Process Models
Ed Fredkin
we can say that s2 is a model of s1 if there are things about s2 that
are similar to things about s1. I would like to start a thread with
the goal of clarifying the characteristics of a certain sub class of
models which I think of as "process models." Below are examples as to
what might constitute a process model.
A process is a system that is actually undergoing temporal evolution.
While in flight, a radio controlled ź scale model of an airplane is a
process model of a real airplane in flight.
http://www.netaxs.com/~mhmyers/rc.tn.html
Of course, model airplanes as process models are inexact, especially
when it comes to the pilot. Running movies or ongoing videos are also
process models and so is a computer running Microsoft's Flight
Simulator. Newton's laws and the laws of aerodynamics are not process
models even when the laws describe the dynamic behavior of an
aircraft.
DVD's containing movies of aircraft in flight or containing flight
simulation software are not by themselves process models of an
aircraft in flight.
We exclude, as models, the thing itself; s1 is not a model of s1.
Further, it seems unreasonable to say that one hydrogen atom is a
process model of another hydrogen atom. This gets more interesting
in the case of computer-like process models of physical phenomena such
as cellular automata.
Ed F
Gerard Westendorp
[..]
> I would like to start a thread with
> the goal of clarifying the characteristics of a certain sub class of
> models which I think of as "process models." Below are examples as to
> what might constitute a process model.
>
> A process is a system that is actually undergoing temporal evolution.
Most of physics seems to be about rules to construct the future from
the present.
Computer programs also have a kind of time, the number of computation
steps.
But relativity seems to tell us that time is not so special.
We could try to get rid of state-time asymmetry by keeping
a big log file of all simulation steps. So a D-dimensional
array of bits changing with would become a D+1 dimensional
array that no longer changes.
The fact that the (D+1) array is a simulation would correspond
to the fact that not all arrays are allowed, you have
to obey the specific laws of time evolution. This would
then be just a special case of arrays of bits that have to
satisfy a set of constraints.
[..]
> We exclude, as models, the thing itself; s1 is not a model of s1.
It seems sensible to require some kind of "less than or equal to"
criterium: A computer program can be a model of the universe, but
is the universe also a model of that particular program?
Gerard
daniel B miller
[snip]
> But relativity seems to tell us that time is not so special.
> We could try to get rid of state-time asymmetry by keeping
> a big log file of all simulation steps. So a D-dimensional
> array of bits changing with would become a D+1 dimensional
> array that no longer changes.
>
> The fact that the (D+1) array is a simulation would correspond
> to the fact that not all arrays are allowed, you have
> to obey the specific laws of time evolution. This would
> then be just a special case of arrays of bits that have to
> satisfy a set of constraints.
>
mathematical model and what Ed is calling a 'process model'. Using your
terminology, the process we are seeking is an algorithm that allows us,
using finite computational resources, to take a subset of the D+1 array
(this would usually be thought of as a space-like section of dimension
D, often confusingly called a 'time-slice'), and derive the state of the
rest of the array, usually through an incremental algorithm that
specifies the state of array points in another slice contiguous with the
first slice, and so on.
A few more points about this: if you want to propose a deterministic
Universe, then the output of the process must be unique in one
direction: only one future state is possible given the present.
Similarly, if you want a reversible world, the mapping must be
one-to-one: for every future state, there is only one possible precursor
state.
Note that in this model it is possible to evolve the system using the
equivalent of different intertial frames: this corresponds to taking a
'slice' that is not exactly perpendicular to the axes of your matrix.
Issues come up in a discrete model because you need to decide exactly
what array points are in a slice; but this should all be derivable
explicitly from the process itself.
As a thought experiment, imagine programming a simple, 1D CA, with
nearest-neighbor rules. Now ask yourself this question: can I program
it in such a way that some cells are more than one time-step ahead of
other cells? It turns out you can, as long as you don't 'exceed the
speed of light', which in this case is simply one cell left or right per
time step. Imagine it this way: what do we need to specify the state of
an arbitrary cell at position (x,t)? We need three cells: (x-1,t-1),
(x, t-1), and (x+1, t-1). Those cells themselves depend on the five
cells spanning (x-2, t-2) to (x+2, t-2). This is simply the 'past light
cone' of (x, t). Clearly, we can evolve this CA from inital state
forward in time in many different ways.
-dbm