Hi Confused2, TRoc, Jal, Montec, Laserlight et al,

I am not entering a vague argument about the "Aether" based on "waves" since "waves" are not an "Aether". And I will not be coerced into discussing "Aethers" of all kinds since nobody has ever found an "Aether" and nobody knows, as a consequence of that non-result, that we are able to discuss unknown properties of the "undiscovered Aether". I could just as authoritatively discuss the numbers of angels that can dance on the head of a pin since the "properties" of angels are also equally unknown. But I am sure that a million "eager souls" who would only love the opportunity to begin a theological discussion in the middle of this wandering and vague debate on what is supposed to be physics.

I had a quick look at Jal's papers and I am unsure what can be derived without some kind of interpretation of how this fits into this current topic of the Double Slit Experiment (but no matter... much of what is being bandied about seems only peripherally involved with the basics at this stage). Let me see if I can make some sense of this rather poorly organized cacophony of ideas. It seems you are trying to invoke a realistic interpretation of how electromagnetic waves can be divided into smaller and smaller sources each of which spread only in the forward direction at the speed of light on the surface of a spherical expanding shell. If you could explain that then the summation of a large number of individual sources would make sense such as that interference pattern made up of a "slit" in the form of a "plus sign". Clearly the double slit equation does not explain anything but the most basic case of ideal interference between two coherent sources. I understand that Confused2 will not move from the solution from that one simple generalization to the real world where there is "far more going on". Laserlight seems to be suggesting that:
I though by now you would all realize that the individual photon's wavefront cannot be really known and it is the result of "searching all paths" in the Feynman sense. The photon particle is "indivisible" and I also thought this would also be "obvious" and anyone who has done any experimental work will see that this is indeed the case... at least when dealing with phenomena in "free space". Of course photons can be "joined" and "split" under very controlled conditions using highly coherent situations. We have that in holographic "reconstruction" and also in parametric down conversion as previously noted. This is not "debatable" since they are the results of experiments that are repeatable. What is also the result of experiment is the distribution of energy in individual photons can be moved from one point on its wavefront into longitudinal modes as shown by those images pointed to by TRoc earlier on:
Shaping of a Terahertz Pulse by a Slit in a thick screen
This is a very interesting result that shows that a single half-cycle terahertz photons or indeed a number of coherent half-cycle terahertz photons are "smeared out" into a broad distribution of wavelets. The question is since this is showing a large number of wavelets is this taking the original single pulse with a narrow expression on the wavefront and recombining the energy into a different group of frequencies and new photons? Alternatively is it delaying some photons so that they now comprise a section of sinusoidal radiation? I think the latter must be the case. The "pipe" is a "resonant chamber" that oscillates at a particular frequency. The incident photons "blow" into this "pipe" and it sets up standing waves with anti-nodes at both ends of that pipe. This is clearly an "oscillator circuit"... in an under-damped cavity... that will destroy the qubit that is being carried by the original wave photons. There is an experimental paper that accompanies this discussion here which indicates what happens for a single slit modifying the slit separation and the slit thickness independently and together...
Spatiotemporal shaping of terahertz pulses
What it reports is this... for slits (or holes) with "thin" cross section relative to the wavelength of the radiation, severe dispersion of the high frequencies will occur and this ultimately leads to a relatively sharp roll-off frequency for a specific slit width of
f(rolloff) = 1.5C/Πd
For thick cross sections these slits (or holes) behave just like organ pipes or cavities.
The "dispersion" of high frequencies is well known and is used in many instruments at optical frequencies. Note in fig 3 that the pulse transmitted by the thick filter is chirped and oscillates with a period that decreases as the slit width decreases. In the useful case of the former thin slit (or hole) a typical application is this kind of Fourier optical processor which utilizes the dispersion spatially when passing the "mask" which is usually a circular aperture but an even better mask is one which also includes airy disks in the opaque mask.

