Chapter 9: Fundamental Physics

Section 11: Uniqueness and Branching in Time

Spacetime networks from multiway systems

The main text considers models in which the steps of evolution in a multiway system yield a succession of events in time. An alternative kind of model, somewhat analogous to the ones based on constraints on page 483, is to take the pattern of evolution of a multiway system to define directly a complete spacetime network. Instead of looking separately at strings produced at each step, one instead maintains just a single copy of each distinct string ever produced, and makes that correspond to a node in the network. Each node is then connected to the nodes associated with the strings reached by one application of the multiway rule, as on page 209.

It is fairly straightforward to generate in this way networks of any dimension. For example, starting with n A's the rule {"A" "AB","AB" "A"} yields a regular n-dimensional grid, as shown below.

If each node in a network is associated with a point in spacetime, then one slightly peculiar feature is that every such point would have an associated string—something like an encoded position coordinate. And it then becomes somewhat difficult to understand why different regions of spacetime seem to behave so similarly—and do not, for example, seem to depend on the details of their coordinates.

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From Stephen Wolfram: A New Kind of Science [citation]