# The LaFreniere Wave Model

*“Standing waves are not made of travelling waves. It is a totally
different wave system which behaves in accordance with Hooke's law.
Electrons must have been created in the past using incoming waves. Such
a situation is not likely to happen because aether waves frequency and
phase very rarely coincide for a given point, but it is still possible.
One chance out of billions and billions. However, once it has been created,
the electron can remain stable because its standing waves are constantly
amplified by aether waves. Without incoming energy, the electron would
still emit spherical outgoing waves. So it would rapidly fade out. Obviously,
it needs replenishment. This is accomplished by powerful and constant
aether waves. Travelling waves penetrating through standing wave antinodes
are deviated because of a lens effect. A small part of the energy is
transferred to the standing waves. This constantly refilled energy allows
the electron to exist forever and means that in-phase IN waves are not
needed any more. The electron just needs constant and powerful waves
incoming from all matter in the universe, whose phase or wavelength
may be different. Then it goes on vibrating and pulsating spherical
waves eternally.” *

So, based on the paraphrasing of Gabriel LaFreniere’s words above,
this discussion will now attempt to characterise his description of
the electron wave model. Based on the description of ‘*The Electron’
*in *LaFreniere’s website*, we might reproduce the diagram below, which
contains 2 equations, although it may not be immediately obvious as
to whether there is any physical or mathematical justification for them.

Unfortunately, while LaFreniere placed so much importance on these equations, he did not seem to spend too much time explaining these waves in terms of the terminology used or the mathematical derivation that supports them.

Note: Based on the LaFreniere quote above, it is possible that the only practical purpose of these wave equations within the WMM model is to help produce analogous simulations. As such, they are not necessarily the wave equations that describe the actual causal mechanisms at work. We might also need to question whether the resonance frequency of the electron is being forwarded as a natural frequency of the fabric of space and further question the nature of the 'lens effect' that is assumed to maintain this resonance.

While these things may be obvious to some, the rest of
us may only recognise the basic form of the Sinc function, i.e. sin(x)/x,
in the phase wave, which also turned up in the mathematical derivation
of the *wave equation*.

[1]

As previously shown, the equation in [1] can be derived from two
travelling waves, as shown below in [2], although we might now have
started to question the physical reality of a wave amplitude being
extrapolated to infinity due to the [A0/x] expression, where [x] can
be equated to the 1-dimensional radius [r] from the wave-centre and
why the superposition is quantified in terms of a '*subtraction*'
process:

[2]

However, the following animation appears to suggest that the cosine
functions in [2] are now replaced by two ‘*quadrature*’ waves,
travelling in opposite directions, which [1] associates with the implied Sinc function.
So while the *Wolff* and LaFreniere
models appear generally consistent in the description of the resulting standing wave
in [1], i.e. when stationary, the underlying description
of the travelling waves are now linked to different formulations.

Note: In LaFreniere's
website discussion of
*
Huygens Principle*, he suggests that the sum of all Huygens'
wavelets incoming from the internal surface of a hemisphere would
conform to the shape of the 'quadrature' wave shown above. How this
applies to a wave-centre positioned arbitrarily with respect to
other wave-centres is unclear.
However, Huygens'
wavelets from the other hemisphere would then presumably account for
the wave coming from the other direction in the animation above,
which in superposition create the 'phase' or 'Sinc' waveform shown.
It is possible that these waves would then be unaffected by the
velocity of the wave-centre, so while the perceived wavelength of
waves from the forward and backward hemispheres would change, within
the moving frame of the wave-centre, the waves would remain
symmetric - see *animation* below.
However, the main discussion of such issues will be deferred to the
'*Physics of Matter Waves*'.

It is possibly sensible to make some initial attempt to explain the
terminology of ‘*phase*’ and ‘*quadrature*’, as it is used
by LaFreniere to label the waves being described. However, it is not
clear whether the following explanation aligns to LaFreniere’s intended
definition. The form of the following trigonometric identity is often
used in the derivation of many wave equations, where [θ] is a linear
function of some variable, e.g. [ωt].

