Exact Models
Ed Fredkin
We can have continuous models of discrete or partially discrete systems,
such as PDE's for hydrodynamics. We can have discrete models of continuous
systems such as the typical modeling by writing a computer program. We like
to say that such systems can be modeled by a computer program but what this
usually means is that some of the state variables in the computer program
correspond in some fashion to some of the state variables in the system
being modeled. A good example is an aircraft simulator, where a digital
computer models the gross variables of an aircraft (total mass, speed,
thrust, heading, angles of attack, bank and yaw, etc.). Of course,
innumerable other facts about the aircraft are left out of the model. In
addition, there are all kinds of things happening in the computer doing the
modeling (MS Windows...) that have nothing to do with the real aircraft.
Interestingly, there is one aspect of an aircraft simulator that is very,
very close to an exact model, and that is in the cockpit instrumentation.
The reason is that a good simulator uses essentially the same cockpit
instrumentation as does the aircraft. There is another kind of model -- the
exact model -- that only applies to discrete space-time-state systems.
If we assume that nature is, at the very bottom, a discrete space-time-state
system similar to a cellular automata, then it will be possible to model
nature on a computer. However, it would also be possible to build a
hardware system capable of running an exact model. An exact model would
mean that at each discrete instant of time there is a one to one onto
mapping from every state variable in the model to every state variable in
the physical system being modeled. If we assume that the rule of the model
is the same as the rule of most-microscopic nature then every fact about the
evolution of the sequence of states of the model would be identical with the
evolution of the sequence of states of a similar volume of real space time,
provided they both started out in the same overall state.
There is a very important consequence of an exact model of physics that is
clearly true yet hard to grasp: the exact model is not merely a model of
physics, it is physics. The bits in the exact model are a tiny sample of
real space-time physics. It is no different (except for boundary
conditions) than a corresponding volume in the real world.
This relieves us from the "tyranny of universality problem". Since any
universal computer can model any digital process, there seems to be no way
to know if one such model is better or more appropriate than another.
However, there would be only one possible exact model. Most likely it would
be relatively easy to determine that it is the correct model; in that it
would be perfectly and exactly correct in all ways.
Ed F
akha...@yahoo.com
An exact model is a fascinating philosophical idea for physics.
Physics itself is a set of models and many new models consider
previous ones as approximation. No excuse for approximations or
scaling any more – every computer bit counts as simplest physical
object and nothing is behind!
The question is how to make first steps in redefining most fundamental
notions (space, time, energy) and come up/down to rules of physics.
The similar questions (about structure of physical space) are on
agenda in attempts to build unified theory of physics but people there
do not limit themselves to so strict rules.
It is easy to pass judgment on the strict rules. They bring either
tremendous success or immediate failure.
Alex
charliew2
Ed Fredkin wrote:
> It's true that there are all kinds of ways to model all kinds of
> systems. We can have continuous models of discrete or partially
> discrete systems, such as PDE's for hydrodynamics. We can have
> discrete models of continuous systems such as the typical modeling by
> writing a computer program. We like to say that such systems can be
> modeled by a computer program but what this usually means is that
> some of the state variables in the computer program correspond in
> some fashion to some of the state variables in the system being
> modeled. A good example is an aircraft simulator, where a digital
> computer models the gross variables of an aircraft (total mass,
> speed, thrust, heading, angles of attack, bank and yaw, etc.). Of
> course, innumerable other facts about the aircraft are left out of
> the model. In addition, there are all kinds of things happening in
> the computer doing the modeling (MS Windows...) that have nothing to
> do with the real aircraft. Interestingly, there is one aspect of an
> aircraft simulator that is very, very close to an exact model, and
> that is in the cockpit instrumentation.
I would tend to call this a GUI (graphical user interface), and distinguish
it from the underlying model. The GUI is a way of handling user
input/output, and it is formulated such that the look and feel of the GUI is
as close as practical to the real interface. In this case, a real aircraft
would have a GUI, and it is possible for the simulator to have the exact
same GUI as the real aircraft. In addition, at this point, it is not
possible for the model to be an exact representation of nature. Thus, my
distinction.
> The reason is that a good
> simulator uses essentially the same cockpit instrumentation as does
> the aircraft. There is another kind of model -- the exact model --
> that only applies to discrete space-time-state systems.
>
> If we assume that nature is, at the very bottom, a discrete
> space-time-state system similar to a cellular automata, then it will
> be possible to model nature on a computer. However, it would also be
> possible to build a hardware system capable of running an exact
> model. An exact model would mean that at each discrete instant of
> time there is a one to one onto mapping from every state variable in
> the model to every state variable in the physical system being
> modeled. If we assume that the rule of the model is the same as the
> rule of most-microscopic nature then every fact about the evolution
> of the sequence of states of the model would be identical with the
> evolution of the sequence of states of a similar volume of real space
> time, provided they both started out in the same overall state.
You are assuming that nature is, at its "core", deterministic. This is a
widely held hidden assumption. I don't know if it is true or not, but I
would "like" it to be true (and I'm not sure why).
