If not Doppler, what type of transformation does Hubble's law utilize?
I'm not sure I understand what you mean by transformation. You may be asking how the pattern of increasing distance that the Law describes produces redshift.
Hubble Law does not talk about redshift. Redshift does not enter into the equation. The equation simply gives rate of increase of distances
So I am guessing you are wondering how does the increase of distance physically produce the redshift. (because otherwise I can't make sense of your question)
One way to think about it is via Maxwell's Equations. They are geometrical and govern wave propagation. In an environment where distances are not increasing they guarantee that the most recent undulation (at the advancing wavefront) will have the same wavelength as the one preceding it. There is a geometry of how the E and B fields, and their partial derivatives, interact. In fact the wavelength of the preceding undulations will be duplicated.
But what if, in the meanwhile, the distances between the prior wave phases has increased?
Say the wavelength is one lightyear (a long wavelength for sure!) and in the course of one oscillation, which takes a year, distances have increased by a slight percentage. Then by the geometry of wave propagation, the new wavelength must imitate the slightly increased previous one.
And in fact this is what astronomers have measured, using their best model. The redshift factor of light from a distant object is equal to the factor by which distances have expanded during the time the light has been traveling. This is not a Doppler shift rule.
The redshift has its own rule
a(now)/a(then) = z + 1
the ratio of scalefactors is the increase in distance during the light's travel time, and z+1 is the ratio by which wavelengths are extended. wavelengths expand right along in parallel with space if you want to put it in those terms. (which is all right as long as you think of space as just a bunch of distances, and don't objectify it.)
I hope I interpreted your question right! To summarize, the question is how does the Hubble Law increase in distance result in redshift?
I answered by recalling how waves propagate, the geometry of Maxwell equations in the context of increasing distances. Other people may have other explanations they prefer.
And does Hubble Law have anything to do with Doppler? No the equation does not involve Doppler. and the redshift equation about the scalefactor ratio a(now)/a(then) does not involve Doppler. So introducing Doppler into the story would be unnecessary complication and could easily confuse people. Mathematically ugly IMHO. That's how i see it.
Thanks, Marcus. Your perspective deserves study. Please see http://en.wikipedia.org/wiki/Hubble's_law - "Hubble's law is the statement in physical cosmology that the redshift in light coming from distant galaxies is proportional to their distance." I think there is great disagreement as to what the variable dependent to distance is in the Hubble law.
Also, I have read in many books (like my most recent read - Zero: The Biography of a Dangerous Idea) that the Doppler shift is directly involved with linear universal expansion. That I do not believe.
Hi marcus, the funny thing is that Maxwell's Equations is only math and not physics. Similarly as Newton's Equations in gravitation. As the "attractive forces" are only mathematical models of the "real stuff" (the curvature of spacetime) in physics of gravitation, the "waves" are only mathematical models in EM, and not very reliable neither. That's we we rely rather on "photons" and their redshift telling us something about sapace and time. E.g. why would we assume that space expands rather that it is not time running slower in deep space due to the amount of matter between us and those galaxies (as was once Einstein's idea)?
A quote from Cosmology by Michael Rowan-Robinson, 3rd edition, page 65:
"...we have a natural explanation of the Hubble law, with the cosmological redshift being interpreted as a Doppler shift."
Out of context, I'd have to disagree, Loren.
For small redshift, like << 1 then cz is approx the recession speed.
So as long as he qualifies what he says and makes it clear that he is just talking about approximate interpretation over a small range of z, then it would be OK. I'd have to see adequate context to know what he is actually saying.
But I doubt it is worth discussion. The law is always stated
v = H0 D
where H0 is the present value of the parameter, D is the present distance as it would be measured by stationary observers at this moment, and v is the current rate that D is increasing.
It does not say anything about redshift and in fact it would be false for most choices of D if you interpreted v naively as redshift as in the rough approximation of v by cz.
BTW Loren, thanks for calling my attention to the Wikipedia article. I've noticed Wikipedia is not entirely reliable, and it is good to be warned where one of their articles is misleading.
there is no natural way to interpret recession speed as redshift that consistently makes sense because the relationship is model-dependent. How redshift and recession speed actually connect depends on what parameters you choose for Lambda and Omega_matter, to mention just two.
Separate names with a comma.