User talk:Awarburt

Talk page, Hello World.

To the anonymous person who disagrees with my correction to the frequency-based redshift formula, as derived from the wavelength-based redshift formula, please don't hesitate to get in touch with me if you would like a more thorough explanation. It is a bit counterintuitive, especially since the incorrect version gives numerical results that are reasonable (but not quite right).

You're right, of course
I tried to make explicit what you correctly promoted in the redshift article:

Talk:Redshift.

Let's hope the others see the light.

69.86.225.27 (talk) 04:27, 27 November 2011 (UTC)


 * Umm, there's something very wrong with that. Based upon the approximation that the emitted frequency is close to the observed frequency, the formula is fine and works well, but it gives inconsistent results at high redshift. I thought I understood what was happening, but I'm not sure anymore. 128.59.171.194 (talk) 00:23, 29 November 2011 (UTC)

Andreas Warburton (talk) 01:42, 29 November 2011 (UTC) Thanks to the person who added the more explicit explanation after my edit. Just to be clear, I am not claiming that the frequency formula (and for that matter, the wavelength formula from which it's derived) that I modified is the definitive and recommended expression to use in all redshift situations and interpretations. Whatever shortcomings the frequency formula possesses, the wavelength formula will possess the same.

Andreas Warburton (talk) 11:11, 2 December 2011 (UTC) Just a follow-up: I think I now see where the confusion lies in the literature. A useful e-mail discussion with Joshua Schroeder helped to elucidate this for me. I'm using Marc L. Kutner's 2nd Edition of "Astronomy: A Physical Perspective" in my Intro Astrophysics course. This is a popular but not too sophisticated text used in many freshman-style astro courses worldwide (incidentally, it's also cited in the Wikipedia article on redshift.) I had noted that Section 5.2.1 of this text appeared to be at odds with what was posted in Wikipedia.

Kutner Section 5.2.1 clearly employs the differential change of variables to arrive at the expression

delta(nu) / nu_0 = - delta(lambda) / lambda_0   [1],

where nu_0 and lambda_0 are the emitted frequency and wavelength, respectively.

While Kutner 5.2.1 makes the non-relativistic assumption that the radial velocity v_r << c when equating Eqn. [1] above with z = v_r / c, it does not explicitly invoke this assumption when spelling out the d(lambda) / d(nu) = - c / nu^2 change-of-variables derivation of the above relationship between delta(lambda) and delta(nu). Kutner's differential approach to relating delta(lambda) to delta(nu) must be implicitly predicated on a non-relativistic v_r << c assumption that results in small frequency and wavelength shifts.

As a sanity check, I also consulted a slightly more advanced text, "An introduction to modern astrophysics", by B.W. Carroll and D.A. Ostlie (2007), which in its Section 4.3 effectively derives a frequency-based redshift expression from a wavelength-based redshift *definition* by simply substituting the lambda = c / nu equation. Unlike the Kutner version, the Carroll & Ostlie frequency expression concurs with what is currently in Wikipedia.

The Kutner approach seemed at first quite reasonable because it was reminiscent of the differential change-of-variables procedure one rightfully does when converting the Planck function between its frequency and wavelength variants. Having now thought about this further, I agree that the differential approach is not generally appropriate to the redshift change-of-variable application. In this vein, I would say that Kutner's text is a bit misleading and should probably be corrected. Its treatment of this topic is slightly surprising for such a popular textbook in its second edition.