Introduction of Wave Model Issues
This discussion might be seen as an introductory overview of some of the issues that a reader may wish to consider when reviewing any of the wave structure models, as discussed within website3. The scope of website3 might also be considered in terms of the Timelines and Sources summary, while also highlighting that the wave models inferred all differ in the details of their respective wave structures. However, while accepting the limitations of the various reviews, all models were perceived have various problems and exist far below what can be empirically verified. As such, a fundamental issue needs to be tabled upfront:
Is the idea of any wave model simply wrong?
While the idea of any wave model has to be questioned, if the idea is simply rejected in favour of a particle model, then this model must also be questioned in terms of its own fundamental issues, for example:
What is the substance of a fundamental particle like the electron?
In part, this issue is considered further in a discussion entitled ‘The Substance of Matter’, where it is suggested that the only ‘substance’ that might possibly replace physical mass is energy. We might initially consider this idea by a transposition of Einstein’s equation [E=mc^{2} → m=E/c^{2}], although this simply leads to the next question:
What is energy?
For the purposes of this overview, it will be suggested that the fundamental idea of energy might be introduced as a potential difference [dU] between two points in space [dx] that can manifest itself as a force [F].
[1]
Again, while accepting the simplicity of this initial description, it suggests a causal nature for all motion or action in the universe. However, as defined, potential energy [U] is a scalar quantity that only exists at a single point in space when measured relative to some other point, which leads to another question.
How does the potential energy [U] of a point in space change?
Again, as a scalar quantity, potential energy [U] offers up no mechanism of change, nor does the classical idea of a force [F], without some form of interaction between the two points defined by [dx]. From empirical experiments, we know that any change in position affecting distance [dx] takes a finite amount of time to ‘propagate’ between the points of measurement, such that it requires a physical mechanism to explain how this change is transmitted. In this context, wave mechanics may provide a possible answer in terms of wave propagation, where the potential difference between two points in space is transported by a wave of some description. However, the description of most wave models usually infers some form of wave media that can support the physical propagation of energy between two points.
Note: The idea of space itself being a wave media presents its own set of problems, not only in terms of the apparent rejection of the idea by special relativity, but more fundamentally as to whether the granularity of space can be displaced as an offset that supports the idea of a potential difference.
However, this overview is not attempting to address such issues, as the purpose is only to highlight some key points that a reader might wish to consider further when reviewing any of the different wave models. Therefore, we will return to the Einstein’s equation [E=mc^{2}] as this description does not address the physical volume inferred by any mass [m], such that we might need to consider the implications of volume [V], starting with the SI definition of energy [E].
[2]
However, as can be seen, [2] makes no reference to the volume [V] occupied by mass [m], such that we are led towards the mathematical abstraction of a point particle, which does not correspond to any particle within the standard model.
So, how do we reconcile [2] with physical reality?
If we accept that mass [m] implies the energy [E] contained with some volume [V], we might introduce the idea of an energy density [ρ] as follows:
[3]
As such, it might be informative to revise [2], such that it reflects the energy density [ ρ ], as defined in [3], along with the volume occupied by mass [m].
[4]
While the transposition within these equations might appear a little pedantic, they highlight a number of key issues. First, simply accepting even Einstein’s most famous equation at facevalue can limit understanding to that of an abstract mathematical model without reference to physical causality. Second, if we cannot define the substance of mass [m] of a fundamental particle, like the electron, other than in terms of an energy density [ρ] within some volume [V], we also have to question whether the SI units of energy [E] can be defined in terms of mass [kg]. However, just making reference to energy density [ρ] has not explained how this ‘particle’ energy is localised in space or how it is distributed within its volume [V] or how it moves with the attribute of kinetic energy [½mv^{2}], which brings us back to the issue of ‘causality’.
Note: The issue of causalityis considered to be a key litmus test of any mathematical model. While the causal description accompanying a mathematical model can still be wrong, if the cause leading to an effect makes some logical sense, probability might suggest that the model may be on the right track.
The link in the note above makes reference to some perceived causal issues associated with the quantum descriptions of a force, a field, a particle, a photon, a EM wave, the Schrodinger wave, wave propagation plus time and energy. We might also question the idea of special relativity (SR), from a causal perspective, if we cannot explain how time dilation and length contraction actually take place within a frame of reference subject to an essentially arbitrary relative velocity [v]. While most may assume that SR has been empirically verified many times since being published in 1905, its foundations are still based on the mathematical assumptions of the Lorentz transformations, which provide no causal mechanism for either time dilation or length contraction.
