A Class of Models with the Potential to Represent Fundamental Physics
  1. Introduction
  2. Basic Form of Models
  3. Typical Behaviors
  4. Limiting Behavior and Emergent Geometry
  5. The Updating Process for String Substitution Systems
  6. The Updating Process in Our Models
  7. Equivalence and Computation in Our Models
  8. Potential Relation to Physics
  9. Additional Material
  10. References
  11. Index

8.21 Specific Models of the Universe

If we pick a particular one of our models, with a particular set of underlying rules and initial conditions, we might think we could just run it to find out everything about the universe it generates. But any model that is plausibly similar to our universe will inevitably show computational irreducibility. And this means that we cannot in general expect to shortcut the computational work necessary to find out what it does.

In other words, if the actual universe follows our model and takes a certain number of computational steps to get to a certain point, we will not be in a position to reproduce in much less than this number of steps. And in practice, particularly with the numbers in the previous subsection, it will therefore be monumentally infeasible for us to find out much about our universe by pure, explicit simulation.

So how, then, can we expect to compare one of our models with the actual universe? A major surprise of this section is how many known features of fundamental physics seem in a sense to be generic to many of our models. It seems, for example, that both general relativity and quantum mechanics arise with great generality in models of our typeand do not depend on the specifics of underlying rules.

One may suspect, however, that there are still plenty of aspects of our universe that are specific to particular underlying rules. A few examples are the effective dimension of space, the local gauge group, and the specific masses and couplings of particles. The extent to which finding these for a particular rule will run into computational irreducibility is not clear.

It is, however, to be expected that parameters like the ones just mentioned will put strong constraints on the underlying rule, and that if the rule is simple, they will likely determine it uniquely.

Of all the detailed things one can predict from a rule, it is inevitable that most will involve computational irreducibility. But it could well be that those features that we have identified and measured as part of the development of physics are ones that correspond to computationally reducible aspects of our universe. Yet if the ultimate rule is in fact simple, it is likely that just these aspects will be sufficient to determine it.

In section 7 we discussed some of the many different representations that can be used for our models. And in different representations, there will inevitably be a different ranking of simplicity among models. In setting up a particular representation for a model, we are in effect defining a languagepresumably suitable for interpretation by both humans and our current computer systems. Then the question of whether the rule for the universe is simple in this language is in effect just the question of how suitable the language is for describing physics.

Of course, there is no guarantee that there exists a language in which, with our current concepts, there is a simple way to describe the rule for our physical universe. The results of this section are encouraging, but not definitive. For they at least suggest that in the representation we are using, known features of our universe generically emerge: we do not have to define some thin and complicated subset to achieve this.