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  Why Seek Frequency Domain Continuum Models?
Anthony G.Booth Original: 05 Feb 01
Copyright Last update: 31 Dec 04

**    Motivation

I am an engineer and a student of cybernetics motivated to the study of quantum electrodynamics in order to seek:
  1     Better creative models for room temperature electro/photo/chemical developments.
  2     A class of very general cybernetics models (not elucidated here), for which electrodynamic modelling is potentially a valuable and intriguing instance.

The conventional sense of "prospecting for gold" in the mines of new physics ideas or discoveries is not for me a significant motive; it is merely a distraction which is sometimes amusing and other times a nuisance. In other words, I am not, at heart, a physicist.

To these ends I have read and thought over some physics in the past couple of years. I am trying to find either a way in which continuum field theories can account for a necessary appearance of quantal form in the results of observations or else a clear indication of why such a model could never exist. I have not yet reached either conclusion. Needless to say, I do not regard the old symptoms like cloud chamber tracks, photo electric effect, Compton scattering, Millikan droplet motion etcetera to be sufficient in themselves as proof … there is still too much possibility of accounting for these with a continuum model operating with short term coherence and subject to the inherent structure of an observation process.

But why should I try to go beyond the currently widespread physics models which flow from the quantum ansatz and normalisation of wave functions? The answer to this, under both of the motivations listed above, is that it appears to be necessary if we are to gain the grasp and freedom needed to factor the models in ways that will best suit everyday work involving many parties. The process of simplification is already at large on an informal basis typified by concepts used in photonic and semiconductor engineering, materials science, spectroscopy and in the many branches of chemistry. Purely quantal models as currently presented are often too hard and confusing to use in predicting the likely behaviour of novel electro-physical structures, apparently even for physicists!

In looking for a more philosophical basis for seeing that this is a real problem and how it might be approached I have also written another note under the title "Reconciling Physics with Cybernetics".

In particular there seems to be an opportunity to have more explicit ways of modelling the dynamic perturbation of states of ensembles of atoms. We are hemmed in on the one hand by physics models based on invariance and on the other by engineers using thermodynamics. Between these two established ideas there appears to be room for a large field of modelling of evolutions which are slow in terms of electron resonance wave periods but fast in terms of electronic circuit processes. This opportunity for modelling concerns, by and large, a frequency range between 108Hz and 1014Hz.


**     Approach.

My deliberations so far have brought me to a point where I would like to use a set of components for the dynamics model thus:
  1   Eigenmode characterisation of atomic electronic structures (Laguerre polynomials etc.) using the Klein-Gordon (sometimes called Klein-Gordan) equation with electric and magnetic potential functions (scalar and vector respectively), complete with characterisation for relatively slow dynamic perturbations of the eigenmodes and hence also of the potential functions.
  2   Description of purturbations of the eigenmodes and their excitations and the concomitant changes in the electric and magnetic potential functions.
  3   Energy and phase evolutions described in a Bloch space caused by interactions (minimally being the quadratic amplitude case) between an electromagnetic wave (either resonant or radiant) and two atomic electronic eigenmodes.

Neither Schrödinger nor Dirac forms of the electron field model are suitable because they cannot handle (even slowly) change of geometry or free electron radiation. This is because they are not Lorentz invariant models.

The resulting model along with predicates of the inherent form of an observer would then be used to establish how bifurcation phenomena occur, and so manifest quantisation.

From the physics reading I manage to do I have the impression that studies of perturbations are mostly in the static sense. As distinct from this I am most explicitly interested in looking at the way that weak electrodynamic interactions produce eigenmode evolutions through local shifts of potential causing both space and frequency realignment of the eigenmodes along with rebalancing of the energy between eigenmodes. In models of this type we handle the weighting dynamics of superposed quantum states explicitly. The object would not be so much to work out these actual eigenmodes as to show mathematically that there is a basis in causality to believe:
  a)   That the only stable excitations would be quantised in the usually expected way, and
  b)   That the dynamics of the attendant Rabi-like transition processes could be estimated and discussed.

If this work has already been done then please let me know where it is recorded.


**     References and Background Reading

Sorry, nothing here yet!


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