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==Wolf Effect==
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Come on guys, I've re-instated the Wolf Effect. The article is about ''causes'' of redshift. The Wolf Effect is real, Wolf's paper has been peer reviewed, and the mechanism confirmed in the laboratory. To remove it based on the person who included it, or to suggest that a fact based on a reference to a valid peer reviewed article is "nonscientific meanderings", does surprise me. Surely standard cosmology is not ''that'' insecure? --] 00:03, 7 September 2005 (UTC)
I've re-instated the Wolf Effect again. Joshuaschroeder mentions that he "removed effect that is not like other redshifts". But the page is about DIFFERENT mechanisms for producing redshift, so yes, it is different. You could have removed the item "3. Gravitational effects" for exactly the same reason. --] 14:38, 7 September 2005 (UTC)
:Sorry, Ian, but you've missed the point on this one. A redshift is defined at the top of the page. This effect does not result in the same shift of spectrum but also results in distortion. One could also include ] as a way to change light's frequency, but that's not a redshift. Likewise this effect whether it is true or not does not admit redshifts as defined in the article. ] 19:09, 7 September 2005 (UTC)
::I've double double checked this, you are correct that the Wolf Effect ''may'' result in distortion. But if you check the paper by Emil Wolf and Daniel F V James, they mention that "under certain circumstances the changes in the spectrum of light scattered on random media may imitate the Doppler effect", that is without distortion.
:::That's also beside the point. In "certain" circumstances (read "special" there or "contrived") you can get Compton Scattering to mimic the Doppler Effect. And if you allined all your scatterings in the same way you could do it without distortion too. That's not a reason for including the Compton Effect as a cause of redshift. It isn't. A cause of redshift has to be free of these extra conditions. We aren't in the business here of explaining all the ways one can distort light's frequency. A redshift is very strictly defined. ] 20:30, 7 September 2005 (UTC)
::I also contact Emil Wolf himself, and he email back to say that "it is virtually impossible to distinguish between the cosmological redshift and a noncosmological one because shifts in the spectral lines can be the same in both cases. However, there are quite a few laboratory experiments which show the correctness of my prediction".
:::Fine. He predicts that you can under "certain" circumstances imitate a Doppler Effect. That's not a redshift: that's an imitation of a redshift. I might be able to build a machine that could mimic the Doppler Effect, but that would not be a redshift, it would be an imitation of a redshift. ] 20:30, 7 September 2005 (UTC)
::In other words, ''any'' Doppler redshift may contain an intrinsic Wolf Effect redshift, and there is currently no way to dinstinguish between the two. More information on request via email --] 20:16, 7 September 2005 (UTC)
:::"Any" Doppler redshift may contain some manufactured photons that were created by a God who stole energy from them en-route too. That's beyond the scope of this article. The effect is correctly removed. ] 20:30, 7 September 2005 (UTC)
I've re-instated the Wolf Effect again. It is a valid mechanism for generating redshift. Period. That you have decided that this is a page on a "certain version of redshift" is not implicit in the generic title "redshift". If you feel that the text requires further qualification, then feel free to explain that further on on the article.
If the Compton Effect can also generate a redshift then I shall do some more research, and include it too. This is an inclusive page, not an exclusive one.
For the benefit of others who may not see the text that you consider contentious, I have included it below:
<table border=1 cellspacing=0><tr><td>'''Contentious text (inserted after cause #3. Gravitational effects.):'''
:There are also other possible causes, less commonly cited but still relevant to some physical situations, such as:
::4. '''The Wolf Effect.''' Physicist ] has found that two non-] sources that emit beamed energy, can interact in a way that causes a shift in the spectral lines. It is analogous to a pair of tuning forks with similar frequencies (pitches), connected together mechanically with a sounding board; there is a strong coupling that results in the resonant frequencies getting "dragged down" in pitch. The Wolf Effect can produce either redshifts or blueshifts, depending on the observer's point of view, but is redshifted when the observer is head-on. ]. Later research has revealed that "under certain circumstances the changes in the spectrum of light scattered on random media may imitate the Doppler effect" ]. A subsequent 1999 article by Sisir Roy ''et al'' have suggested that the Wolf Effect may explain discordant redshift in certain quasars ].</table>
--] 21:31, 7 September 2005 (UTC)
I tried to compromise by creating a page for the Wolf Effect. I have to say that I basically agree &ndash; probably to no-one's suprise &ndash; with ] here. To be a genuine redshift, the frequency must be multiplied by ''z''+1 for ''all'' wavelengths. In the case of the Wolf effect, that is certainly not true for arbitrarily short (hard) wavelengths or arbitrarily long ones: it could only hold for a band. That being said, of course it is ''a priori'' possible that the Wolf effect could be confused for a Doppler shift in quasars. &ndash;] 02:00, 8 September 2005 (UTC)
