# The Wolff Wave Model

*“Two waves can be combined in only two forms, which are the structures
of the electron-positron. These are combinations of the IN and OUT spherical
waves. The IN waves reverse direction at the centre to become OUT waves.
Spin occurs when the IN wave arrives at the centre and rotates continuously
in order to transform into the OUT wave. However, rotation cannot be
allowed to twist up space without limit and spherical wave amplitudes
must continually and smoothly change while changing direction of motion.
The IN wave amplitude at the centre must be equal and opposite to the
OUT wave. It turns out this happens using a known property of 3D space
called spherical rotation in which space rotates continually around
a point and returns to its initial state after two turns.” *

So, based on the paraphrasing of Milo Wolff’s words above, this discussion
will attempt to characterise his description of the electron wave model.
It might be argued that this model rests on the previous mathematical
derivation of the *wave equations* and the *
relativity transform,
*which are both based on the papers of Robert Gray. Clearly, in the
‘*physical world’*, any single wave-centre may be surrounded by
billions of other wave-centres, which conceptually extend outwards in
all directions into the visible universe. As this can be more than
a little difficult to visualise, an attempt has been made to simplify
a reference model to just 3 wave-centres, e.g. [XYZ], such that we might
consider the effects of wave-centre [Y] moving with a velocity [v] with
respect to the media in which [XZ] are stationary.

An animation representative of the diagram called *
Doppler Config-4* may also
provide a point of reference to this discussion. While the model attempts to reduce the actual complexity to a minimum,
there are still a number of distinct interfaces, which act as both the
source [S] and receiver [R] of the waves as suggested in [1] below,
which are then assumed to form the standing wave structure of matter:

[1]

So, based on the diagram above, the moving wave-centre [Y] must be
both a *‘receiver [R]*’ and ‘*source [S]*’ of waves subject
to *Doppler effects* in the ‘*forward [F]*’ and ‘*backward [B]*’
directions of motion. Hence the notation used to identify the various
interfaces within each wave-centre, i.e. [XYZ]:

- FO = Forward Out wave
- FI = Forward In wave
- BO = Backward Out wave
- BI = Backward In wave

However, despite the attempt to simplify the model, complexity creeps
back into the discussion as we begin to consider the various effects
at work within each reference frame, i.e. the source [S] and receiver
[R] interfaces within wave-centres [XYZ]. For example, while there is
an inference that an [OUT] interface must correspond to some
IN wave source,
there is still a degree of ambiguity surrounding the process described
as ‘*spherical rotation’ *, which would allow an [IN] wave to
be ‘*reflected*’ back as an [OUT] wave within a wave-centre that
also results in a 180° phase shift. Of course:

*If spherical rotation does not occur, where do the IN-OUT waves
originate? *

Clearly, this is a fairly fundamental issue, but we do need to seriously
question the idea of spherical rotation because within the normal description
of wave superposition, waves are simply assumed to pass through the
same point in space without being reflected. Of course, without spherical
rotation, a major modification of the diagram above would seem to be
required, which would then affect the underlying wave mechanisms at
work within the Wolff model. One possible alternative will be outlined
in the next discussion ‘*The laFreniere Model*’, but for now,
we shall try to consider just a few of the details associated with the
‘*Wolff Model*’.

*So what is a wave-centre in the Wolff model?*

The diagram above showing the [XYZ] configuration might be used as
an initial framework for discussion, where the IN wave at wave-centre
[Y] on the forward interface [Y_{FI}] is assumed to have originated
from interface [Z_{FO}]. Based on Wolff’s description, the IN
wave received at wave-centre [Y] is then subject to spherical rotation,
which causes a 180° phase-shift and becomes the corresponding OUT wave,
which is then transmitted back onto the forward interface [Y_{FO}],
which the next diagram now tries to illustrate in a little more detail:

If we accept that the IN wave at the moving wave-centre [Y_{FI}]
originates from the stationary wave-centre [Z_{FO}], the wave
propagating from [Z-Y], through the media, would not be subject to any
*Doppler effect*. As [Z] is a
stationary source of IN waves at [Y_{FI}], only when perceived from within the moving frame
of [Y] would the *virtual Doppler effect *apply, as illustrated.
However, the virtual Doppler effect does suggest an increase in the
wave arrival rate must be perceived at interface [Y_{FI}], which
would then affect the transmission rate of OUT waves from [Y_{FO}],
if continuously linked to the IN waves via spherical rotation. The diagram
then suggests that these OUT waves would then be subject to the *
normal
Doppler effect *on the return forward path between [Y-Z].

*How might this effect be shown in a wave simulation?*

The following simulation attempts to show how the IN and OUT waves might be broadly interpreted as aligning to the framework diagrams above and equation [1]. However, the first animation shows the situation when the central [Y] wave-centre is stationary with respect to the media, as are [X] and [Z].

The upper traces show the individual travelling waves, both IN and
OUT, for the forward [YZ] and backward [YX] interfaces, which in the
case of [v_{Y}=0], are all equal in terms of frequency and wavelength.
The lower traces then shows the superposition or standing wave in red,
which over time, creates the grey trace that might be seen as the energy
profile of the standing wave in time.

*Note: we might wish to question an implication within the animation
above linked to the cosine functions in [1]. Is it realistic to model
the wave amplitude increasing towards infinity, which only gets cancels
in the mathematical abstraction of the Sinc function? Another issue
cited against this model is the uniformity required to create a 3D spherical
symmetrical IN waves that increases in amplitude according to [A0/x],
which in the Wolff model appears to be a continuous requirement.
*

The Freebasic program used to generate both animations, above and
below, can be reviewed here: *
WSM Simulation-2*. However, if we now
consider the same configuration when wave-centre [Y] is in motion, we
have to account for all the possible Doppler effects outlined above.

