The galaxy rotation argument has been presented for quite a while now as evidence against the Setterfield theory and I've also prepared a little bit of an anlysis against the quote Helen provided in the other thread defending Setterfield theory. Here goes!
Originally posted by Helen:
Barry has recently finished a paper in which the problem of galaxy rotation speeds is addressed. I have asked him for permission to quote part before publishing. Here it is. One note has been added for clarification in the text. It is in parentheses. Also, lambda has been replaced here by L for ease of reading the equations and paragraphs:
It is good to know that Barry has decided to take this serious objection seriously.
A changing ZPE, with an inversely changing speed of light, c, brings into question the veracity of galaxy rotation rates because they are measured by Doppler shifts.
In other words, they would appear to disprove Setterfield theory.
Now the Doppler equation contains c terms, as in equation (125) below. Therefore, it might be thought that high c values would circumvent measurement of velocities, unless they, too were correspondingly higher.
Yes, one might indeed think that very thought. Here's why. Light has a wave pattern. It travels out from a star with wave after wave going forth in a definate pattern, a definate spacing of the waves. But if the star is ALSO moving towards us, then every time a follow up "wave" or "crest" of light goes forth from the star, it must be adjusted by the fact that the star, having moved a little bit towards us in the meantime. This crowds the waves closer together as they come towards us.
And, if the star happens to be going away from us, it stretches out the waves.
Now a moments reflection will show that this crowding and stretching is, of necessity, taking place right there at the time and place the very waves of light are being made, not in transit, or when they reach us. So, at the time they leave the star, the two key factors that are involved in determining how much stretching or compressing takes place would be (a) the speed of light at that time and (b) the speed of the motion towards or away from us. Nothing else would be involved at all.
But it has already been shown in equation (19) that Gm is unchanged by variations in the ZPE and c. This means that actual galaxy rotation rates and orbital velocities will remain within the usual range and would not be higher.
Setterfield CDK theory, being a YEC rescue theory, is constrained by the need to tie the number of years since the beginning of the universe to about 10,000. He speeds light up by millions of times in the beginning of the universe to make us able to see things at the astronomical distances they are seen. But what does it mean to say that light is millions of times faster? Faster in relation to what? It is in relation to orbital velocities, at least. Nobody can deny that the definition of a year is the time it takes the earth to circle the sun. That's an orbit. Setterfield theory insists there have only been about 10000 earth orbits to take place while light has traveld over distances of billions of light years and then slowed down to only one light year per year. That is what Helen is referring to in the above sentence.
So what is the velocity that is actually being measured by the Dooppler shifts? In examining this, we use the relativistic Doppler formula. Let a periodic wave of frequency, f, be emitted by a rotating galaxy that has one side approaching an ovbserver with velocity, v. From the observer's frame of reference, the frequency, f*, is given by [191]
f* = f + [fv/c] + [fv^2/(2c^2)] + [fv^3/(2c^3)]... (this is equation 125)
Using the frequency is a tricky thing here, because it involves both the length of the waves and the speed of the waves. This allows a certain confusion to come in to play, which allows Setterfield to perform his verbal gymnastics.
Now equations (8), (9), and (11) show that, with an increasing ZPE and declining c, atomic and emitted frequencies, f, will decline in proportion to the speed of light.
Setterfield theory requires that regardless of the speed of light, the wavelengths of the emitted light do not change, only the speed of the wave as it moves through space. This affects the frequency of the wave, of course. It is a necessary thing for the wave lengths to not change, or else ADAM would have been blinded, trying to see things by light of such long wave length they could not be focused by his normal sized eyes.
Therefore, since f and c move synchronously when in transit, the ratio (f/c) in (125) will be unchanged as the strength of the ZPE varies.
This is an important part of Setterfield physics, folks, as the speed of light slows, the wavelengths never change, only the frequencies change, and they change in direct relationship with the speed of light change. Keep that in mind.
alternatively, since c=fL ( where L is wavelength, and, as per earlier in the article, L is constant as c varies), this ratio may be written as (1/L), where L is the emitted wavelength. Equation (125) then becomes
f* = f + [v/L] + [v^2/(2Lc)] + [v^3/(2Lc^2)] ... (this is equation 126)
The mathematically challenged readers will be unable to follow this but here goes anyway. Setterfield has conveniently neglected to mention the all important initial ratio derived by these formulas.
If a given v in equation 125 remains the same but the c is pumped up by a factor of a million, what happens to f*?
All the expressions following f have an enormously bigger C in the bottom of their fractions. You all know that 1/1 is much bigger than 1/1,000,000. Given the the v of equation 125 is, for galaxy rotation amounts, typically less than a thousandth of the speed of light in our modern era, what happens to f* in such cases?
I leave it to your imagination just how little f* will diverge from f if c is pumped up like that. (Hint: about a million times less than it would today). Just scan the equation, folks, see for yourselves! So the RATIO f* to F would be very very close to one, they would be practically equal, for commonly observed rotation rates in the galaxies.
Since frequencies drop in transit proportional to c, then frequency, f, on the right hand side of (126) will be the frequency at reception of the photon whose wavelength is L. Note that L may be intrinsically redshifted when compared with laboratory standards, and f at reception will reflect that.
Right there, folks, in this very phrase above, Setterfield mentions again how the frequencies are going to drop in proportion. This means, friends, according to the elementary principles of mathematics, that f*/f will STILL BE THE SAME in the new, slower light environment, that is ALMOST IDENTICAL T

NE, which is what Ute and I have been all along saying, his theory predicts the rotation of galaxies should be practically immeasurable. Nevertheless, Setterfield blythly continues on:
Now the classical Doppler formula only has the first two terms in equations (125) and (126). In addition, it can be seen that the second term in (126) is independent of c. In other words, the classical Doppler velocity that will be measured when c varies is the same as the actual velocity of approach of the galaxy limb to a first approximation.
One senses somehow that this last phrase is intended to cinch the matter, but note the sneaky way he refers to the classical doppler formula. The first term v/l can be allowed to stand alone without mentioning c in the classic equation, all right, but that is because the classic equation assumes that light has a constant velocity all along the route. The classic equation could not take that form if light speed variation were contemplated at all, and we all know that the scientists who developed those equations did so without regard to any thought of light speed changing.
The wording is somehow suggestive, on the surface, of saying Setterfield physics should result in no observational differences at all in the appearance of galaxy rotations across the universe. But when analyzed for content, it all falls apart.