===Neutral point of view Criticism===
: (Nit: I think you meant ]) ] 05:34, 14 September 2005 (UTC). Thanks, corrected. --] 09:10, 14 September 2005 (UTC)
1. Redshift that shifts all frequencies is a special kind of redshift, so this page appears to EXCLUDE other kinds of redshift.
::This is a matter of definition. I disagree. &ndash;] 03:38, 14 September 2005 (UTC)
:::Exactly, ''Redshift'' is the generic term and consequently has an ambiguous defiinition depending on who is using the term. Specific types of redshift are qualified as ''Doppler'' redshift, as ''graviational'' redshift, and as ''cosmological'' redshift, etc. It does surprise me that some of these terms were removed from the article, making it even more confusing for someone trying to find out what these types of redshift mean. --] 09:10, 14 September 2005 (UTC)
2. If the Wolf Effect is a special kinds of redshift that deserves its own page, then so does Doppler redshift, Cosmological redshift, and Gravitational redshift.
::I would agree with that, except that these three phenomena are all connected by the principle of relativity: they are all the same effect in general relativity, or at least related closely enough that it is impossible to practically distinguish between them. &ndash;] 03:38, 14 September 2005 (UTC)
::: They certainly deserve their own pages. Sorry to be picky, but the astronomical context sometimes gives some clues on how to distinguish them; this however is not meant to imply support for including the Wolf Effect. ] 14:35, 8 November 2005 (UTC)
3. The Wolf Effect will also produce a full-spectrum redshift, with no characteristic signature, that is IDENTICAL to a Doppler redshift.
::No, it can't. See my comments above. &ndash;] 03:38, 14 September 2005 (UTC)
:::See the paper "" by Emil Wolf and Daniel F V James, in ''Rep. Prog. Phys.'' 59 (1996) 771–818, where they write: "Suppose now that the anisotropy in the correlation function g(R; T) is strong in one particular direction This expression shows that the relative frequency shift is independent of the central frequency _0 of the incident light and thus imitates the Doppler effect.". In other words the Wolf Effect may produce a redshift that is IDENTICAL to the Doppler redshift.
4. As it stands, this page is biased against any redshift mechanism that does not support Big Bang cosmology. Some of this information appears to have been censored:
<table border=1 cellspacing=0><tr><td>
Other causes of redshift have been proposed, and are sometimes known as ''non-cosmological redshifts'' or ''intrinsic redshifts''. Examples include ], ] ] (Coherent Raman Effects on Incoherant Light), ], ] and the ]. Some of these redshift mechanisms have a characteristic spectrum, but some (such as the Wolf Effect) may, under certain circumstances, produce a redshift that is identical to a Doppler redshift.</table>
--] 13:45, 12 September 2005 (UTC)
:It's best not to cry conspiracy. The reason that you want to include alternative explanations for redshifting is because you, Ian, want to see one be correct. It's an agenda called POV-pushing here at Misplaced Pages and it is not allowed. To be honest about redshifts we need to include honest reporting. There are no ways to use the alternative mechanisms as diagnostics in astronomy or physics. When and if such a thing were to occur, we would certainly include it in the article. ] 13:43, 14 September 2005 (UTC)
::1. This is not a page about certain redshift mechanisms that can be used as diagnostics in astronomy or physics. This is a page about redshift. That's what the titles says. Some redshift mechanisms can be used for one purpose, others for another. It is important to mention this. To exclude some redshift mechanism because they do not fit ''your'' idea of usefulness is also POV-ing.
::2. I found "compton scattering" mention in over 1600 articles in the Astrophysics Data System (ADS), over 4000 articles if you include Physics and arXiv e-prints.
::3. Your removal of the terms "Doppler Redshift", "Gravitational redshift", "Intrinsic redshift" and "Cosmological redshift" means that people searching for these terms will no longer find this page.
::4. The Wolf Effect WILL produce a redshift that is IDENTICAL to a Doppler redshift. See my reference above.
::5. The CREIL effect WILL also produce a redshift, though it has a characteristic spectrum, characteristic of a Quasar.
::6. The article should be INCLUSIVE with qualifications if necessary, rather than EXCLUSIVE and censoring.
--] 16:11, 14 September 2005 (UTC)
I've returned to this article after an absence of a few months
and re-read it. My goodness, you folks have been busy! Perhaps
unsurprisingly, I would side with ]
and ] that the ] should
not be mentioned as a primary cause of redshift, given that we're
also considering excluding e.g. ]
and other wavelength-dependent effects (that is, wavelength-dependent except
in some very limited and specific physical situations). This isn't to say
that there shouldn't be links to these effects from this article, but rather
they shouldn't be listed as primary causes alongside gravitational redshift
et cetera.
The comparison with
the featured Italian article is interesting; it is similar to ours, but no
mention is made of interpretations outside the scientific consensus.
Can anyone comment on the effect that moving such material to other
pages has had on other articles? Indicentally, you can get a
hilariously clunky automatic translation of the Italian article from Google.
] 14:28, 8 November 2005 (UTC)


