Observing Time and Gluing the Universe

Time exists in reality but not the duration of time we observe.

Let us view the universe as a totally ordered set of states ,time is the ordering set,e.g. it is like a stack of pages but numbered by moments. For example if the set is the natural number then each state has one nearest one before and after it,also time begins at zero ,nothing before it. If the set is positive fractions then there is no next state and between every two states there are infinite other ones ,also there is nothing before or at zero yet there is no initial state,i;e. no beginning of the universe.In modern Physics we use the real numbers as the values for the time-parameter but there is not one valid argument for doing so!For now I do not make extra assumptions on the totally ordered set ,so everything said will be generic.

A state of the universe is a situation when there “is” something in it ,a force, a particle,galaxies,..,whatever! We cannot observe a state of the universe as observation will need time passing by as we experience it and a moment has no duration hence does not exist in the universe .In different states everything in the universe has changed (but we do not care if it is observable or not) ,just being in a different state changes everything(!).

It is possible for observers of the universe to identify some objects in different states ,but this is done by observing properties of the object (or event) ,whether the object is absolutely identical to some object observed earlier cannot be proved ,we “believe” it is even if we observe changes in it (e.g. movement of electrons inside an atom,but we think the atom is essentially unchanged) .Observing changes is a cognitive process we feel as taking time and we associate time to the observed change, in fact even we see the change as a process in time (see later again). There are many billions of billions of state changes of the universe,billions of times more than the number of events in the universe.We can only observe finitely many thing so we observe not much at all!

However the notion two for the number remained unchanged in any passing of states,so by creating abstract meaning we created something outside the state changing of the universe!!! I once called humans “time-hybrids” because of this.Now the memory we have keeps track of (analyzed) observations,hence by putting some information about some state of the universe in our memory we keep this registered on a state billions of states after the actual event we planned to observe . The story inscribed in our memory is thus obtained as if we are walking through life with giant steps,billions of states in each step,yet recorded as a continuous film of our deeds. The memory give us the impression of time passing by yet the memory itself is constructed in terms of meanings (at least what we can word about it is) thus a priori partially invariant. But the functioning of the memory changes in time so the invariance breaks down on account of internal processes.It is a big difference to recognize,let us say a landscape, by walking around in it or to have in the mind a description by ideas (meanings)of how the landscape is constructed. Animals certainly have pattern recognition and a memory allowing the first type of memories But I do not know whether they have a memory for abstract ideas not just patterns (I doubt it somehow).Now you get the idea that our concept of measuring is based on several extra not provable assumptions,if you measure the beginning of some event or object then by the “time” you measure the end or whatever other situation ,the event or object is a billion states further and you still have the philosophical problem whether it is the identical object (it is not really as the state changed!) and whether the quantity you want to measure (is it even expressible as a quantity ,perhaps it should be a series of quantities),did not change too in the state changes. So there is much more uncertainty in reality than in quantum theory .

Gluing the universe .

When objects are in some state of the universe all interactions between them are in the same state ,for us the definition of interaction is a process in passing time but in the universe the interaction is defined in the same state . If a(t) and b(t) are in the state at moment t in Time,the total ordering index set (think of page numbers of the book of the universe) then an interaction i(a(t),b(t)) is in the same state . That is so for all b(t) interacting and also there can be a gravitational interaction and other ones,like magnetic say,between the same objects.Now the glue between two states (earlier I just mentioned it as a transition function) is the effect of those interactions. That means in each state following the state at t,say the state at t’, a(t’) and b(t’) will have changed ,position ,velocity,impulse,temperature,…,and also the new interactions i(a(t’),b(t’)) have changed. First we have identified a(t’) as the same object as a(t) in a different state even if its structure may have changed somewhat,that means that we view an object as( a section of the étale space of the universe over the time T) as a map from T to the book of the universe (all states seen as a whole) such that t is mapped to some a(t) in the state at moment t. So we could treat an object as defined sheaf theoretically once we introduce topologies in the universe and in Time.Now when we observe all this we observe some change from moment t to t’ and we see this effect at t’ of the interaction defined at t as the interaction viewed in time passing as a process.Because we also view the interaction between a and b as a section ,the contribution of the interaction at t and the contribution of the interaction at any t’’ between t and t’ ,agree with the defined interaction at t’,so indeed the interaction between a and b appears to us as a process !

Thus our observation in time passing by creates from a momentary state of the universe a connection to a consequent one by the processes of change (and these depend on the identification of objects in different states (hence de facto on a sheaf-theoretical interpretation of objects as sections! That is why in my non-commutative model for space-time ,cf F. Van Oystaeyen,Virtual Toppology and Functor Geometry ,Marcel Dekker Publ. Co. ,New York, the sheaf theoretical approach works and in fact is natural in the light of the nature of the universe in this definition (which I believe to be founded on minimal assumptions.

So the confusing situation about humans observing reality as processes in a non-invertible time passing by ,where time only consists as a total ordering of states maybe completely clarified as explained above. You can choose the set T as the ordered real numbers and calculate happily like modern Physicists are doing or you can actually view T as a total order define on a very big but finite set (there are many such but reality defines which one !) and get a completely discrete picture of a granulated universe.

In any case we did invent the time interval between t and t’ as the glue of the book of the universe….as time goes by!