>
> There is a very important consequence of an exact model of physics
> that is clearly true yet hard to grasp: the exact model is not merely
> a model of physics, it is physics. The bits in the exact model are a
> tiny sample of real space-time physics. It is no different (except
> for boundary conditions) than a corresponding volume in the real
> world.
>
> This relieves us from the "tyranny of universality problem". Since
> any universal computer can model any digital process, there seems to
> be no way to know if one such model is better or more appropriate
> than another. However, there would be only one possible exact model.
> Most likely it would be relatively easy to determine that it is the
> correct model; in that it would be perfectly and exactly correct in
> all ways.
>
> Ed F
Question!!! Given that any measurement has noise in it, and given that
quantum mechanics imposes limits on how accurately a measurement can get,
how is it possible to construct such a model and verify it as being THE ONE
correct model, to the exclusion of all others?
ueb
..
> If we assume that nature is, at the very bottom, a discrete space-time-state
> system similar to a cellular automata, then it will be possible to model
> nature on a computer. However, it would also be possible to build a
> hardware system capable of running an exact model. An exact model would
> mean that at each discrete instant of time there is a one to one onto
> mapping from every state variable in the model to every state variable in
> the physical system being modeled. If we assume that the rule of the model
> is the same as the rule of most-microscopic nature then every fact about the
> evolution of the sequence of states of the model would be identical with the
> evolution of the sequence of states of a similar volume of real space time,
> provided they both started out in the same overall state.
Hmm. Physicists are even not aware of the rules of "most-microscopic
nature", and wildly speculate about it. How will you experience the rules
of an adequate model ? Is it not better to test known rules like the
Einstein-Maxwell equations, and find out their _real_ domain of
applicability ? I have successfully demonstrated that the domain of
applicability of the Einstein-Maxwell equations is far wider than
people believe, and includes even "most-microscopic nature".
> There is a very important consequence of an exact model of physics that is
> clearly true yet hard to grasp: the exact model is not merely a model of
> physics, it is physics. The bits in the exact model are a tiny sample of
> real space-time physics. It is no different (except for boundary
> conditions) than a corresponding volume in the real world.
I have already demonstrated it :-)
http://home.t-online.de/home/Ulrich.Bruchholz/
> This relieves us from the "tyranny of universality problem". Since any
> universal computer can model any digital process, there seems to be no way
> to know if one such model is better or more appropriate than another.
> However, there would be only one possible exact model. Most likely it would
> be relatively easy to determine that it is the correct model; in that it
> would be perfectly and exactly correct in all ways.
That might be not well possible, because the rules of nature are
incomplete.
Ulrich
Ed Fredkin
"charliew2" <char...@ev1.net> wrote in message
news:10aats1...@corp.supernews.com...
> I'm going to "step out of my place" (I'm not a physicist) and comment.
> >
> > There is a very important consequence of an exact model of physics
> > that is clearly true yet hard to grasp: the exact model is not merely
> > a model of physics, it is physics. The bits in the exact model are a
> > tiny sample of real space-time physics. It is no different (except
> > for boundary conditions) than a corresponding volume in the real
> > world.
> >
> > This relieves us from the "tyranny of universality problem". Since
> > any universal computer can model any digital process, there seems to
> > be no way to know if one such model is better or more appropriate
> > than another. However, there would be only one possible exact model.
> > Most likely it would be relatively easy to determine that it is the
> > correct model; in that it would be perfectly and exactly correct in
> > all ways.
> >
> > Ed F
>
> Question!!! Given that any measurement has noise in it, and given that
> quantum mechanics imposes limits on how accurately a measurement can get,
> how is it possible to construct such a model and verify it as being THE
ONE
> correct model, to the exclusion of all others?
>
The answer is simple. We should be able to derive, analytically, all of the
laws of physics from a mathematical description of an exact model. This
would obviously have to include QM, Std. model, SR & GR. A clue as to how
this can happen can be seen in the Salt Model. It is trivial to show that
some laws of physics are exactly modeled in Salt; examples are conservation
of momentum and angular momentum. It appears that it shouldn't be too hard
to show conservation of energy and charge. CPT symmetry is a natural aspect
of the Salt model. While Salt is a big step forward in the process of
thinking about discrete models of physics, there is still a long way to go.
As is discussed in "Introduction to Digital Philosophy" and "Five big
questions with pretty simple answers", given an exact model similar to Salt,
there are only 8 parameters that define every fact of physics. Given the
values of B, L, T, P, D, R, A and I, every fact of all of physics (all of
science and all of everything else!) is exactly determined. In the Salt
model, B=1, L=1, T=1, P=6, D=3, R is the CA rule, A is the age of the
Universe in units of T, and I is the initial conditions at the point of the
Big Bang. In our current units, B=hbar, L is the CA unit of length, T=L/c,
P is the number of time phases and D is the number of spatial dimensions.
It's all pretty simple and something like this is possibly the way things
work.
ueb
> You [Ed Fredkin] are assuming that nature is, at its
> "core", deterministic. This is a
> widely held hidden assumption. I don't know if it is true or not,
> but I would "like" it to be true (and I'm not sure why).
"Classical" continuum physicists did like it too. But it is
unfortunately false, simply for lack of rules.
Ulrich