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==Expansion Today==
|action2link=Misplaced Pages:Featured article candidates/Redshift/archive1
Can anyone explain why, while the image is thousands of years old, the red shift today isn't due to expansion today? I am looking at this knowing about the tests where the wavefront arrived faster than the speed of light, but information arrives at exactly the speed of light. ] 17:03, 30 October 2005 (UTC)
|action2date=22:45, 23 December 2005
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:Are you asking about how to apply ]? Or are you trying to reconcile ] vs. ]? Either way, the consistency of the interpretation comes from the formulation of ] in the ]. Let me know if that helps. ] 07:56, 31 October 2005 (UTC)
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I am trying to resolve whether the light expands the space or the space stretches the light (current article statement). It is similar to the question of whether mass curves space or curved space creates mass. If light expands space then the amount of redshift can correspond to the amount of light travelling between two objects, as opposed to how long the light has been traveling. The current article expresses degree of redshift as a function of successive stretching of light.
The ] article talks of electomagnetic repulsion. It seems to me that redshift might be a result of that repulsion. ] 17:05, 31 October 2005 (UTC)
:Light does not "expand" space as space expands due to the details of the ] -- light is not required for them to work. ] 18:49, 31 October 2005 (UTC)
::From what I can tell from the ] article, it doesn't give any reason for the expansion, it simply models it. In fact, it is simply the core model upon which extensions have to be bolted on for it to even begin to descrbe the universe. So it, in itself would not discount the possibility of light being the cause for the expansion. ] 03:29, 1 November 2005 (UTC)
:::The derivation of Friedmann cosmology comes from the ], the ], and the ] coupled with ]. To derive the cause of the expansion one need only invoke these three ideas and the ] is automatically derived. Expansion is the most general form a universe described with those assumptions can take. However, ss to what "causes" the expansion, there are nominal explanations provided by ]. ] 10:25, 1 November 2005 (UTC)
::::But none of those seem to rule out light as the reason for expansion either. ] 03:20, 2 November 2005 (UTC)
:::::I don't understand what "rule out light as the reason" is supposed to mean. An empty universe expands the same way a universe with light expands according to the theoretical models. ] 12:59, 2 November 2005 (UTC)
My understanding of the models is that they describe the expansion but aren't complex enough to encompass the concepts of "a universe with or without light"
:Indeed they are. An empty universe (without radiation or matter) is called ].
I hadn't looked at the Misplaced Pages article ] when I made my last post, and I am uncertain what you mean by your use of the word nominal. The article hints at potential expansion causes but doesn't go into any depth. ] 17:43, 2 November 2005 (UTC)
:No, the details of how the expansion comes from inflation are rather thorny, but it is there. The idea is simply that the inflaton field causes inflation and establishes the scale factor and we are expanding based on Newton's First Law of dynamics. ] 18:32, 2 November 2005 (UTC)
:: currently turns up only one hit, an outdated version of ]
:::Try what I actually wrote ] 01:58, 3 November 2005 (UTC)
::::When light expands energy is transferred. If that energy isn't transferred to the expansion of space, where does that energy go? ] 18:29, 5 November 2005 (UTC)
:::::Energy is not conserved in GR, only energy density in a coordinate sense. Therefore even though an individual light wave has lost energy in its travels, it has the same energy density in ]. It is comoving coordinates that matter in cosmology. Physical coordinates are only applicable to local phenomena. ] 20:21, 5 November 2005 (UTC)
==Statistical Decay==
I devised an equation which is now posted on my website, because since 1958 I have not believed the Expanding Universe or Big Bang theories. It is an ordinary statistical decay equation of the kind used to describe radioisotope decay.
It took until 1982 to develop it, through considerable experience and education, so it was not developed lightly. It is on the first page at http://www.eskimo.com/~mikel137/index.htm#home , toward the bottom. It is the ordinary partial differential wave equation with the insertion of a diffusion term which uses the Planck action quantum as the diffusion constant.
The resulting lifetime seems to agree with the observed red shift, and is in addition, within the range of half-life decay times measured for several radioisotopes, as well as being described with an essentially identical decay process.
The equation seems good enough to present it as a candidate for an intrinsic photon decay process in the Misplaced Pages entry on Red Shift. But a Misplaced Pages article must meet standards of brevity and clarity with which I am not familiar, and my writing is, uh, difficult. - Michael Lewis
:Difficult writing can be improved by other Wikipedians. But the main Misplaced Pages standard you seem unaware of is described at this link: ]. I'm also skeptical at times of mainstream tax-supported science - in particular, the "social sciences" might better be described as a political correctness cult. But Misplaced Pages is intended to reflect prevailing opinions, not to change them. Has your theory been published anywhere other than your own website, or is it you against the world? Sometimes one guy is right and the world is wrong, but there are other places to promote such things. ] 15:57, 25 September 2005 (UTC)
(Reply to Art LaPella) Thank you for the reference to the "No original research" standard. I did not know of that. Since it is my own work, it's not appropriate to Misplaced Pages, which is reasonable. Perhaps someone else will refer to it someday but it's not empirical yet. The equation or one like it would have been written during the twenties or thirties or soon after the war if things had been different. The document, which includes the equation I wrote, has a Library of Congress Copyright Number (it is a CD file document) and is hosted also at
http://members.chello.nl/~n.benschop/indx-red.htm ...
http://groups.msn.com/HubbleRedShiftbyPhotonDecay ...
and the local site referred to above
http://www.eskimo.com/~mikel137/index.htm#home .
Whether the equation this author proposed is correct and in the best possible form or not, a photon decay equation which describes the red shift is certainly possible. Thus, it should be written well by competent mathematicians, put into the public domain, and comparison made over time with the dominant Doppler velocity shift.
- Michael Lewis
There is an exception of sorts:
It does not refer to original research that is published or available elsewhere (although such research may be excluded if editors consider the source to be disreputable or inappropriate).
] 17:03, 30 October 2005 (UTC)
== Values of Z ==
What are the values of z over the distance of the universe? After the first section z is never mentioned again.
:z=0 is today. z=infinity is the fiducial singularity of the Big Bang. The farthest z that can be seen is the z=1100 CMB. ] 20:20, 5 November 2005 (UTC)
==Definition of terms==
Since they are in use, why don't we mention and qualify the terms:
*'''Doppler redshift'''
*'''Cosmological redshift'''
*'''Gravitational redshift'''
--] 15:02, 6 November 2005 (UTC)
:We can mention them. We already define them in the article. ] 16:32, 6 November 2005 (UTC)