[3]

When [φ=0], then [3] reduces to the ‘*phase*’ component
and the ‘*quadrature*’ component is zero. However, the original
program ‘*Aether06.bas*’, used to create the animation
above, appears to suggest that two ‘*quadrature*’ waves are added
to create the ‘*phase*’ wave, which then has the form of a Sinc
function. So, putting the issue of terminology to one-side, it might simply
be more useful to show the mathematical interconnections between the
equations being implied by the animation above:

[4]

We might first expand and re-arrange the form of [4] as follows:

[5]

We might now manipulate [5] using the identity in [6] to produce [7]:

[6]

[7]

In the current context of a wave model, we might wish to correlate the measure of space [x] and time [t] to wavelength [λ] and frequency [f], such that we might recognise the standard form of 2 travelling waves propagating in opposite directions based on [7]:

[8]

However, we still need to show the relationship between what LaFreniere
calls the ‘*quadrature’* waves and the ‘*phase*’ wave through
the superposition of 2 travelling waves, now anchored in [8]. We might
start by simply adding two versions of [7] travelling in opposite directions:

[9]

This addition immediately suggests that the sin(ωt) expressions would disappear leaving what appears to be two travelling waves:

[10]

At this point, we might wonder if the form of [10] is so different to [2] if we add the [A0/x] factor, i.e.

[11]

However, what might be recognised more easily in [11] is the form of the Sinc function sin(x)/x, which then avoids the implied infinity associated with [A0/x], when [x=0]. This said, the form of [11] has now extended sin(x) to sin(kx±ωt), which does not produce the Sinc function in that the infinity at [x=0] is not avoided. In fact, we can see a comparison of [11] versus [9] in the animation below. Without the sin(ωt) factor in [9], the blue and green waves would simply extend to infinity as illustrated by the red waves.

So, by way of practical commentary, we might realise that the amplitude
of the waves, as implied by [11], cannot actually extend to infinity
in the ‘*real*’ world. If so, we might accept that the equation
required to described these waves needs to be modified and, as such,
this is what [8] appears to do. Of course, whether these equations are
actually correct is another matter entirely. However, what is also important
in the comparison between the Wolff and LaFreniere models is that IN-OUT
do not exist independently on the forward and backward interfaces, i.e.
spherical rotation is not assumed. For in the LaFreniere model, the
‘*quadrature*’ waves, as described by [8], appear to pass through
the implied wave-centre at [x=0]. As this is key to the asymmetry problem
highlighted in the *Wolff model*, we shall return to this point later
in the discussion. For now, we shall return to [10] to continue the
process of reconciling the '*addition*' of the two quadrature waves with
the phase wave using the following identity:

[12]

Substituting for [A=kx] and [B=ωt] used in [10] we get:

[13]

Again, we might add the detail [A0/x] and convert the cosine function to sine by adopting a phase angle [π/2] for a better comparison with [12], which is now based on the superposition of the quadrature waves defined in [9] and originally in [4]:

[14]

So, at face value, we appear to have shown some mathematical consistency
between the two wave models. However, the description of the quadrature
waves in [8] may be more realistic in that infinite wave amplitudes
are avoided without the mathematical abstraction of the Sinc function,
which appears to rely on the addition of [±] infinity at [x=0]. Equally,
the superposition of the travelling waves is now defined by the '*addition*'
of the quadrature waves rather than the '*subtraction'* of the cosine waves,
as required by the mathematics of the *original wave equation*
derivation.

