Causal Set Theory developed by Rafael Sorkin in 1987 provides a key underpinning to LQG as a theory of Quantum Gravity and to the author’s Decision Network Theory . it postulates that it is not necessary to know the geometry of space-time- only the causal order of all elements within it.
Causal elements may be clustered into sets or Causets, clusters of space-time quanta or events related by causal connections. It is an order relation.
These causal elements or quanta link in causal networks and grow over time corresponding to the expansion rate of space-time. At the same time the theory predicts accurately this expansion rate or the current value for the cosmological constant.
A Causet, to be more precise, is a discrete set of elements - the basic spacetime building blocks or "elementary events". But whereas in the continuum, spacetime is described, mathematically speaking, by an elaborate web of relationships among the point-events carrying information about contiguity, smoothness, distances and times, for the elements of a causet the only relational information carried is a "partial (or quasi-) order" - for some pairs x, y of elements- the information that x comes before y, or, in other cases, that x comes after y. This ordering is the microscopic counterpart of the macroscopic relation of before and after in time.
This conceptual framework shares quite a lot in common with LQG. Like LQG it argues that space-time is a dynamic and discrete entity and evolves through quantized networks, according to the order in which events take place in time- that is within a causal order.
It corresponds however, even closer to the conceptual framework of the D-Net model, because of its abstract causal nature and independence from geometric constraints. The causet nodes reflect the decision nodes of the D-Net framework.
Friday, May 23, 2008
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