Issues Currently Challenging the Wave Model           The state of play

    Contents

♦   Introduction
The Issues:
♦   Welding Together
♦   Negative Frequencies or Not?

♦   General Comments
♦   References and Background Reading
 

   Introduction

Regarding the development of a wave model as laid out on the website wavemodel.org, this document summarises where the mission has reached and as things change keeps in focus those issues that seem to be the main obstacles to furtherance of such a model.  I am all too aware that, if this model is to make any progress it will need to deal with an array of conceptual, analytical and phenomenological challenges for a very long time to come.  Here is the current game as I see it.

For general comments on the state of play in attacking the problems please refer to the General Comments section below.  Here follow some current specific issues.

More recently:
1 May 06 -   Adding the analysis of the 4-vector of correlations between the substrate field and its first derivatives is clarifying this picture (The earlier analysis looked at the 4×4 matrix of correlations between first derivatives only).  Amongst other things it appears to be headed for a proper account of 4-vector potential (I was originally sceptical of the need for this).  It also appears to make good account of Aharonov-Bohm effects and their origination as wave couplings.  This material is due in the foreseeable future to bring a refinement of the rôle of Maxwell field couplings in the "Smooth and Quantal Properties ....." document and a substantial update to the "Dynamics of Complex Waves" document.

The structure emerging from Ediv in the new essay on Dynamics of Complex Waves supports this well enough.  A reversion of Echarge in smooth.html to its original form (with modulus of frequency) will now allow this to come together.  Work will now continue on this basis.

   General Comments

This project began with the objective of clarifying some issues of modelling in electrodynamics, but has reached out, like it or not, to touch matters far more general.  As is suitable to its electrodynamics remit it offers the unification of Maxwell and De Broglie waves as they appear in electronic and even, as a prospect, in nuclear processes.  It then happens that the same model suggests how gravitational effects come about.  That then is a big span of unification!

So as its first objective the project faced the question of whether a continuum model would lead usefully to an emergence of the traits of quantisation and uncertainty as are described in the current physics accounts but without the artifice of any quantal "Ansatz".  It has become clear that the answer to this question is positive.  There is a usefully simple continuum model of complex waves that displays quantal behaviour.  Along with it the question of uncertainty then pivots mainly upon understanding the full implications of the observer being no more than part of the overall system being modelled, and in that matter the rôle and processes of amplification are key.  So the underlying process is then described as a locally causal continuum model.

A possible path into the subject following those issues is via Essential Structure in Physical Observation and/or Smooth and Quantal Properties of the Complex Wave.  Any model that produces the effect of quantisation must also produce a value for the size of the quantum, or of the famous constant to which it is related called the "Fine Structure Constant".  This model is explained in that respect in the second of those two essays and the value it currently produces for the electronic charge is high by about 0.5%.  There is more work to be done in this area concerning, amongst other things, how spin affects this figure, and that work is currently ongoing with a view to obtaining good account of this discrepancy.  Anyway, what is most basically interesting is the way it demonstrates the possibility of such emergent quantisation at all.  The analysis may be a little tricky to follow in detail but the model is not at all outlandish.  The conventional "Ansatz" type of theoretical model involving wave function collapse at some point in time is thereby brought under attack, at least in its status as being in any way uniquely fundamental.

The unification that this approach produces comes about through a wave model that is actually simpler than the one with which the project set out on its investigation of electrodynamics.  At the beginning the Maxwell and De Broglie waves were modelled separately, thus requiring two forms of wave equations.  In the more recent work presented in Dynamics of Complex Waves both of these wave systems are shown to arise from a common basis and that basis is arguably simpler than either of the two original equations.  As an unsought bonus the model then also displays effects that are gravitational in nature.

As things stand it will be a little while before all of these features are presented and worked through quantitatively and in detail, but the picture presently promises that it will be possible to complete that task.

Until further checks are completed it remains unclear whether this model will survive as self-consistent and then whether it will be truly compatible with either natural phenomena or with conventional quantum mechanics and the "Standard Model" of nuclear particles.  However, it is already clear that it has value as a means of comprehension, and brings into cohesion a variety of concepts that have traditionally appeared as arbitrary and disjoint.

The prospect for accounting for the superficial aspect of the appearance of particles looks to be a routine matter, dealing with such as Compton effect, cloud and bubble chamber tracks, Stern-Gerlach phenomena, photoelectric effect, Aharonov-Bohm effect etc.  Similarly the otherwise anomalous effects of apparently non-local deviations of correlation in particle detection can be submitted to a new view in which there appears every possibility that the results will stay within the range of phenomena attributable to a locally causal, though not in detail observable, wave system.

All of this work is, on my part so far (AGB), in a state of patchwork draft, and will probably remain to some degree that way.  A complete and early conclusion over issues as widely set at these would hardly be possible.  Fortunately that more tentative approach is made workable by taking advantage of the plasticity of electronic documents and Internet methods.

The broad outline needs, as well as one or two more central pieces, a collection of secondary articles written to deal with peripheral matters such as accounting for individual phenomena.  Also it would be valuable, and at the outset perhaps not too challenging by comparison with conventional quantum field theories or the agonising many body Lagrangian problems, to make direct use of the model to set up some electrodynamic finite element computational modelling ... atomic, molecular or crystalline.  Collaboration in this work has begun, but have we any more interested parties or volunteers for such activities?  Please contact me if so.

   References and Background Reading