*But what about
spherical rotation?*

Clearly, this would appear to be a fundamental difference in the two wave models under consideration, which then raises a number of secondary issues. However, we might start by considering another paraphrasing of LaFreniere words:

*“Standing waves are not made of travelling waves. For calculation
purposes, such waves can indeed be considered as two sets of waves travelling
in opposite directions. This is a very useful method for computer programs.
However, one must observe what is really going on inside the medium
substance when standing waves are present. One may need incoming travelling
waves in order to establish standing waves, but they are no longer needed
once the system is well established.” *

Based on these words, LaFreniere would seem to be drawing a distinction between the formulation of the wave equations used to create the various wave simulations and the physical reality of these waves. For LaFreniere’s model appears to be a two-stage process in which the wave-centres are first created and then maintained by IN waves having different phase requirements. Only in the first instance are the IN waves required to be in-phase, while all subsequent IN waves, after creation, are only required to maintain the energy lost by the standing wave in the form of OUT waves. We might use one of LaFreniere’s many animations to illustrate what he appears to be suggesting:

Again, we might use LaFreniere’s own words to initially describe the animation above:

*"Without incoming energy, the electron would still emit spherical
outgoing waves. So it would rapidly fade out. Obviously, it needs replenishment.
This is accomplished by powerful and constant aether waves. Travelling
waves penetrating through standing wave antinodes are deviated because
of a lens effect. A small part of the energy is transferred to the standing
waves. This constantly refilled energy allows the electron to exist
forever. Outgoing spherical waves weaken according to the square of
the distance law. The electron too produces outgoing spherical waves.
Those are regular travelling waves, because the electron is rather made
of standing waves, amplitude can no longer be the same everywhere in
both directions, making them ‘partially standing waves’. Finally, even
farther, just outgoing travelling waves remain."*

While the term *'lens effect*' is not really understood,
it might be linked to the idea that the very high-energy density within the
wave-centre node may both '*refract*' and '*diffract*'
IN waves of various frequency, such that the lost energy associated
with the OUT waves can be '*replenish*'. However, this is purely a guess at
this stage as it is unclear how energy would be imparted to the
resonating electron wave-centre by such mechanisms.

Note: Refraction is the change in direction of waves that occurs when waves travel from one medium to another. However, refraction is usually accompanied by a wavelength and speed change. On the other hand, diffraction is simply a bending of the wave around obstacles, i.e. the high-density wave-centre region.

While the totality of LaFreniere's wave model may still be far from
clear, there may be enough of an insight to start considering some of the pros
and cons in comparison to the *Wolff wave model*. These are itemised in
the bullets below to allow future cross-referencing, starting with the
pros:

- The fact that the quadrature waves avoid the infinite
amplitude at [x=0] appears to be more realistic, although the
scope of these wave equation appear to be limited to the
simulation models.

- By rejecting the idea of spherical rotation,
the discontinuity within the wave-centre between the forward
and backward waves appears to be avoided. It might also be
argued that by rejecting the idea of spherical rotation, the
waves remain consistent with the description of superposition
and simply pass through the same point in space-time, at least,
after the initial creation of the wave-centre.
- The two-stage model separates out the low-probability
of OUT waves becoming in-phase IN waves that increase in amplitude based
on [A0/x] to a one-time event in the evolution of the universe rather
than being a constant requirement as appears to be suggested by the Wolff model.
- The idea of a standing wave maintaining its
existence independent of any further IN waves is consistent with the
idea of harmonic resonance, which in a lossless system would oscillate
forever. However, as illustrated in the animation above, the wave-centres
must lose energy in terms of the OUT waves that ultimately emanate from
the wave-centre; hence the requirement for IN wave energy, but without
the in-phase requirements.

- There is a possible suggestion in this model that '
*the media of space*' may have a frequency, or set of frequencies, at which it might naturally vibrate, such that it might sustain a '*resonance*' associated with a standing wave in a semi-lossless manner. These standing wave patterns would represent the lowest energy vibrational modes of the media, i.e. space, which may explain why only a few specific modes of vibration might be associated with the '*appearance*' of '*particles*', e.g. electron, with specific mass [m] that actually reflects the frequency [f]-energy [E] of an underlying standing wave structure.

