Hi all,
While I appreciate the idea of "stream-lining" our approaches, it is probably too much to ask of a group of volunteers that are all living busy lives, all in different parts of the world.
No one has the time to "moderate" consistently, and I, for one, do not have the time to "post the answer", and respond to every possible question, within the time frame of a week. A "week" is 2 or 3 posts for me, realistically.
At any rate, we'll just continue as we have been, eh?
I'd like to comment of more "semantics", which really seems to "define" our ongoing problem: because Science has been built by very many separately developed parts, each "specialist" has their own set of tools, and definitions. Many that are left "growing in the garden", are indeed "weeds", but some "editors" like to leave these in, to convey the "awkwardness" of our historic approach. I think that this is a mistake; however, because we do not have the "final answer", this is tantamount to saying "we're not pulling any weeds because we are still deciding what weeds are", and that is probably just "the way it must be" (for now).
The show must go on! What are our teachers and professors to do, say "everyone is free to do what ever they want, because we haven't figured it all out yet"? NO, they must "teach" the theories, and in some fashion or another, act as though "we know", even though we don't (have the final answer). The kids would not pay any attention if this were not the case. At the higher levels, the "cracks" start to become visible, and the "nude emperor" can be peeked at by those who look hard.
GE has some good points about "math", especially the "abstract" kind, which is essentially, "infinitely interpretable", or at least, enough ways to cause really good arguments!
I agree with Godel, in that we can not ever have the "last answer", because the question has not even formed yet. That is in my own "twisted version". However, I find just enough philosophical room to squeeze this statement in:
This does NOT mean that we can not have a unified, self-consistent way of looking at everything we know NOW, and leave the door to "future questions" open, in the same self-consistent manner. A perspective that says "future questions can only be answered in terms relative to what already exists now" does not disagree with Godel.
If we have the "all inclusive", self-consistent model, and each and every time something "new" pops up, and is answered satisfactorily by said model, then that is our zenith. We do NOT have that now, so I find it rather pointless to go on about such things. We are trying to "clean up" the inconsistencies that are present in our current, competing models.
Semantics & Definitions:
GE and LL had a pretty good go at the "difference" between "standing" waves, and "traveling" waves superimposed. There is no difference, AFAIC, because they are "equivalent". The only "wrong" answer is to say that ONLY one or the other is valid. This is a perfect example of "dualistic": the duality is only observable from an opposite position, which requires "movement" (from your position) to see.
Because they are dynamically related, either perspective is ok; but it seems that adding another perspective, that is neither, is even better. Finding the "density" pattern in the longitudinal nodes, and transforming that into a perpendicular "intensity pattern" is a good "trick", but it seems to be inconsistent.
If we are seeing a transverse (to axis) pattern on the screen, why didn't we include the transverse mode pattern of the wave interferences? Certainly, the slit wall constitutes a boundary that we must include. The Talbot distance would seem to indicate that we must shift from "normal" (ideal) of TEM modes, given by the "plane wave" of "monochromatic frequency", and attempt a hybrid mode interpretation.
This is the curvature of the near field, possibly held together by "resonant unity", expanding in such a way as to decrease the possible paths, in a "beat by beat" transaction process, that recognizes the "convenience & efficiency" of reducing the number of paths to "full clicks" of "fundamental size" (whole cycles, wavelengths), and "half clicks".
If we assume that the fundamental frequency is the axis, then as we move away from the "new source" (slits), the "intensity", which we know to decrease by a factor of ¼ as the distance (from "new" source) r is doubled, takes on a "resonant" definition: it is the fundamental frequency, "continually revived".
When we interfere sources (>1), "something" is causing the inverse of the ISL. In the DSE, we find that the intensity at the axis is 4x (2a^2, a=1) that of the "side lobes". Fractional parts of the side lobes are re-directed to the fundamental, so that the amplitude is double there. This makes the side lobes "less intense", of course. These fractional parts can not be "symmetric", in the sense that the pairs can NOT be the same. This simple limit allows, for example, 1/4 and 3/4 to "pair up", but not the 1/2 points; these cancel to produce the "off phase" dark bands in the fringe pattern. [this is from the side lobe's perspective, or the straight line from center of slit to screen]
These fractional inverse symmetries are equivalent to transverse modes. Symmetric positions left or right of the axis can NOT be "in phase". When you combine this with the idea that the fundamental frequency IS the axis, the same left or right interval taken from those symmetric positions will have frequencies that are + or - by the same ratio.
This leaves an interpretation that says that the frequency of the axis will reduce by 1/2 at 90 deg (perpendicular, "left side"), or increase by 2 at the 180 deg (perpendicular, "right side"). These lines NEVER are involved "at the screen", in the fringe pattern, that is why it is INCORRECT to think of this as a "color change". The spread that you see in the fringe pattern represents a very "slight" change in frequency. Not only have these frequencies never been measured in the DSE, we are, even now, just BARELY able to measure frequency with the kind of "slight variation" (accuracy) that I am talking about.
In order to calculate this "angle limit", we just need to know f_0 (fundamental frequency), and the RI for f_0 (which gives v_0, the fundamental velocity). From there, measuring from the "sides closest to the axis" of each slit (thereby incorporating the separation of the slits) to the axis point at the screen, we set our inversely paired df (change in frequency) to arrive at the same place AND time, to superpose amplitudes. This is a very slight change from just the "path lengths" model.
It is critical to note, that these 2 "rays" are not traveling at the same speed. Their mean velocity is that which is calculated by the RI for that f , and that allows them to arrive simultaneously. This is with the agreement of the equi-spaced observers of the screen, perpendicular to the axis. Ones to the left of axis will see a "blue shifted" beam that is EXACTLY the opposite of the "red shifted" beam, as seen by observers on the other side of the axis. The Doppler shift is already in the RI calculations.
The next "pair" of simultaneous beams is the straight lines from slit centers, to screen. Relative to the axis, these frequencies are symmetric (equal) by the same rate: 1/2 . They are off phase, both relative to each other, and the axis (f_0). Remember that, in general, "off phase" produces beats (difference), while "in phase" produces sums. So, this off phase beat breaks the symmetry limit of 2, and quite easily explained, drops below our 1 octave limit in the visible band.
This explanation works for either a quasi-monochromatic laser beam, or a "white light" mixture, narrowed by the slit. The difference is in our perception, and "light gathering" ability. The term "black and white interference fringe" is a contradiction in itself, as noted by Mr. Berry. They are a product of the way that we see, as is the term "intensity". Mixtures of frequencies that "sum" to above our threshold are seen as "white", and those that "beat" immediately fall below perceptive range.
Either way, the original frequencies are still there. The equipment that we have designed to "measure" this, so we're not "depending on perception" (ha!), operates exactly the same. We set a threshold energy level (tuning out the "dark" current), so that essentially we have this result: everything "less than 1" = 0, and everything "over 1" = 1. I have given the full technical argument already, with our avalanche detectors, and the photoelectric effect.
I'm way past the ASL (attention span limit), as noted by maybe. Questions are always welcome.
regards,
T.Roc
Search for the butterfly! 
But warning taken, will not take it personal yet I still have much reading to do on this subject on this post and the input given so I do not repeat what has been said. 
. 
and the component measured along its direction of motion, its helicity, must be 
. The OAM is a separate spin quantum number that takes values from 0 to infinity... the way it has been classically been manipulated was through the use of tiny holograms to modify the packets.
