17. Causality in DM

We need to develop a new model of causality that will fit into the mathematical results indicat­ing the functional relationship between the state of a point and states throughout all of space-time. In a DM model, the state of a cell is a digit. Whether or not it has a functional relationship with a particular other cell depends not just on the spatio-temporal relationship, but also on the state of other cells. Unlike ordinary physics, where effect can decrease with distance, in DM the prob­ability can decrease with distance, but the effect cannot! The question can best be framed by asking whether causing a particular cell to turn on and off will cause another cell at another place and time to blink. The answer depends on the states of lots of other cells. Strangely enough, you would have to be God to arbitrarily turn on or off just one particular cell, and the result would clearly be that the probability that any particular cell in the information cone would be affected is a num­ber close to 1/2. In other words there is no action that has substantially more of an effect than arbi­trarily changing one cell.

Let us define an atom of causality. We will say that d_s',t' is a cause of d_s,t if we can write the following equation:

d_s,t = d_s',t'v_s,t,s',t' + r_s,t(1 - v_s,t,s',t'),

v_s,t,s',t' is a variable that has the value 1 or 0, and that takes into account everything in all of space-time, aside from d_s',t' that could affect the state of d_s,t. So long as v = 1, d_s,t = d_s',t'. When v = 0, d_s',t' is unable to affect d_s,t and the local neighborhood rule r_s,t applies. In a DM model there is a v for d's spread outside of the normal light cone. When v_s,t,s',t' cannot be one, then there is no causal relationship between d_s,t and d_s',t', even if d_s,t is in the normal light cone. Another way to explain this is that the steps we take to set up an experiment to determine a particular event set other causal chains into action. Since in DM there is no such thing as a locally determined ran­dom number, every particular event is related to what caused it. This means that the information cone from that event is not just focused on the one space-time point of the event, but instead it emanates from the diffuse volume in the space-time information cone that precedes the event. In particular, if that past includes setting out instru­mentation to measure the results of the experi­ment, then the steps taken to set up the measur­ing apparatus end up affecting the event. A short­cut to seeing the effect is to look at the experi­ment running backwards, which must be equiva­lent to looking at it running forwards because of reversibility. The catch is to deal properly with phenomena such as amplification and dissipation in microscopically reversible systems.