|action3=GAN
==Variable particle mass theory==
|action3date=18:43, 17 January 2006
*], The title of the article says "Redshift", not "''Actually observed'' Redshift". The statement noted that it was theoretical, and I see no reason not to keep it.
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*Presumably we should remove "cosmological redshift", since it has not been demonstrated in the laboratory, and we don't know whether it has been observed either.
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--] 18:21, 8 November 2005 (UTC)


|action4=FAC
:No one said "demonstrated in the laboratory". This article should not be a dumpster for any huckster's fanciful suggestions. ] 20:17, 8 November 2005 (UTC)
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|action5=FAC
==Request for arbitration==
|action5link=Misplaced Pages:Featured article candidates/Redshift
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|action6=WPR
I see that you have marginalised other redshift causes even more, by moving them to the bottom of the article. Consequently I have put in a ]. If it is accepted, there will be an opportunity to say more. --] 23:46, 8 November 2005 (UTC)
|action6date=29 December 2006
: Request for arbitration is quite serious - are you sure there are no other avenues? ] 00:59, 9 November 2005 (UTC)
|action6link=Misplaced Pages:Today's featured article/December 29, 2006
::Yes, I do regret having to go down this path, but feel it is a last resort. As mentioned on the ] page, we have had discussions, and I feel that there are infringements of Misplaced Pages policy that are fairly serious. --] 09:50, 9 November 2005 (UTC)
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|maindate=December 29, 2006
I do not think we should go down this route. The underlying question is, should the
|currentstatus=FA
wikipedia present the view of the overwhelming majority of the scientific community, and
|action7=PR
not give voice to minority opinions that do not follow the accepted
|action7date=20:31:53 18 October 2006 (UTC)
consensus? Or should the wikipedia give equal weight to all options, however their
|action7link=WP:Scientific peer review/Redshift
standing in the community?
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I think the casual, non-expert reader of any encyclopedia would expect nothing less
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== Redshift of gravitational waves ==
I don't know for sure, but I suspect that there are at least three professsional
or professionally-trained astronomers (including me) contributing to this article,
all of whom appear to prefer moving these alternative explanations to the bottom
or even to a page of their own.] 16:27, 9 November 2005 (UTC)


The lead says, "Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena." But then it would be true that gravitational waves are subject to redshifting by gravitational potentials. Is this true? ] (]) 18:07, 28 October 2023 (UTC)
:On the one hand, you are quite correct, and I understand your perspective from an astronomical point of view. On the other, there are professional scientists in physics and optics (I have rerferenced at least three), who would disagree with astronomers marginalising their point of view. I have no problem with Doppler redshift, Cosmological redshift, and gravitational redshift, all having their own pages. But as a launching point for redshift in general, popularity and relevance to astronomy is not as important as explaining redshift as a general phenomenon which applies to more fields than just astronomy. --] 18:03, 9 November 2005 (UTC)


== Charts and age/lookback calculation ==
The fact remains that these effects are the only effects that are frequency independent. Any physicist can tell that the Wolf effect cannot be frequency independent &ndash; how could it affect radio waves and cosmic rays in the same way? &ndash; and thus is not a true redshift. It may be frequency independent in some band, which could cause it to mimic a redshift in certain circumstances. I suspect that if you asked the authors of the paper you cite, they would agree.


Hi {{ping|Parejkoj}} regarding , could you please give me more actionable criticism than "not sure these are a good fit"? I worked hard to make charts the lay readership can actually use when interpreting the groundswell of very early JWST observations filling the news these days. The existing proper distance plot you favor goes to z=10,000 so fully half of it will almost certainly never correspond to any observations, and the log scale axes aren't at all layperson friendly. My charts are designed to do what laypeople readers are most likely going to want to do when they read a z number, and do it clearly and easily. I am most interested in learning how you think they may be improved.
:The Wolf Effect may produce full-spectrum, frequency independent, redshift. I have provided three peer-revieweed papers that back me up. I have emails from at least three authors confirming my understanding. And "may produce" does not mean theoretically contrived either. And since this is a page on Redshift, it should also include frequency dependent redshift. --] 18:50, 9 November 2005 (UTC)