Note: A mathematical model might be described as epistemological in scope, especially if limited by empirical verification. As such, the effectiveness of such a model may only be judged by the probability of predicting the final outcome without necessarily making any reference to physical causality. While epistemology encompasses the study of knowledge, ontology is more orientated towards the study of reality. In this respect, an ontological model may attempt to anchor its description to physical cause and effect mechanisms.
In part, the previous outline has simply attempted to summarized that particles and waves are generally considered to be two distinct ideas, but which are merged within the concept of a waveparticle duality. While we might understand the sematic convenience using the idea of a particle or wave in different descriptions, we possibly need to question whether fundamental physics really needs two different causal descriptions.
So, does the idea of a waveparticle duality make any physical sense?
The idea of some form of waveparticle duality has its roots in the early development of quantum mechanics, although some of the contradictions can be traced back to the much earlier debate about the nature of light between Isaac Newton and Christiaan Huygens. However, in 1900, the work of Max Planck on Blackbody Radiation alluded to some form of quantisation of energy, which was then further supported by Einstein’s paper on the Photoelectric Effect in 1905. However, the idea of some form of duality possibly became more abstracted within the idea of Complementarity as proposed by Neils Bohr in 1927. In essence, complementarity was a philosophical argument, where the nature of an object, e.g. electron, has complementary properties which cannot all be observed or measured simultaneously. While we might accept that physical causality within the subatomic domain of protons, neutrons and electrons may not be directly observed or necessarily measured without disturbing the coherence of a quantum state, this does not automatically mean that causality ceases to exist, only that we do not have a causal model that can be verified.
Note: The questioning of accepted models is not a rejection of all the ideas within these models, only that the issue of causality has to remain front and centre to any acceptance. Therefore, if causality is missing, the door must be left open to other ideas, such as a wave model of some description that may only exist below the subatomic domain.
In the note above, we might perceived the ‘Achilles' heel’ of all the wave models in website3 in that the waves may only exist at a scale far below our ability to directly verify. However, if a wave model, such as the OST model, can provide mathematical support for its assumptions augmented with a causal rationale, then it may still be worthy of further research. So, in summary, the reader might wish to consider some of the following issues when reviewing the wave models in website3.
 The building blocks of elementary
matter, i.e. an atom, is 99.9999999999999% empty space if described
in terms of the perceived volume of the proton and electron within a
hydrogen atom, where hydrogen constitutes 75% of all the matter in the
known universe.
 If we reject the substance
of particle matter in the subatomic domain in favour of an energy density
of some description, it requires a causal description as to how energy,
as a scalar quantity, propagates throughout the universe.
 While the idea of a wave is
generally accepted as a mechanism that can propagate energy between
two points, mechanical waves require a propagation medium, although
an electromagnetic (EM) wave is described as selfpropagating without
reference to any propagation media.

We know that radiation is energy that makes no reference to mass, despite
the SI implication that energy units include mass [kg]. However, the
description of radiation has its own form of duality, e.g.
photon particle or
EM wave, which the links below outline in a little more
detail.
 We might first consider this
apparently conflicting duality in terms of how the velocity of light
[c] in a vacuum can be reduced when passing through a transparent medium,
such as water or glass. For while there is empirical agreement on the
revised speed, the actual causal explanation as to why the velocity
is changed differs in these models.
 Within the EM model, the propagation
of the EM wave is assumed to slow within a material due to the disturbance
caused by the wave's own electrical field as it propagates pass charged
particles within the material on route. Typically, these particles will
be electrons rather than protons due to the large difference in massenergy
and this effect is often equated to the electric susceptibility of the
medium. By a similar argument, the magnetic field of the EM wave also
creates a disturbance proportional to the magnetic susceptibility of
the medium. So, as the electromagnetic fields oscillate within the EM
wave itself, charged ‘particles’ in the material also resonate at the
same frequency. As such, there is a superposition of different oscillating
fields with the same frequency, but not necessarily with the same phase.
As a consequence, a resulting superposition wave may have the same frequency,
but a shorter wavelength, which results in a slower phase velocity [vp=fλ].
 Within the photon model, a
photon always travels at [c], but can be delayed due to collisions i.e.
absorption and emission, within the atoms of the material. In these
terms, it is assumed that the idea of a photon slowing down due to the
refractive index of the material must be a statistical average of the
time for [n] photons to pass through the material.
 While most sources assume
that the EM wave model has been superseded by the photon model, it is
unclear that EM waves are quantised. In the case of a photon, quantisation
is linked to an atomic orbital transition, although this energy appears
to be better described as a finite pulse that is either emitted or absorbed
within an atom. However, there is no structural wave model for a photon
plus a photon has never been observed in transit as the energy is only
ever measured in terms of an orbital absorption transition within the
detector equipment.

