[TinyTree]

We can consider any physical system, including the entire universe, as a Markov chain.

It is established that in order to understand the behavior of markov chains, it is frequently required to run monte carlo simulations of the behavior of such mathematical objects.

http://perso-math.univ-mlv.fr/users/vandekerkhove.pierre/pdf/Entropy04_ss.pdf

For a cellular automata, consisting of an infinite one dimensional series of cells which are either on or off, we can
define the probability matrix for the transition of a specific cell to the next state as a function of probabilities with a stochastic matrix.

Here i, j represent the set of available states S = ${0,1,2,\cdots$}

P_{i j} >= 0, \Sigma_{j S} P_{i j} = 1

The above is latex, but I can't figure out how to get it to be displayed that way. I see "Link" "Image" "code" "HTML" "PHP" "Quote" all of which do various useful setting aside but are not mathematical symbols.

In any event, it is not possible to define the entire transition matrix for an infinite object with a finite representation- however, it is possible to define the transition matrix for an individual cell with specific neighbors.

As to whether an infinite transition matrix makes any sense or not- I am reserving judgement for the moment.



http://www.reti.dist.unige.it/reti/Documenti/MarkovChains.pdf

[AntonioLao]

Originally Posted by TinyTree We can consider any physical system, including the entire universe, as a Markov chain.

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. This is an indirect proof that spacetime events are mostly disconnected from each other yet spacetime is completely connected that is to say that every point is connected.

[brueggert]

Is every "point" connected, or might there exist some quantum unit of spacetime, which would imply either a disjoint union of "points" or "points" with a mysterious "aether" in between.(?)

[Guille]

Originally Posted by brueggert Is every "point" connected, or might there exist some quantum unit of spacetime, which would imply either a disjoint union of "points" or "points" with a mysterious "aether" in between.(?)

Hi, welcome.

I think we should leave aether to philosophers, and centre on facts. The quanta of spacetime (which I believe to be the photon-and have scientifico-mathematical points to believe such) are connected, but, as Antonio wrote, only one to one. I believe this is true, and yet, although each event is impplied only by the just previous one (and I believe the minimum space of time we can devide events or by which change can occur is planck's time constant), that event was impplied by the one before, and that one by the one before...and it goes all the way to BB or earlier (???).

[AntonioLao]

Originally Posted by brueggert Is every "point" connected

Every point is connected but no point is doubly nor triply nor multiply connected.

[Guille]

Originally Posted by AntonioLao Every point is connected but no point is doubly nor triply nor multiply connected.

Actually, all points are doubly connected: if you see, it must be connected to the one before, and after it goes by, and we enter the new point, it should become connected to the one after it.

[AntonioLao]

Originally Posted by GUILLE Actually, all points are doubly connected

Directionally speaking, the connection is singular because clockwise and counterclockwise can be differentiated but Lorentz transformation cannot distinguish between CW and CCW.

[brueggert]

Then we're talking about Minkowski spacetime, which is locally flat. I'm hesitant to jump to a description of the universe without filling in some steps inbetween. Perhaps this has already been covered and I may be hindering the converstaion, as I am obviously new to this...

[AntonioLao]

Originally Posted by brueggert Then we're talking about Minkowski spacetime, which is locally flat.

Not flat if there is mass at the center. Einstein took care of this dilemma by formulating his general relativity.

[brueggert]

Right, but if we are trying to say how spacetime is connected in the universe, and then evaluate the validity of viewing the universe in terms of a Markov chain, proof of a certain connectedness in terms of Lorentz transformations can only apply over areas of spacetime that appear flat. What about a succession of three (or more) events in a region of spacetime that is not flat? What about right before, during and after the Big Bang?