The LaFreniere Model
Given the perceived problems raised in the previous discussions, the attention is now switched to the LaFreniere wave model to see whether it can avoid any of the issues outlined. At face value, one key differentiator of the LaFreniere wave model appears to be the rejection of the continuous IN-OUT wave model, at least, as described by Wolff. We might use the following quote by LaFreniere as a starting point:
Spherical standing waves are not made of in-waves and out-waves. This is indeed a very useful and effective method for displaying standing waves. However, this point of view absolutely does not correspond to what is really going on.
However, trying to figure out what LaFreniere actually thinks is ‘really going on’ is not always easy based solely on the translated pages of his website. Unfortunately, like Wolff, LaFreniere appears not to have ever described the mathematical derivation of his wave equations in a formal paper, which might then have been more easily reviewed. As a consequence, an initial attempt has to be made to pull together some statements related to his wave model, which are spread across his website, e.g.
Standing waves are not made of travelling waves. It is a totally different wave system which behaves in accordance with Hooke's law. For calculation purposes, such waves can indeed be considered as two sets of waves travelling in opposite directions. However, one must observe what is really going on inside the medium substance when standing waves are present.
While the translation of LaFreniere’s original words may have misrepresented his intended meaning, it seems that travelling waves are still required to initially establish a standing wave-centre in both the LaFreniere and Wolff models. However, what LaFreniere then goes on to imply is that the oscillation of the standing wave-centre can persist as a form of harmonic resonance, conforming to Hooke’s law, see inset right for basic definition, which is set in motion by the original travelling waves. While he provides the following example, the analogy might need to be questioned:
For instance, using a loudspeaker, one can produce standing waves inside a pipe. The travelling waves penetrate inside the pipe, and on condition that the wavelength is compatible, a resonance is obtained. Turning off the loudspeaker will not make the resonance stop immediately. Theoretically, a lossless system continue to vibrate eternally. The air is simply compressed inside antinodes, then the pressure energy is transferred into kinetic energy, and so on. The same process occurs for lossless springs moving back and forth, as predicted by Hooke's law: the extension is proportional to the force. The point is: there are no more travelling waves there. Just standing waves.
However, the following animation produced by LaFreniere seems to make it clear that the standing wave-centre could not be maintained for long if it radiates energy in the form of OUT waves, i.e. it is not a lossless system:
While the following quote may go some way towards explaining some of the apparently contradictory statements in the previous descriptions, it is not necessarily clear as to what actual physical mechanisms are being suggested, e.g.
….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. This can be explained by a lens effect…This means that in-phase incoming 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 as a spherical wave eternally.
Based on the animation above, the stability of any standing wave ‘resonance’ would appear to have a very short existence in the absence of input energy to replace that emitted by the OUT waves per cycle. So, building on the previous quotes, LaFreniere asserts that:
..the electron, which is a spherical standing wave system, does not need in-waves in order to be replenished. It needs an amplification process to prevent it from fading out. This is done by all external waves going through it, and undergoing a lens effect. This amplification process allows the system to go on oscillating permanently.
However, at this stage, it is far from clear exactly what mechanism causes the standing waves to be ‘amplified’ or what is exactly meant by a ’lens effect’ as the only description found appears to be limited to the following paraphrased quotes:
- The Amplification Process:
Any standing wave system will very quickly radiate all of its energy. In order to be stable it must be fed with energy. This energy first came from waves which were already present inside aether, but now comes from all the electrons within the Universe. Those waves contain huge quantities of energy, which is constantly recycled and returned to the aether in all directions. Electrons are amplified by incoming waves from all other electrons in the Universe.
- The Lens Effect:
Although it is not a well known fact, the lens effect really works too. This can easily be tested inside air, for example. Depending on its mechanism, a compressible medium should transmit faster waves if the pressure is higher. Standing waves alternately compress then dilate the aether substance inside antinodes. Then the wave speed is slower or faster according to the compression ratio and the wave is progressively scattered. Because energy cannot be lost, there is an action and reaction effect which explains the electron amplification process.
If we assume thaat the WSM model is basically a mechanical longitudinal wave model in terms of its general principles of propagation. The formula for the velocity [v] of a longitudinal wave in a mechanical propagation medium takes the following form:
Where the quantity [ρ] corresponds to the density of the medium, while the quantity [E] is generally defined in terms as the modulus of elasticity of the medium. However, the scope of this modulus depends on whether the propagation medium is likened to a gas, fluid or solid. Easily compressible media, e.g. gases, have a low value of [E], while almost incompressible fluids, e.g. water, have a very high value for [E]. For general assessment, we might simply assume that space is incompressible like a fluid and therefore has a very high value of [E]. However, if [E] is a constant for the medium of space, no matter what its actual value, there is a suggestion that the velocity of wave propagation through space, especially as described by LaFreniere's lens effect, may support the suggestion that waves may propagate more slower in the region of high-density standing waves. However, if we ignore the probability of creating a 3-dimensional standing wave system based on a specific configuration of in-phase IN and OUT waves, a damped system that loses energy will require further energy to be input at an ‘appropriate’ frequency. Within a resonannt system, this frequency is often referred to as the ‘driving frequency’ required to maintain the resonance, which is also explained in terms of the ‘natural frequency’ of the system, which in this case is the 'fabric of space'. While the maintenance of a wave-centre resonance may only require the input energy to equal that lost in terms of its OUT waves, it would seem that the ‘driving frequency’ would have to correspond to the ‘natural frequency’ of the space media and have any appropriate phase. Therefore, we possibly need to table the next question:
Why does the process of wave superposition not continue to effect the wave-centre resonance after its creation, if travelling waves continue to pass through the wave-centre?
