[TinyTree]

Originally Posted by AntonioLao From reading thru at http://en.wikipedia.org/wiki/Markov_chain it is understood that the probability of a future event only depended on the present event and not any event of the past, this implies that the connectivity of events is exactly singular and there can only be one and only one connection between two events at a particular point in time.

Yes, it is correct to say that the probability of a future event is only contingent on the present state of the universe. There are two probabilities for such an event:

1) The probability of the event with the given universe configuration (the current position we are in on the markov chain)

2) The probability of the event at the specific time t given specific initial conditions. This probability is distinct from 1 in that we are "eliminating the knowledge" of the present. That is to say- we are assuming the present still is one among many potential states which the universe could be in. Then we can ask what the probability of that state is absent of all knowledge except initial conditions. This is the probability of the state vector.

Note it seems possible, although I am not proving here, that the probability of 1) may be "low probablility" yet lead to a higher probability for 2). That is to say- these are not necessarily directly correlated. Moving from the current configuration to a less probable one with respect to the present position on the Markov chain may lead to a higher probability for 2. Simple example: a low probability quantum decoherence event tied to an atomic bomb that destroys all living things for 100 kilometers. This is a low probability event in 1, but leads to a higher probability for the state vector for 2 if it does go off.

As for your statement about connectivity- it is a very good question- what is the nature of connectivity for our universe? IE- it is obvious that spacetime is a "completely connected" mathematical solution. However, it is also deterministic, thus does not immediately come into play with the nature of nondeterministic evolution of the universe.

So then we have to ask: what is the connectivity of the universe? IE- how and why do chemical bonds form? they are quantum phenomena, where the interaction of electron shells of distinct atoms interact

[AntonioLao]

Originally Posted by TinyTree what is the nature of connectivity for our universe? IE- it is obvious that spacetime is a "completely connected" mathematical solution.

Although each point of spacetime can see all the numerous other points, each point has a probability of making a decision which of the six closest neighboring points to connect to in the next time interval but in order to connect it must first disconnect. Both connect and disconnect imply the exchange of energy at the quantum level. This quantum of energy is really the square of the usual energy that we are familiar with.

[TinyTree]

Originally Posted by AntonioLao Although each point of spacetime can see all the numerous other points, each point has a probability of making a decision which of the six closest neighboring points to connect to in the next time interval but in order to connect it must first disconnect. Both connect and disconnect imply the exchange of energy at the quantum level. This quantum of energy is really the square of the usual energy that we are familiar with.

I am not sure it is this simple. In quantum electrodynamics there exists a probability distribution of interaction (of say, a photon impinging on an electron and exciting it) for numerous electrons.. Thus, this photon is "connected" (potentially) to more than one electron. Thus its connectivity graph is spread out- it is not a one to one correspondence.

[brueggert]

O.K., I see what you are saying. My concern is the following: AntonioLao writes: "this implies that the connectivity of events is exactly singular and there can only be one and only one connection between two events at a particular point in time"
I don't understand how this can be so. If you look at all of spacetime, and then examine our universe in lightcone-coordinates. Take two events (one on the x+ axis and the other on the x- axis)- in 2D it appears that a straight line (constant in time) connects the two points. In reality, aren't the 2D traingular sections actually cones, in which case two goedesics connect the two points?

[AntonioLao]

Originally Posted by brueggert Take two events (one on the x+ axis and the other on the x- axis)-

Space-like intervals of the lightcone are all forbidden for the existence of matter and energy because of superluminal speeds. These are intervals of the wormholes if they exist and they would not be exempted from being singly connected.

[TinyTree]

Check out this link:

http://www.astro.ucla.edu/~wright/cosmo_04.htm

I am not sure I understand your question, but this diagrams the impact of quantum events as lightcones stretching out through the universe . It is well worth a look.

Historical quantum events impact the probability of the state vector around us now. The initial gravitational precipitation points impacted the formation of the galaxies and stars (in addition to the anisotropy observed in the background microwave radiation)

[AntonioLao]

Originally Posted by TinyTree Thus, this photon is "connected" (potentially) to more than one electron. Thus its connectivity graph is spread out- it is not a one to one correspondence.

Not in QFT since the virtual particles have to be considered as the phenomena of quantum vacuum fluctuations. The exposures of the bare/naked charge and the bare/naked mass and exposing the balded/no-hair spacetime singularity.

[brueggert]

Originally Posted by AntonioLao Space-like intervals of the lightcone are all forbidden for the existence of matter and energy because of superluminal speeds. These are intervals of the wormholes if they exist and they would not be exempted from being singly connected.

So they are, but for a Markov chain to represent the universe in its entirety in time and space, space-like circles of the lightcone must be considered for regions (of space) and times when there is no matter present. (Again, I am wary of using the Lorentz tranformations here too, as there may exist high energy densities that would induce a spacetime curvature of significance.) I am wondering if we should not also examine the connectivity between the same "event" (spatial) at two different times.

[AntonioLao]

Originally Posted by brueggert as there may exist high energy densities that would induce a spacetime curvature of significance.) I am wondering if we should not also examine the connectivity between the same "event" (spatial) at two different times.

These high densities regions could the the blackholes. Their probabilities of existence is unity but their entropies are negative. The probabilities of the same event reconnected again is likely to be closed to zero as in having the same mind born in a different brain or body.

[TinyTree]

Originally Posted by AntonioLao These high densities regions could the the blackholes. Their probabilities of existence is unity but their entropies are negative. The probabilities of the same event reconnected again is likely to be closed to zero as in having the same mind born in a different brain or body.

At the risk of sounding like a broken record:

Entropy refers to the probability of being within a LARGE SET of potential phase space positions. The state vector probability refers to the probability of being within a SPECIFIC INDIVIDUAL STATE. Thus, the "probability of existence" I would agree would be unity (as a deterministic phenomena from a later position on the markov chain, but not from the initial conditions necessarily) and I would be interested in seeing the entropy is negative source.

In any event- the black hole "sucks in all information" (probability waves) and gets rid of them- essentially deleting created probability events when they come into contact with it.