In the paper (Circular Motion of Strings…), one result that should be of interest to physicists is the deterministic model of particles decaying according to a ½ life law. Essentially all physicists are certain that there cannot be a deterministic model of half life. But in our paper we demonstrate one. What is true is that if every particle had an internal alarm clock that determined when it should decay, the result would deviate from the half-life law of real particles. I thought up the solution in our paper about 10 years ago, and when I described a possible busy boxes demo of half life to Dan Miller, he produced the program and ran the example in the paper (“Circluar Motion of Strings in Cellular Automata, and Other Surprises” posted on ARXIV, 10 June 2012) on the next day!
As near as I can tell, the physics community’s proof that no deterministic system can model half life goes something like this. “I and my colleagues have tried to think of ways to create a deterministic model of half life and every idea anyone has had so far has failed to result in a proper model. Therefore it is reasonably certain that it is impossible.” Of course, our solution is still very far from showing that underlying physics and quantum mechanics are deterministic processes, but we keep chipping away at the foundations of continuous physics and we I believe that we have seriously injured the “No Deterministic — Half Life” dogma. Of course, so far, our paper has been 100% ignored by the physics community (I haven’t noticed any references or or even a comment by a physicist).