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  below,
which are then assumed to form the standing wave structure of matter:
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 [YFI] is assumed to have originated from interface [ZFO]. 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 [YFO], 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 [YFI] originates from the stationary wave-centre [ZFO], 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 [YFI], 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 [YFI], which would then affect the transmission rate of OUT waves from [YFO], 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 . 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 [vY=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 . 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
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:
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 [fS] at [ZFO] and [XBO].
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'