Of course, if these subsequent waves were not in-phase or had different wavelengths, it would seem that they would ‘interfere destructively’ with the coherence of the standing wave resonance previous created as a one-in-a-billion chance.
So what does LaFreniere’s wave model represent?
The following animation is used in a number of pages of LaFreniere’s website. The waves on the left, top and bottom, have been described in the previous discussion of LaFreniere wave structure , which when added in superposition create the ‘resonance’ waveform on the right.
On LaFreniere page describing ‘The Electron’ he states:
“Using the Huygens Principle, I submitted all of Huygens' wavelets to a Doppler effect. The algorithm then becomes a bit more complicated because the wavelength must shorten regularly from (1–β) forward to (1+β) backward, where [β=v/c]. The computer produced the following result, which is correct only along the displacement axis.”
The concept of the ‘Doppler effect’ has been reviewed in an earlier set of discussions and used to evaluate the Wolff’s continuous IN-OUT model, which appeared to lead to problems with this model - see Doppler Wave Model for more details. While the waveforms above seem to avoid the problem of a discontinuity at the wave-centre, there is still the suggestion that these waves must have an amplitude, which is an inverse function of the radial distance [r] from the wave-centre, i.e. [A/r]. Later on the page describing ‘Spherical Standing Waves’ LaFreniere states:
“The Huygens Principle reveals that energy incoming from only one half of a sphere should cross the focal plane in a very special way, explaining why the central anti-node diameter is a full lambda wide. Then adding the second half produces the whole system”
However, as previously pointed out against the Wolff model, this description does not appear to account for a more probable random distribution of wave sources in a surrounding volume of space. If so, the mathematical derivation of what LaFreniere calls the ‘quadrature wave’ would also appear equally questionable, if it also requires the amplitude [A] of these waves to be an inverse function of the radial distance, i.e. [A/r]. Also, based on other statements, it is difficult to know whether the animation produced are only intended as visualisation of the wave-centre rather than being a physical description of what is ‘really going on’. For example, in Lafreniere’s outline of the Huygens Principle, he ‘suggests’ that the animation below, left, reflects the amplitude sum of all Huygens' wavelets incoming from the internal surface of just one hemisphere of space surrounding a given wave-centre, i.e. the IN wave. The 1D amplitude profile of the ‘Huygen’ IN waves from one hemisphere is shown in the inset bottom left – see LaFreniere Wave Structure for more details of this ‘quadrature’ wave.
So, based on the logic outlined above, the other hemisphere of space surrounding the wave-centre would presumably produce a similar effect, but in the opposite direction, as shown in the animation right. As such, the net effect of these two sets of waves propagating towards the wave-centre creates/maintains the stationary wave-centre below.
However, as pointed out, the description above appears to require a very specific phase relationship between all the OUT-to-IN wave sources, if the [A/r] amplitude profile is to be achieved. Of course, LaFreniere only suggest that this model be required to create the standing wave resonance as a one-in-a-billion chance, after which the resonance can be maintained by IN waves of different phase and wavelength. However, the question that has to be tabled is:
While this question also needs to be resolved, the following snapshot diagrams of yet more 2D wave simulations might suggest that the physical spacing between wave-centres, i.e. electrons, may naturally align to an in-phase booundary. For if the two wave-centres shown below are close together, the waves of each will overlap and create another composite superposition pattern, which in the spacing assumed produces a destructive effect along the horizontal axis that joins them. This absence of wave energy between the two wave-centre causes them to be pushed together by the wave energy on the other side of each wave-centre.
In contrast, the next diagram has shorten the spacing between the two wave-centres by [λ/2], such that the effect above is reversed, i.e. there is now a constructive effect between the wave-centres. As such, the imbalance of wave energy now pushed these wave-centres apart.
Therefore, we might assume that there is an equilibrium point, when the wave-centres are positioned on a [λ/4] boundary. However, it is unclear whether this mechanism could account for the stability of a wave-centre, e.g. electron, in relativistic motion.
How might relative velocity affect the wave models?
As a general comment, both model appear to suggest that IN waves might originate from all the other wave-centres in the visible universe. However, if the Wolff model is a continuous process of superposition of the IN-OUT waves that propagate with velocity [c], it would seem that a local wave-centre in motion would only ‘adapt’ to the phase changes to its IN wave over a large timeframe, i.e. [t=x/c], where [x] could conceptually range from sub-atomic distances to lightyears. Again, it would seem that any wave-centre moving with velocity [v] would be more quickly affected by the wave-centres in close proximity such that the dynamics of any wave model must remain stable within any localised frame. If so, we may have simply returned to the issue that the wave-centre resonance has to be maintain by IN waves of some description, even if they are not in-phase. However, it is unclear why these waves do not affect the stability of any underlying superposition model. As such, these issues also appear to throw doubt of the LaFreniere model and possibly lead to a wider question:
Do these issue effectively negate the possibility of a wave model?