In contrast to the quantised
photon model, a EM wave is described in terms of
Maxwell’s equations and associated with an oscillating charge
– see
EM radiation for more details. In this model, an EM wave
can be sourced by a single oscillating negativelycharged electron in
vacuum with no reference to orbital quantisation. If so, the frequency
of the EM wave would only be constrained by the physical oscillation
rate of the electron, i.e. no obvious quantisation.
 The various descriptions outlined appear to have
little in common in terms of a causal description. If quantum theory
argues that only the photon model exists in the quantum domain, the
EM model might be seen as an approximation, analogous to Newtonian gravitation
in respect to relativity. However, there appears to be considerable
ambiguity in these models in terms of the causal mechanisms at work.
 Let us now return to the issue of space as a physical
media for wave propagation, which is often assumed was rejected by special
relativity (SR), although Einstein’s comments on this issue often appeared
contradictory. This issue was then compounded by general relativity
(GR), which requires space to ‘bend’ and later said to support
Gravitational
Waves, where the curvature of space implied by GR may possibly
be causally explained as a refraction mechanism.  see
The Nature of Contradictions for more details.
 If space is rejected as a media for propagating energy,
it implies that virtually all of the universe by volume has no physical
or causal role to play. However, Maxwell’s equation forwards the idea
that space has ‘physical’ properties in the form of the
permittivity
[ε0] and
permeability
[μ0]of free space, which also underpins the speed of light
[c], such that its suggests that [c] is also the property of space as
a propagation media and why [c] appears in so many fundamental equations.
 As indicated, radiation as a source of energy needs
to make no reference to mass [kg] and, as such, can propagate with velocity
[c] in a vacuum, but where any ‘particle’ with perceived mass [m] is
constrained by special relativity in the range [0..c]. However, if this
matter particle has a wave structure, it needs to explained how it can
remain stationary in space.
 The various wave models reviewed in website3 generally
make reference to some form of standing wave structure, although the
details differ. Milo Wolff first proposed the
WSM
model, although his wave equations were questioned. Subsequently,
Gabriel LaFreniere proposed his
WWM
model and while initially appearing to be similar to the WSM
model, the wave equations were only used for the purpose of creating
his wave simulations. In practice, the WWM model is really forwarding
the idea of a particle being some form of a stable resonance structure
oscillating in space, although the detail of this resonance model is
often lost behind his numerous wavebased 2D simulations  see
websiteX for English translation of LaFreniere’s original website.
 John Macken’s
OST
model pursues another different standing wave model called a
rotar, which isolates angular momentum from the rest of
spacetime within a superfluid. While Macken has written a very technically
detailed book, his model is often difficult to comprehend due to the
structure of the book.
 Purely as a personal preference, the idea that the
myriad
of subatomic ‘particles’ correspond to some form of resonance
structure has some general appeal that might also be supported within
a causal model. From the standard model perspective, over 200 different
particles have been identified, although the existence of many are only
transitory in highenergy collision experiments. In more general terms,
most of the particle model can be defined in terms of 17 fundamental
particles, i.e. 6 types of quarks, 6 types of leptons, plus 4 types
of forcecarrying bosons and a Higgs boson. However, all matter particles
have an antimatter counterpart, e.g. the electron counterpart is called
a positron. Within the quantum model, each particle type exists within
its own
quantum field, although their description, and
existence, is subject to much mathematical abstraction.
 In practice, the structure of an atom only makes
direct reference to just 3 particles, the proton, neutron and electron,
although the neutron will decay into a proton, electron and antineutrino
– see Free Neutron Decay. In addition, the existence of the 6 types
of quark is essentially inferred from indirect experimental data.
 In the context of some, as yet unknown and speculative resonance model, all particles might simply reflect a specific resonance frequency that can be supported by the fabric of space. By analogy, we know that acoustical resonance patterns projected onto a 2dimensional plate reflect an underlying standing wave structure, such that any pattern with a given energyfrequency is constrained to an integral wavelength. How this might work in 3dimensions would become increasingly complex, although atomic orbital patterns might support the general idea as a causal mechanism.
This is possibly enough speculation for the reader to consider the
pros and cons of the various wave models reviewed todate. While it
is unclear whether any of these models come close to the actual reality
at work in the subatomic domain, they appear to raise valid issues that
the accepted models of science also appear to struggle to answer, often
with little reference to any physical causality.