic tools to speak about these things...