In this case, it is assumed that the simulation has to extend the previous outline of the virtual and normal Doppler effects on both the forward and backward interfaces, i.e. [YZ] and [YX], although what reference frame applies also appears to be an issue. While the assumptions underpinning the simulation above may be wrong, they are based on the following arguments:

- The WSM model assumes the existence of a wave propagation media.
- The wave propagation media is an absolute reference frame.
- While the wavelength of the IN-OUT waves is a function of the source
velocity,

the standing wave exists in the reference frame of the propagation media. - The phase relationship between the IN-OUT waves is a function of time.

It is possiblly unclear whether any single *‘observer’,* stationary
with respect to the media, would ‘see’ the animation as shown. In part,
this issue has been previously discussed under the heading of ‘*Relative
and Relativity Transforms*’ where the perspective of
*special relativity*
was assumed. However, as previously highlighted, relativity denies the
existence of any absolute reference frame, such that any inertial
reference frame can simply claim to be at rest, which is contrary to
the description of the *asymmetric Doppler effect*, which accounts for
a propagation media. In the model adopted in this discussion model,
i.e. wave-centres [XYZ], only [Y] is in motion, while [XZ] are at rest
and because the propagation media is assumed to exist in this model,
this orientation cannot be reversed. Obviously, in the macroscopic world,
any observer within any reference frame must represent a wave structure
consisting of billions of wave-centres. However, for the purposes of
this discussion we might assume that our observer exists within the
stationary reference frames of [X] and/or [Z]. These observers will
then attempt to quantify the wave attributes of the moving wave-centre,
e.g. [Y]:

*What might they describe? *

According to the Wolff model, [X] and [Z] are both sources of [OUT]
waves, which arrive at [Y] as [IN] waves. However, because [X] and [Z]
are both stationary with respect to the media, there is no Doppler effect
associated with the waves propagating through the media towards [Y]
from either [X] or [Z]. Again, according to the Wolff model, these
waves will arrive at a point in space, i.e. the wave-centre [Y], and
will then be ‘*reflected*’ back through the process of spherical
rotation. While the velocity of [Y] affects the arrival rate of [IN]
waves at [Y], as described by the virtual Doppler effect, it is difficult
to associate this process with any internal mechanism within [Y] that
might then be the cause of time-dilation associated with the [OUT] being
reflected at [Y]. While we are at this point, we might also table another
question concerning the wider kinematics of any wave-centre:

*What mechanism causes a wave-centre to move with velocity [0..c]
in the Wolff model? *

This question is orientated towards the Wolff model because an
initial review of Wolff's papers appears to offer up little in
the way of explanation of the wider '*physics
of matter waves*', although this may only be a temporary
oversight on the part of the reviewer. However, returning to what amounts to a purely Doppler description,
the virtual Doppler effect associated with the velocity of [Y] does
cause a change in the wavelength, i.e. (1±β), in the forward and
backward direction. As such, this effect extends into the propagation
media, suggesting that the standing wave formed by the superposition
of [IN+OUT] waves must account for these effects, as shown in the animation.
However, the superposition of the [IN-OUT] waves on the forward and
backwards interfaces, i.e. [YZ] and [YX], appears to lead to a discontinuity at
the wave-centre [Y], which is difficult to explain away.

*So what reference frame is meaningful? *

At one level, the waves become independent of the source or receiver once transmitted into the media. So, as described, the standing wave must exist as a wave structure that oscillates in time due to constant changes in the phase between the travelling IN-OUT waves. As described, we might characterise the wavelengths in the following terms and illustrate the values shown in the simulation, which at this point do NOT account for relativistic time dilation effects, as yet:

[2]

However, it is highlighted that the simulation makes no account for
any change in frequency. However, if the IN and OUT waves are linked
by spherical rotation, it might be argued that frequency of these waves
is still being driven by the source frequency [f_{S}] at [Z_{FO}]
and [X_{BO}].

*Note: When the OUT waves from
[Y] arrive at [X] and [Z], the physical change in wavelength
propagated through the media is interpreted in
the form [c=fλ], such that a corresponding change
in frequency is perceived within the frames of [X] and [Z]. *

This said, all *‘experiments’ *within the simulation model do
not appear to result in any symmetry between the forward and backward
standing waves. This lack of ‘*symmetry*’ can be seen in the simulation,
which then results in a discontinuity of amplitudes at the forward to
backward interface at the centre of [Y]. So while accepting that this
‘*amplitude* *distortion*’ might be the result of not properly
accounting for the reference frame of observation, there appears to
be a problem in this model or, at least, the simulation of it. Of course,
if the suggestion of an error is true, we would have to seek an alternative
explanation that might correct the asymmetry shown and, as such, we
will now turn our attention towards the *
laFreniere’s model.*

*Note: If we were to try to reverse the configuration, such that
the observer existed within the stationary reference frame of [Y], this
frame would have to consist of billions of wave-centres, all stationary
with respect to each other, but now surrounded by wave-centres moving
with respect to the media in the same direction and velocity*.

As indicated, this discussion is only part of an initial review
process trying to understand some of the scope and implications of
the matter wave model. Therefore, some of the concerns raised
against the Wolff model may be proved to be unfounded; although it
is clear that mainstream opinion would simply dismiss the whole
idea. However, some of the general issues raise to-date can be found
in the '*Summary: Progress Report*'