As for the equations, there are already no fewer than '''thirty-six''' display equations in this article, including lengthy integral solution derivations which have nothing practical to do with redshifts. Let me ask you, if someone gives you a redshift value, and asks you to calculate something with it, the age of the universe or lookback time is likely to be pretty high up on the list of possibilities, right? ''None'' of the 36 display equations already in this article allow you to calculate those; mine do.
::Nowhere in the papers you showed us did it indicate that the same effect would be seen for gamma rays and radio waves. Emails are irrelevent ]. ] 19:12, 9 November 2005 (UTC)


Can we agree to delete the AP calculus derivations instead of the math which is immediately useful for values of the subject of the article? ] (]) 02:24, 16 November 2023 (UTC)
Speaking of which, a topic which has generated some interest recently as a possibile explanation for the Type Ia supernova data is ]&ndash;] mixing, similar to the ] that has recently been discovered. While I don't think many cosmologists buy it, it ought to be mentioned, perhaps on the ] or ] pages. &ndash;] 18:32, 9 November 2005 (UTC)


:Yes, this definitely should go on the ] page. ] 18:43, 9 November 2005 (UTC) : Seconded. I too would like to understand why this revision makes sense. ] (]) 15:56, 16 November 2023 (UTC)


:I agree that the big derivation is unnecessary, and I have removed it. I'm not sure the resulting text is fully coherent; please help clean it up! In particular, we could use some links to articles that do said derivation; I don't have access to the textbooks linked at the end of the Expansion of Space section. There are probably other equations in this article that should be removed, as the article itself is quite bloated. That said, I'm not sure how those derivations are "AP calculus" while your integral is not.
I hope you don't mind me interjecting some comments on this discussion, since it involves some of my work from a few years ago:
:If someone gives me a redshift value and asks me to calculate something from it, I'm going to use one of the various numerical integration tools provided by e.g. Ned Wright or astropy.cosmology to perform the calculation (unless I'm a student in a class being asked to write my own numerical integrator). All of the things one would want to calculate are derived from the integral for the FLRW scale factor; I'm not finding that integral written out on any of the obvious pages, so that might be a worthy addition, probably to ] or ]). The version you added to ] is specific to the current best LCDM parameters, so is not general enough (and probably should be removed from that page, too).
:I hadn't noticed that the existing proper distance vs. redshift plot went to z=10,000 (I had noticed that it has far too small of fonts). For its purpose--showing the scale of the universe to past the CMB--that's probably fine. I think two plots like that--one to large redshift, the other to z~15, both showing distance on one axis and lookback time on the other--would be useful, shown side by side. I'd remove the callout to a JWST galaxy: that's going to become outdated very quickly. I'd also remove the values written along the curve: they make it cluttered. I'll try to quickly put together something with astropy and matplotlib. - ] (]) 18:56, 16 November 2023 (UTC)
::@] Thanks! There's source code on the chart file description on Commons. I used to set Omega_Lambda from Omega_mass for a flat cosmology. I really like the numbers along the curve for the more bendy graph, but as that is so uncommon these days I suspect there's a better way. I put in the furthest observation for the labeled current year to give laypeople readers an idea of how far we've come along the range JWST was designed for. Anyway, I can't wait to see what you come up with! ] (]) 19:07, 16 November 2023 (UTC)
:::As I said, unless you're in a class, it's almost never worthwhile to code up your own cosmology integrator. Just use astropy.cosmology, which has various cosmologies built-in (or you can set your own parameters directly). - ] (]) 20:04, 16 November 2023 (UTC)
::::Your graph is far better than the old one, but it is in no way near what layperson and pre-tertiary students might be expected to be able to use when interpreting redshift discussions in the news or their schoolwork, respectively. I replaced the old graph with yours, replaced my two graphs, and replaced the equations showing how to calculate age of the universe and lookback time directly as more immediately practical and useful than the vast majority of the remaining display equations. ] (]) 12:29, 20 November 2023 (UTC)
:::::Most readers wouldn't be able to use your equations either: they'll need a computer to evaluate the gamma function, at which point they might as well do it properly with one of the available numeric integrators or, even better, one of the many online tools that do it for you. I've removed your expression from the Age of the Universe page as well. We should do a better job linking to the full expressions on ] and ], but partial solutions to those for a particular choice of parameters don't really belong here.
:::::I'm also skeptical that any lay reader would be able to interpret any of the redshift vs. X graphs we show, and certainly using a graph to get the value of something is not at all a common skill. Graphs are useful for showing the qualitative shape of things, not typically for quantitative analysis (especially when there are equations one can evaluate directly).
:::::With your changes, we now have two graphs of lookback time covering roughly the same redshift range, which seems excessive. Yours I find to be very cluttered, due to all the numbers. Do you really expect readers to read numbers off a wikipedia graph to determine numerical values? Given the section you placed it in, I'd rather remake my plot to go out to at least the CMB (~1000), but then the lookback time isn't very informative (which is why it was a log plot before). I'm also not sure that there's much benefit of having separate lookback time and age plots, and if we do want them, they should probably be just made on the same graph. - ] (]) 00:11, 21 November 2023 (UTC)
::::::{{Re|Parejkoj}} Suppose you read (the hilariously titled for popular treatment) , but not the title of the original paper, and you want to know the z values for the "teenage" (2 to 3 billion years after the big bang) galaxies. Which of the two lookback time graphs can you actually do what with? The reason the numbers look like clutter to you is because as a professional you have both the familiarity with tools and skill such that you don't need to depend on actually usable graphs to get answers to common questions. In any case, I'll try putting python alongside the age formulas and see if you like that. It is ''not'' an "approximate expression," it's the ''exact'' closed form of the integral in parameterized Lambda CDM cosmology, contrary to


