Chaos, DT, Quantum theory, SD-paradigm
Posted: Wed Jan 12, 2005 11:18 am
Posted by Nijland <lukkenaer@planet.nl>
To the members of the SD list,
I renewed my membership to this mailing list some days ago,
and I hope to have a fruitful discussion with some of you about the following problem.
I constructed (some ten years ago),
a simple model of the dynamics of the orbit of the planet Mercury,
according to the theory of relativity.
The system dynamics model has two level variables
(spatial position and velocity) and two feedback loops (a positive and a negative loop).
The behaviour of my ""sun-planet"" model exhibited the rosette pattern,
as expected from the theory of relativity.
I did some experiments with different values of the basic parameters,
and with different values of the solution interval (dt).
Choosing the value of dt (too) large, produces very irregular patterns.
I interpreted such behaviour
as an artefact originating from a too large solution interval (delta t).
In some models (e.g. the population dynamical “May-model”)
I found that chaotic behaviour may be abolished
by reducing the solution interval dt.
Now, 10 years later, I am reflecting again on this matter.
With some alterations my “sun-planet model” may also be applied to
the dynamics of electrons around protons in an atom.
Some questions arising are,
Might it be possible to provoke
deterministic chaos in a system dynamics model of the atom?
Especially if more than one electron are involved?
Might it be possible to interpret (explain) any observed ""deterministic chaos""
in such a model, as ""quantum behaviour"" of electrons in atoms (in the sense of the quantum theory)?
If an absolute minimum time interval exists (dependent on the constant of Planck??),
then simulations of any phenomena on micro or nano scale,
with a smaller solution interval (dt) than this minimum time interval are not realistic.
If simulations (for micro phenomena) with such a minimum solution interval would show deterministic chaos,
and this chaos would show quantum characteristics
(regularities in the probability distributions of the outcomes),
and these statistics would correlate with the empirical statistics found in atoms
(position distribution of electrons),
then quantum theory might be explained by classical physics ??
Is there (introductory) literature about system dynamics as a
philosophical paradigm for unification of other paradigms (theory of relativity and quantum theory)?
I hope that anyone of this list can give me some useful direct information,
or literature references about the questions posed above?
Geert Nijland,
Renkum, The Netherlands
Posted by Nijland <lukkenaer@planet.nl>
posting date Wed, 12 Jan 2005 10:31:07 +0100
To the members of the SD list,
I renewed my membership to this mailing list some days ago,
and I hope to have a fruitful discussion with some of you about the following problem.
I constructed (some ten years ago),
a simple model of the dynamics of the orbit of the planet Mercury,
according to the theory of relativity.
The system dynamics model has two level variables
(spatial position and velocity) and two feedback loops (a positive and a negative loop).
The behaviour of my ""sun-planet"" model exhibited the rosette pattern,
as expected from the theory of relativity.
I did some experiments with different values of the basic parameters,
and with different values of the solution interval (dt).
Choosing the value of dt (too) large, produces very irregular patterns.
I interpreted such behaviour
as an artefact originating from a too large solution interval (delta t).
In some models (e.g. the population dynamical “May-model”)
I found that chaotic behaviour may be abolished
by reducing the solution interval dt.
Now, 10 years later, I am reflecting again on this matter.
With some alterations my “sun-planet model” may also be applied to
the dynamics of electrons around protons in an atom.
Some questions arising are,
Might it be possible to provoke
deterministic chaos in a system dynamics model of the atom?
Especially if more than one electron are involved?
Might it be possible to interpret (explain) any observed ""deterministic chaos""
in such a model, as ""quantum behaviour"" of electrons in atoms (in the sense of the quantum theory)?
If an absolute minimum time interval exists (dependent on the constant of Planck??),
then simulations of any phenomena on micro or nano scale,
with a smaller solution interval (dt) than this minimum time interval are not realistic.
If simulations (for micro phenomena) with such a minimum solution interval would show deterministic chaos,
and this chaos would show quantum characteristics
(regularities in the probability distributions of the outcomes),
and these statistics would correlate with the empirical statistics found in atoms
(position distribution of electrons),
then quantum theory might be explained by classical physics ??
Is there (introductory) literature about system dynamics as a
philosophical paradigm for unification of other paradigms (theory of relativity and quantum theory)?
I hope that anyone of this list can give me some useful direct information,
or literature references about the questions posed above?
Geert Nijland,
Renkum, The Netherlands
Posted by Nijland <lukkenaer@planet.nl>
posting date Wed, 12 Jan 2005 10:31:07 +0100