So the bullets above might be seen as a simple summary of some of the possible advantages of the laFreniere model. This said, there are still a number of issues that this model needs to explain, which we might cite as cons:

- The model appears vague as to when in the evolution
of universe, the wave-centre/particles might have been created by the
low-probability events described. For these low-probability events must
have occurred some 10
^{80}times, if all the particles in the visible universe are to be accounted. - Based on the exponentially falling probability
of creating 10
^{80}low probability events, it would seem that there must have been some very special circumstances in existence within the early universe that helped reduced the odds and allowed the basic building blocks, i.e. particles, of the universe to be created en-masse.

While there may be more material ‘*hidden*’ in the various pages
of *LaFreniere's website*, he does make an attempt to address the issues
above in a page on *‘Evolution’* from which the following is extracted:

*“So, let's postulate that matter is made of waves and that those
waves need a carrier: aether. Assuming this, you may imagine any hypothesis
about its origin. In accordance with the Causality Principle, any effect
has a Cause. And because our material universe is made purely out of
aether, this Cause cannot be material any more. So it should be un-material.
You may explain the World's origin the way you prefer. You may also
give this most honest and sincere answer: "I don't know".
And so, in my opinion, one should postulate that an aether filled with
waves which contain a lot of energy had to exist in the beginning of
times. Then the continuation was foreseeable: 1) Because the aether
is finite and elastic, a "Big Bang" followed by an expansion
occurred. 2) This explosion produced strong and abundant longitudinal
travelling waves. 3) The waves created a lot of electrons and positrons.”
*

While the pros and cons arguments above are only meant as an
introduction of the issues, within this general review phase, we might now consider the results of the animations
below, which are thought to be representative of the LaFreniere wave
model, where the wave-centre is assumed to have a relativistic velocity
[β=0.5c]. Again, it is highlighted that this animation does NOT
yet account for time-dilation, as required by the *
Lorentz Doppler effect*.

So, in the traces left, we see the quadrature waves moving left-right
(blue) and right-left (green), which are modified according to the
*Doppler
effect*. These waves are then added in superposition to
created the
standing wave (red) in the trace bottom-left, which is then displayed
in grey as an aggregation over time. The animation on the right is simply
the simulation extended to 2D/3D with the standing wave (red) superimposed
by way of reference.

Note: If we assume that the blue and green waves in the simulation above are being produced by stationary upstream and downstream wave-centres, then the Doppler shift of the wavelengths shown must be a virtual Doppler effect in the frame of the 'red dot' moving with velocity [B=0.5c]. As such, the Doppler effect being shown would not exist in the fabric of space, although the OUT waves of the red dot being sustained by the blue and green IN waves must be producing another set of Doppler shifted OUT waves in the forward and backward directions that do propagate through the fabric of space and are a function of the velocity [B=0.5c]. However, the complication of this assumed model is that it is unclear how these OUT waves would then combine in superposition with the blue and green waves. For the description of the LaFreniere model appears to suggest that the 'natural' resonant frequency of the electron wave-centre is simply 'sustained' by IN waves of all frequency and phase, such that there is not a clear 'picture' of the totality of wave superposition taking place.

*So which model is right?*

Without yet having time to review the full detail of all the work produced by either
*Milo Wolff* or
*Gabriel laFreniere*, it is difficult and premature to make
any definitive decision. However, the Wolff model appears to have a
number of problems, which at this stage, cannot be easily resolved.
There also appears to be a lack of detail regarding the kinematics associated
with the Wolff model, which *Lafreniere’s website* does attempt
to address. Of course, it should be highlighted that the wisdom of accepted
science will tell you that both models are wrong. If so, you must return to
some of the ideas in quantum theory, e.g. *
QFT* or *
QED*,
and then ask yourself whether these models really answers all the questions
raised by the *WSE model *or* *the section on *
speculative
science* as a whole. Alternatively, we might consider a
fundamental different wave model, e.g. the
*OST model*.

Note: Some of the general
issues raise to-date can be found in the '*Summary: Progress Report*',
while a further discussion of the issues raised will continue under
the heading '*The Physics
of Matter Waves*.'