To derive the age of the universe from redshift, numeric integration or its closed-form solution involving the special Gaussian ] <sub>2</sub>''F''<sub>1</sub> may be used. For early objects, this relationship is calculated using the ] for mass Ω<sub>m</sub> and ] Ω<sub>Λ</sub>, in addition to redshift and the Hubble parameter H<sub>0</sub>.
1. The term "redshift" is not used just by astronomers. it refers to any process which increases the wavelength of light, or more broadly, any wave. Thus to include only effects which cosmologists think important would leave an article that is incomplete and misleading, to say the least. Further, the Doppler effect and the gravitational field can also produce blueshifts, depending on the relative motion or gravitational potential of the source and observer. Both of these effects also will change the widths of lines (so that the ratio of line width to wavelength is fixed).


:<math>\text{ageAtRedshift}(z) = \int_z^{\infty} \frac{1}{(1 + z') \cdot \sqrt{\Omega_{\Lambda} + \Omega_{m} \cdot (1 + z')^3}} \, dz' \cdot \frac{977.8}{H_0}</math>
2. The "Wolf Effect": Emil Wolf is a very highly respected optical physicist, who in 1986 discovered an interesting optical effect which can cause the shift of spectral lines, due to the correlation properties of a random light source. The effect tends to increase the wavelength rather than to decrease it (i.e. redshifts are more prevalent). Numerous experiments have confirmed the veracity of his predictions. In certain circumstances, specifically the scattering of light from random, highly anisotropic media, the shift in the of the spectrum of the scattered light mimics the Doppler effect in that the wavelength difference divided by the original wavelength is independent of wavelength (i.e. Δλ/λ is constant for different spectral lines.) Like the Doppler effect, it can produce red and blue shifts; in theory, since the spectral shift depends entirely on geometrical factors, it holds for *any* wavelength. A variety of applications of this effect have been studied, including synthetic aperture imaging, cryptography, optical frequency standards and a possible role in interpreting the spectral shifts in cosmology.


::<math>= {}_2F_1\left(\frac{1}{2}, \frac{1}{2}; \frac{3}{2}; -\frac{\Omega_{\Lambda}}{\Omega_{m} \cdot (1 + z)^3}\right) \cdot \frac{2 \cdot 977.8}{3 \cdot \sqrt{\Omega_{m}} \cdot (1 + z)^{3/2} \cdot H_0} \, \text{Gyr}.</math>
3. Although to date there has been no observational evidence to confirm or deny its relevance to astronomy, there are some of predictions which might lend themselves to experimental tests. The authors who investigated this (me included) had in mind the explanation of "anomalous" spectral shift. There is observational evidence (NGC 4319 + Mk 205 for example) to suggest there may be a small population of AGNs where something rather odd is going on: we wanted to find out if the excess redshift of these AGN might be due to some unexpected optical effect, and if we could produce some prediction which might lend itself to observational tests (e.g. relationships between the spectral shift and line asymmetry parameters or the jet columnation angle). I am not aware of anyone having undertaking any observations of this, but I have moved into another area of science and have not been keeping up on the literature.
] 22:41, 9 November 2005 (UTC)dfvjames


Or in Python,
==Neutrino redshift==
I notice that ] has removed my information on "neutrino redshift" without any discussion. As a test suggested by a professional scientist in a peer reviewed article, and of direct relevance to redshift, I don't understand why it was taken out? I had written:
<table border=1 cellpadding=1 cellspacing=0><tr><td>
'''Neutrino redshift: Testing non-cosmological redshifts'''


<syntaxhighlight lang="python">
Doppler redshift (due to movement) and cosmological redshifts (due to space expansion), will affect neutrinos in a similar way to photons. But non-cosmological redshift that may be due to energy-loss mechanisms, will affect neutrinos
from scipy.special import hyp2f1 # hypergeometric function 2F1 is in integral solution


H0 = 69.32 # Hubble parameter, median of disparate approxiamations
Chuck Gallo has suggested comparing the neutrino redshift of an object with its photon redshift. If they are similar, it would suggest the cause is due to Doppler or cosmological redshifts. But if they neutrino redshift is much smaller than the photon redshift, it would suggest that an energy-loss redshift mechanism .</td></tr></table>
Om = 0.317 # Density parameter for matter Omega_mass from arxiv:1406.1718.pdf p. 8
--] 19:07, 9 November 2005 (UTC)
OL = 1.0 - Om - 0.4165/(H0**2) # set parameter for dark energy density Omega_Lambda
# to a flat curvature, from https://www.astro.ucla.edu/~wright/CC.python
# (on https://www.astro.ucla.edu/~wright/CosmoCalc.html which see)


