Indeed, I've always thought there was a dubious assumption there. There isn't a universal time to pace the clock tics of a simulation. Relativity forbids it. Anyway, time is a subjective illusion.
Back to the question: So what happens when the simulation "diverges" from regularity? Some possibilities: a) The universe ends b) Pink elephants pop up everywhere c) It's already happening
I like (c)
Ok. How about:
The multiverse is a very long qubit-string. (This is an informal statement to drive intuition.)
Being a qubit string it simultaneously exhibits all of its potential information-states.
If there is something like this qubitstring simultaneously exhibiting all possible information
states, then note that to do computation, within that qubit-string, no actual computational
process need take place. Any tour through any subset of the information states (i.e.
"visiting" one information-state after another after another...) can be
considered equivalent to a computation. Any tour through a subset of the information
states which is such that the "direction" of the tour is restricted to only those successor
information-states Si+1 (of the state Si we're currently at) which are different from Si
by only a single bit-flip in a single position in the bitstring, and where that bit-flip
would only happen based on some function of only the state of the bits in a local vicinity
of the flipping bit, can be considered equivalent to a computation which is comprised
solely of localized operations, similar to the kinds of computation we understand.
So the universe (or any observable universe) could be a tour through a subset of the
information-states of the qubit-string multiverse, which is such that the tour
computes only self-consistent spaces and objects, perhaps using only local computational
steps (part this computational locality is part of the secret of ensuring consistency, locality,
metric etc properties of the space and the objects, prehaps).
Observers which were self-aware substructures WITHIN the set of objects computed
in a "consistent" tour, maybe can only observe other information states which are also
within that tour.
TIME AND LIGHTSPEED
As Wolfram postulates, the concept of time and speed of light c within such an
informational universe may be related to how fast the informational changes (from one
state to another) can propagate (across the qubitstring) using only local computations
as the medium of state-change propagation. It is wrong to suppose that this implies
"computational time" outside of the qubitstring. "How fast state-change propagates"
is purely a question of how the metric spacetime that the consistent tour defines
can evolve in form within a consistent tour.
The tour itself could be imagined to be real if you like (with the
qubitstring really in some god-quantum-computer-thingy which has a god's-now-program-
pointer which moves from state to state in the consistent tour).
But it is better to think of the consistent tour as a virtual tour, an abstraction,
defined by nothing more nor less than its BEING a subset of information states, and an order
of traversal of those (very large) information states which is such that the ordered set
of information-states IS and CONJURES reality.
OBSERVERS, AND TOUR-TRAVERSAL AS THE TIME ARROW FOR OBSERVERS
An OBSERVER is a set of local subsets of the some of the set of information-states in the
consistent tour which is the universe. The notion of locality there is information-distance.
OBSERVERS can observe any aspect (part) of the information states in the tour which has
the following properties:
1. The observable substates must be within a light-cone of the observer. Photons or waves of light are
information travelling through the set of information-states. They are closely related to the putative
"local computations" which are imagined as defining sensible localized change between sets of
information states. So the observable substates are those that are reachable from the observer
states by local computations. These observation computations are computations that can
affect the observer-part of the "now" information-state based on the prior-to-now configuration
of other adjacent-to-the-observer parts of the prior-to-now information states, with the information
moving at a speed of one local computation (or is that one bitshift) per information-state-distance
in the consistent tour. Confusing? Yes I'm confused too. This bit's hard. (Pun intended)
2. Argument 1 implies that only parts (in some informational locality to the observer within the
information-states) of PRIOR-IN-THE-TOUR information-states can be observed by the observer.
That's what being in the light-cone from the observer implies: 1. Informationally-local to the observer's
own states, and also 2. PRIOR in the consistent tour to the "now-in-tour" state of the observer.
In fact we will stand these arguments on their heads now, and say that the consistent-tour direction
must be one in which an observer cannot observe (via light i.e. information packets moving by local
computation) forwards in the tour direction, but can observe (local parts of) information-states that are
backwards in the tour direction.
The time-arrow (state-tour direction) is that direction of information-state-change in which the
changes are like local computations which can communicate information across from one part of the
qubit string to an observer who is (is in?) another part of the qubit string.
Consistent tour direction (through a very large, or infinite?) set of very large (or infinite) discrete information
states has a lot to do, I think, with the information-theoretic concept of entropy, and if this whole
quantum-comp hypothesis is correct, I think we'll find that information-theoretic entropy is in fact identical
to thermodynamic entropy.
Particle interactions are analogous to local computations.
The entropic time arrow must have to do with the fact that the computations only appear to be
a self-consistent-classical-reality-producing set of computations when the info-state-changes are considered
to be going in certain of the info-change directions that they could.
The direction that the consistent tour chooses (and that the particle interactions choose when observation
from within the tour forces them to decohere into classical state) is a direction imposed by consistency
constraints. In fact, the direction is DEFINED BY the consistency-of-classical-reality constraints AND
BY NOTHING ELSE.
A way of thinking about where "NOW" is in the tour of information states is that the PAST in the tour
is CLASSICAL (experiments have been conducted, quantum events have actually chosen a path
from their probability distributions) and the FUTURE in the tour is quantum-mechanical. The possible
successor-states have probabilities WHICH ARE BASED ON THEIR INFORMATION-DISTANCE
from the now-state in the tour.
But the notion of the now-state in the tour is ILL-DEFINED as a global concept (just as it is in physics).
We really just have a NOW-state of a local part of an information state in the tour.
We can say that, as a definition,
the consistent tour visits those information states all of whose parts can choose a successor part-state
by local computation IN A WAY THAT IS GLOBALLY CONSISTENT AT THE SPEED OF
LOCAL-COMPUTATION INFORMATION-CHANGE (i.e. at the speed of light.)
So ALL of the choices of successor-state for each informationally local part of the "now" information-state
in the tour must be consistent with each other, at least in the retrospect that will happen when those
future states can be inspected (at info-lightspeed) by any observer within the tour-states.
THAT is the transformation of quantum potentialities into classical realities.
So all in all I think I agree with Frank. The simulation DOES diverge from regularity, but
the diverging simulation is just one of many "virtual tours" through the "all-information-states"
qubitstring. Some other simulation, defined precisely as that one (or few) which does not
diverge from regularity, is also simultaneously happening (or existent, as an ordered subset)
in the qubitstring. And that non-diverging-into-noise simulation (info-state-tour, I prefer
because it implies passivity (no computer needed)) is the universe.
So can there be other universes?
One way of rephrasing this question is to put it as the question of whether there is
more than one "lightspeed--globally-consistent" tour through a set of all possible
information states, where light is defined as communication, from one part of the
qubitstring to another via local computations, of information.