Fourier Optical Image Processor
Here the input scene become a multiple source (you could have a single point source but it is often more interesting to place a photographic image there as shown. This is a "multiple source" illuminated by coherent light. The first lens could also be a hole as in a "camera obscura" (or it could be a slit... one of two in a double slit experiment). A mask is places around the lens to limit the aperture of the image to a usable portion of the lens (lower the aberration). On a "screen" we now have a multiple diffraction pattern set up which is formed from the overlapping of millions of coherent sources originating from the image plane. Each point source is singly and airy disk as we all have seen. All these airy disks overlap and interfere with each other "constructively" to form an inverted image of all the individual sources on the plane (marked diffraction pattern). This is equivalent to a screen in the DSE. The image contains a repeating pattern of horizontal bars (scanlines) superimposed over the image. These two "artifacts" .... the image of a goblet and the image of the bars are "dispersed" into their complex frequencies radially and the horizontal bars are shown as a series of bright spots in a vertical plane and the goblet is a blob of frequencies in the center of the plane. These frequencies increase as we move to the edge of the Fourier transform plane (the "diffraction pattern" in this diagram which is brought to a sharp focus by the lens) and at the very center of the plane is a point which is the DC (or base intensity) component where much of the energy in the image is concentrated.

Fourier Transform
I would point out that in the case of a single pinhole the image is focussed less accurately at any point in the space behind the aperture as in the DSE this is identical to stopping a lens down to a tiny point where all "rays" pass only through the center of the "pinhole lens". A specially prepared mask with two chevrons removes cleanly these bright spots in the spatial hologram at the "diffraction pattern" from the overall complete diffraction pattern by simply blocking these Fourier components in frequency and spatial dispersion, the component which contains the scanline artifact. If the light is then allowed to pass through this mask the Hologram (spatial dispersion of the frequencies into their basic fringes) of that source plane, what remains is then focussed on a "screen" using a similar lens (usually with the same stopped aperture and the same focal length placed symmetrically on the other side of the "hologram of the 2D image sources"), reversing the hologram forming process but removing through selection the spatial components of the "scanline artifact" (those vertical row of dots in the "diffraction pattern").

This shows how the first lens makes a Fourier transform of the 2D image array of individual sources (at a single frequency... the frequency of the illuminating laser) and the "diffraction pattern" is where this multiple source plane is now sitting as optical frequencies in that "hologram" of the frequencies. A portion of this frequency hologram is removed that relates to this scanline artifact. It is a series of bars in the original image which have a series of Fourier frequency components now spatially orthogonal in this Fourier plane to the original bars. They have been dispersed radially outwards the highest frequencies towards the "rim". The fine detail in this image in in the high frequencies. These components can be selectively removed using the mask.

In summary... the "plane coherent radiation" illuminates the 2D sources in the image transparency. These acts as a large number of secondary spreading sources of different intensity, each one resulting in a "frequency transformed image" in the frequency domain at the position of the "diffraction pattern". The images of all sources occupy the same frequency space with no relative displacement even though originally the sources were displaced physically in space (in the plane of the transparency). Each and every spatial frequency in each and every spatially dispersed source now falls into that single complex plane of "diffraction pattern" where each individual spatial frequency in all sources occupies a single point on a perfect "circle" whose radius is proportional to the spatial frequency.

The position around that circle determines the spatial alignment of a single frequency component at that azimuth from all the original sources as a complex phase since this "point" is the sum of all similar azimuthal frequencies ... not summed as scalars but as complex vectors.... This pattern defines "source particles" fixed in space, this is a two dimensional sources but this could just as easily define three dimensional sources or "particles". We can filter this source information to enhance or express certain attributes in the original sources or even amplify them if we choose using sophisticated computer techniques that parallel this optical process mathematically. This is the science of Fourier image processing used by Hubble, Geophysics or in Military areas where more information is required from a small area of the image. Most of this is exactly duplicated using this simple optical system using a coherent source of plane radiation and two good quality lenses and their associated elements and this is all that optics is about. Some information is lost from the original source outside the evanescent zone, but there are theoretical techniques where this information may potentially be restored completing the description of particles everywhere.

The second lens reverses the transform in the first transformation restoring the 2D sources (with all depth information if required). If particles were composed of this information then a reconstruction of particles can be made as an optical entity. Suppose that a particle is composed of very high frequency "matter waves" and there was a technique in which the particle can be imaged in just this process then this would be a particle theory. "Physics" would be performed by the electromagnetic images of these objects that will obey the laws of conservation of energy. You may ask "where are these matter waves?" They must be everywhere and able to penetrate anything due to their incredibly high frequency.

Cheers