Digital Philosophy takes a definite view of QM that is not aligned with the Copenhagen Interpretation or even with any other contemporary view of QM. We reject the idea that there is such a thing as the irreversible act of observation or that there is the classical world and the quantum world. DP assumes that some DM system is all there is, while imposing informational laws that include conservation of information.
We know that there is no shortcut, in general, to computing the exact future state of an arbitrary computation. But a DM model is not an arbitrary computation. It is an extraordinarily regular and fundamentally very simple computation. Thus, DP allows for an analytical methodology that can compute the probabilities of sufficiently microscopic events. This is a process that stands astride the enormous gap between the kind of simplistic determinism seen in Newton’s Laws governing the motions of the planets, and the fact that exact analytical formulas are essentially helpless at providing shortcuts to the future state of a general process running on a universal computer. Digital Philosophy inexorably leads us to conclude that the analytical methodology that allows one to compute the probabilities is called “Quantum Mechanics”.
“Quantum Mechanics is not a theory about reality, it is a prescription for making the best possible predictions about the future if we have certain information about the past.” — Gerard ‘t Hooft
Thus Digital Philosophy adopts ‘t Hooft’s dictum that “Quantum Mechanics is not a theory about reality.” Digital Philosophy assumes that QM is a set of analytical, mathematical methodologies for computing the probabilities of future states of a DM process, from the limited information we can have about the possible initial states of that process. One might wonder whether it is reasonable for a discrete, deterministic reversible process to be the substrate for what Quantum Mechanics allows us to compute. But QM itself admits that the evolution of the wave function is a deterministic and reversible process.
Those who are not members of the school of Digital Philosophy might ask, “Why doesn’t DM model QM?” or “Why isn’t DM based on Quantum Mechanics?” These are questions that been around since work began on this topic. [1] While it makes sense for QM to be an analytical shortcut to a computational process, the idea of modeling QM by a computational process cannot pass the test of Occam’s Razor. A DM model evolves a system along a particular and exact trajectory. QM is a model that looks at all the possible trajectories and lets us calculate the probabilities. We should be able to derive QM from a correct DM model. Even so, QM will still be the most efficient way to get most answers in physics. Since the Billiard Ball Model of universal computation is an idealized Newtonian model, DM is basically Newtonian. This fact should not frighten the reader, as computational models and Newtonian mechanics already have a lot in common. The idea of basing DM on QM makes little sense. As a theory of physics, QM has essentially nothing in common with Digital Philosophy.
As is commonly done in Cellular Automata Theory, our DM models assume that the number of possible values (or states) at each point in space-time is a small finite number such as 2. We expect that at some scale greater than that of the lattice, DM models will be equivalent to differential equations of physics. This kind of accurate mapping of rules in a Cellular Automaton to the mathematical equations of physics has already been done successfully in several areas, such as in Computational Fluid Dynamics [2] .
The ultimate goal of DP research is an appropriate theory of the most fundamental physics. This is a difficult and ambitious task. Today, DP bristles with glaring deficiencies. On the positive side older DP theories had even more deficiencies. Even the sub-goals of the DP project are quite remarkable. A DP theory of physics, if correct, can allow for perfect and complete understanding of the ultimate laws of physics. It allows for the possibility of an exact description of the early universe. Finally, in theory, a DM system allows the possibility of predicting the exact evolution of a defined set of initial conditions, however in practice this is always impossible with regard to macroscopic real world phenomena. What we will be describing is a DM model that illustrates how different aspects of physics might be a part of a correct DM model.
Imagine that it is long ago and for the first time someone had the original idea to model laws of physics using algebra. He might give as an example:
“T=H/M”, the time it takes an object to fall to the ground is proportional to the height and inversely proportional to the mass.
The idea of using mathematical equations to capture facts of physics is brilliant, wonderful and correct. The equation above illustrates how this might be done despite the fact that it happens to be true under limited circumstances (such as feathers falling through the air). In this paper we want to explain a new way to model physics and we are not deterred by the fact that the particular formulations we give are most likely wrong. If you refuse to consider the DM model because of inconsistencies, errors in the physics or statements that are simply false, you have missed the point. We have come to conclusions and will present specific models and constructs without reasonable justification or verification as to correctness or even self-consistency. Our approach is to communicate, by explanations and examples, the possibilities inherent in a new genre of mathematical thinking about fundamental processes in physics. One should remember that in Quantum Mechanics, almost every paper published during the last 80 years can be seen as flawed when critically viewed from today’s perspective. Yet many such papers contributed crucial concepts in the development of QM. If the idea of a DM model of physics is basically correct, finishing the task of getting it right, once and for all, will be an insignificant task compared to the development of QM. In any case, today DM, as a model of physics, is still work in progress.
A correct DM model allows for other interesting possibilities. It is most likely that the exact definition of physics, including implicitly all laws of science, could be written down unambiguously in one short paragraph. Such a definition would be easily understandable by any intelligent alien. We will give an example as an addendum to this paper.