# Age of universe at redshift z as a closed-form solution to its integral definition,
:Actually I told you that you could just put it on the ] page. ] 19:12, 9 November 2005 (UTC)
def age_at_z(z): # ...which is 27 times faster than the original numeric integration
hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
return (2/3) * hypergeom / (Om**0.5 * (z + 1)**1.5) * (977.8 / H0) # 977.8 for Gyr
</syntaxhighlight>


] is the age of the observation subtracted from the present age of the universe:
::In other words, you deleted it without discussion. And then your "told me" (ie. without discussion). I would still like to know why a test between different kinds of redshift does not belong on the redshift page? --] 19:22, 9 November 2005 (UTC)


:<math>\text{lookBackTime}(z) = \text{ageAtRedshift}(0) - \text{ageAtRedshift}(z)</math>
:::It isn't a test for different kinds of redshift: it is a test to see whether the cosmological redshift is indeed behaving the same way for neutrinos as it is for light. The only reason to do this is in context of those who deny the cosmological redshift in the first place which is why it belongs on the ] page. ] 19:27, 9 November 2005 (UTC)


::::Your point of view is noted. --] 20:32, 9 November 2005 (UTC) ::::::Better? ] (]) 18:59, 21 November 2023 (UTC)
:::::::No, there's no point to any of that. As I keep saying, if someone wants to know the age, comoving distance, or lookback time of a given redshift, they'd just use one of the many calculators we link to. Your python above is completely unnecessary, and doesn't allow for changing the cosmological parameters. Why would someone ever use that expression, when they could just call astropy.cosmology for whatever parameters they wanted?
:::::::If I wanted to know the lookback time for a JWST galaxy at a given redshift, I'd go to Ned Wright's calculator and just get the exact answer. A lay reader would be much better served by us providing more obvious links to such calculators, than providing ad hoc expressions that factor out multiple parameters. - ] (]) 04:39, 23 November 2023 (UTC)


== simultaneous ==
Both Joshua Schroeder and Ian Tresman are correct.
As Schroeder contends, comparing photon redshifts vs neutrino redshifts from the same source can test whether the cosmological redshift is indeed behaving the same for neutrinos as it is for light. If the measured photon and neutrino redshifts are comparable, the Big Bang Doppler/Expansion concepts are verified, and the photons and neutrinos are behaving in similar fashion.
However, if the measured neutrino redshifts are substantially smaller than the photon redshifts, there are two possible sources for the discrepancy as follows.
(1) The neutrinos are behaving differently than photons under
Doppler/Expansion conditions, or
(2) The additional photon redshifts arise from an interaction between the photons and intervening matter as Tresman contends.
This photon/neutrino redshift discrepancy would arise since any neutrino-matter interaction cross-sections would be much smaller than photon-matter cross-sections.
Additional experiments/analyses would be required to resolve the situation.


is not the right word for two descriptions of the same thing changing correspondingly. ] (]) 03:06, 12 December 2023 (UTC)
A related concept is the photon redshifting of the initial Big Bang radiation with space expansion in time to form the present Cosmic Microwave Background Radiation (Big Bang Remnant Radiation).
: Agreed. I removed it as unnecessary. ] (]) 04:51, 12 December 2023 (UTC)
Big Bang Cosmologists have also proposed a similar neutrino redshift behavior for the Big Bang Neutrinos to form a low-temperature blackbody background Neutrino radiation.
For example, see the book "The First Three Minutes" by S Weinberg.
Related Neutrino/Photon analogs are described by Walsh and Gallo in
"Thermodynamic Laws of Neutrino and Photon Emission"
Am J Phys, vol 48, #8, pgs 599-603, Aug 1980.
"ElectroWeak" Theory by Glashow, Salam, Weinberg, et al, integrates the
ElectroMagnetic Forces (Photons) and Weak Forces (Neutrinos) together.

Measurements of the neutrino Big Bang remnant radiation are not likely in the forseeable future because these would be very low energy neutrinos below present detection capabilities.
Comparative measurements of Photon and Neutrino redshifts from the same source are also unlikely in the forseeable future because of limitations of present neutrino "telescopes".
However, cosmologically "integrated" Neutrino radiation measurements of All Quasars are presently underway. These neutrino measurements should provide additional information on the origin of the large Quasar photon redshifts, and the astrophysical locations of Quasars.

Philosophically, Neutrino Redshift measurements are important because they yield independent experimental tests of theoretical possibilities. Many different independent experiments yield different physical facts to continually test and re-test various theories. This is fundamental scientific philosophy.
--] 17:29, 16 November 2005 (UTC)
The reference to Neutrino Redshifts follows.
"Redshifts of Comological Neutrinos as Definitive Experimental Test of Doppler versus
Non-Doppler Redshifts" by C. F. Gallo.
IEEE Trans Plasma Science, Vol 31, #6, pgs 1230-1231, Dec 2003.
--] 19:35, 16 November 2005 (UTC)

