Welcome to the Wave Model Pages

The Emergence of Quanta in a Causal Continuum

  How waves form themselves into matter

We can write down models of variables in continuous space and time so that, defining neither boundaries nor any solid or particulate entities, the waves will gather into persisting forms ... we call them solitons. On this web site a model is presented that displays this property of entities emerging from a continuous field whilst at the same time producing behaviour which corresponds well with the phenomena of physics (currently at least usefully), both macroscopic and microscopic.

  Existing models have to impose their quantal forms

The conventional particle physics is not so complete as this in that it anyway starts with notions of particles and then goes on to rely upon the use of "Planck's Ansatz" as a forced assumption of quantisation. Nor do the "hybrid" developed theories of joint waves and particles achieve operation without imposing an equivalent assumption (Cramer, Bohm, Little etc.). As for the pure wave models (i.e. having no original particles), there are two groups. First there are those that are just descriptions of linear wave structures with presumed arbitrary mechanisms to delimit their entities (Wolff, Hawkings etc.). Of the others which do contain the necessary nonlinearities to produce emergent solitons none displays behaviour which is sufficiently consistent with observed physics to be useful in any significant breadth of application.

  A compact model consistent with nature is possible

Here the pure wave picture is more complete, starts from sparse precepts, and its behaviour corresponds valuably to natural phenomena. Unlike any other existing model it allows the fine structure constant (and therefore the electron charge) to be deduced from its precepts alone without injecting any corresponding constant anywhere. It is purely a consequence of wave field geometry, which in turn is determined by the precepts of the model expressed in its definitive wave equations through their possible wave function solutions. As currently developed in approximate solution it produces a result within 0.5% of the observed electronic charge. It therefore challenges a widespread belief that no such complete model could exist at all.

So far the work covers these issues:

• "Smooth and Quantal Properties ..." describes how the electronic waves generate charge and current and these in turn control the quantisation phenomena in electrodynamics.
• "Wave Topology of a Spin Mode" describes the form of a wave factor which is both necessary and sufficient for existence of matter solitons in a continuous field.
• "Dynamics of Complex Waves" provides a unification underlying both electromagnetic and matter waves so that their separate processes are founded upon a common and even simpler model.

  And why bother with a new model?

This web site is offered as a resource to those who share with the author an interest in the prospect and possibilities of using wave continuum models for atomic, molecular and crystalline physical systems and in particular to clarify how quanta can emerge in a wave continuum model. The particle based models that are currently the conventional ones serve poorly for some of these tasks. The site explores a specific set of modelling ideas but also offers links to other web sites with similar, related or contrasting approaches.

  Essays on Wave Modelling in Quantum Physics:

• Prospectus for a Locally Causal Quantum Wave Model
  A set of criteria regarding the nature of the required model.
• Issues Currently Challenging the Wave Model                       <<< The state of play <<<
  Some of the problems currently needing to be cracked.
• Essential Structure in Physical Observation
  At the heart of any process of observation there are certain basic things that must happen.
• Smooth and Quantal Properties of the Complex Wave    .PDF        <<< Currently main working paper <<<
  Complex scalar waves in continuous space are capable of displaying a special kind of smoothness and spontaneous quantisation.
• Wave Topology of a Spin Mode    .PDF 
  The properties of spin as observed in natural microscopic systems can be accounted for in terms of the behaviour of complex waves.
• Dynamics of Complex Waves    .PDF                                  <<< A unifying model <<<
  The zero d'Alembertian wave equation can produce a surprisingly wide range of behaviour under a noise field.
• Wave Model -- Electrodynamics Concept Map
  How can we bring engineering analysis to bear on quantum mechanics? ... A clickable network if ideas.
• Emergence of Quanta in a Wave Model
  Discussion of how a locally causal continuum model for a wave system can give rise to the emergence of quantal phenomena.
• Reconciling Physics with Cybernetics
  Our concepts of "objectivity" are set too narrowly for certain practical purposes.
• Why Seek Frequency Domain Continuum Models?
  There is a need for better practical methods with assessable approximations.

  Conceptual Outline

The following diagram is a map of the concepts comparing the conventional view of quantum mechanics on the right with an alternative model based upon non-Lagrangian continuum structures on the left. Whereas the realist ideas upon which the current models are based lead to a pair of incompatible sub-models, there is no equivalent problem if a constructivist approach is used at the outset. By clicking on the items in the map a link to explanatory notes is obtained (for those items where they have been written).

Personal and social consciousness Space-time paradigm Dynamics models
Constructivist ideas Second order cybernetics Perception and observation processes Continuum models Fields Interactions Stable attractors Locally causal systems DeBroglie and Maxwell waves Circular causation Weak correspondence principle Quantal emergence Solitons Modulated matrix Klein-Gordon model Smooth scalar wave properties Spin wave topology Quark wave models Space density generalisation Perceptual connection Zero d'Alembertian model Native wave correlations - Maxwell Derived stochastic waves - DeBroglie	Realist ideas Logical positivism
	Entity existence Microscopic experiment Lagrangian dynamics Potential Extremal action Wave-particle duality Correspondence principle Probability basis Gauge theory	Macroscopic metric properties Special and general relativity Riemannian geometry
	Conflict of concepts Non-local anomalies Failure of unification Many body problem

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