== Definition of Redshift ==

I think scienceworld might a good reference: . If someone could find a more authoritative source, that would be good too. In regards to the NPOV dispute, it is settled easily. NPOV would only require inclusion of other theories in this article if they actually purport to fit the standard definition of a redshift and it doesn't appear they do by the claims of the people who created the theory. If the definition of a redshift is really contested, then there must be some verifiable sources presented showing that there is some significant qualms in the physics/astronomy community over the definition of redshift, otherwise it would be such a fringe minority view that it shouldn't be included in this article. ] 23:17, 9 November 2005 (UTC)
:People, the redshift is '''an observation''' of an '''optical phenomenon'''. As the definition in the article says, "Redshift describes a change in the wavelength of light, in which the wavelength is longer, or redder, than when it was emitted at the source." There are many '''mechanisms''' that produce redshifts, including CREIL, the Doppler effect, etc. Redshift is not intrinsically tied to cosmology, and the article should reflect this, ie. there should be no cosmological bias. This root article should discuss all mechanisms that produce observable redshifts in light spectra. Discussion of the Doppler effect as it applies to cosmological redshifts and the Big Bang, and "alternate cosmological theories" should be on separate pages. ] 13:45, 11 November 2005 (UTC)

::Redshift is not just optical. It is observed across all frequency bands. The user above seems to have a bias against cosmology. That does not qualify as a justification for editting this page. ] 16:44, 11 November 2005 (UTC)

:::Mentioning all kinds of redshift is inclusive and balanced. Limiting it to just the cosmological usage is biased. The general definition includes the cosmological one, so it can not be biased against it, where as your definition is biased against all others. I would be delighted to include your definition of redshift on a page on redshift. But not exclusively. --] 19:35, 11 November 2005 (UTC)

::::To claim that the current article is "limited" to the "cosmological usage" of redshift is incorrect. Doppler redshifts and gravitational redshifts are not cosmological. The article lists them. ] 18:44, 13 November 2005 (UTC)
:::::This is silly. Name one use of "gravitational redshift" outside of cosmology. Explain why the sections explaining these "redshift mechanisms" all contain heavy cosmological content (as explained below), yet no mention of other redshift mechanisms beyond the "accepted cosmological theories". --] 03:25, 16 November 2005 (UTC)
:::::::] ] 19:48, 16 November 2005 (UTC)

*One of the most important tests of General Relativity was the laboratory measurement of gravitational redshift of gamma rays. All solar system space missions (especially GPS satellites) have to take gravitational redshift into account for data reception and transmission. ] 12:03, 16 November 2005 (UTC)

:::Re: "Redshift is not just optical," Strawman as it does not address my main point that redshift is '''an observation of a phenomenon that is not in any way limited to cosmology'''. Besides, the definition of redshift present in the page we are discussing limits it to optical phenomena, "Redshift describes a change in the wavelength of '''light'''...". Re: "The user above seems to have a bias against cosmology," Redshift is a science, and cosmology is but one branch of scientific investigation. Eliminating discussion of cosmology from the article is in fact reducing the bias, increasing accuracy, and increasing the breadth and usefulness of the information conveyed. These are the '''only''' valid reasons to edit pages. Discussion of "Cosmological Redshift" should be in its own (sub)category; the general "Redshift" phenomenon should in fact discuss '''all''' redshift (ie. all mechanisms of redshift, with possible links to applications of the theory, such as cosmology). This would be a balanced, informative organization. --] 15:45, 13 November 2005 (UTC)

::::Two incorrect statements above.
::::#The strawman argument is claiming the current article is "limited to cosmology". It isn't. Doppler Redshifts are seen in the sun, for example.
::::#"Redshift is a science". -- Definitely incorrect.
::::As the article now stands, we mention all mechanisms and applications of redshift as they are applied in science. ] 18:44, 13 November 2005 (UTC)

:::::Re: "It isn't. Doppler Redshifts are seen in the sun, for example." Mm-hmm, clearly the sun is not a cosmological object. Let's perform a trivial analysis of the article to determine cosmological content. Cosmology is explicitly referred to by name at least 17 times. It is explicitly mentioned at least once in each and every section, and cosmology-related subjects are mentioned and/or detailed in '''every single paragraph of the article''' (relativity, Big Bang, etc.). The '''only''' cited reference in the article is an astronomy text. Clearly this article is biased. Your reluctance to admit it is honestly astonishing.
:::::Re: "As the article now stands, we mention all mechanisms and applications of redshift as they are applied in science." Please, point out a single '''clear''' non-cosmological example mentioned in the article (ie. not embedded in a discussion of cosmology, alternate or mainstream). You can't. But I'll happily a . And this is ignoring the other obvious ones already pointed out in this "talk".
:::::Re: "'Redshift is a science'. -- Definitely incorrect." Don't be so literal. I meant redshift is topic of scientific study. It is.
:::::--] 03:25, 16 November 2005 (UTC)

:::::I notice at the beginning of the section on "Cause" that statement: "The most commonly-cited causes of redshift are:". As an editor you've chosen to leave this statement unchallenged. What do you think are the less commonly-cited causes, and how does this fit in with your statement that "we mention all mechanisms and applications of redshift"? --] 15:24, 14 November 2005 (UTC)
::::::There is an obscure, but fairly well-known in astrophysical science communities, transverse redshift.

==Wolf Effect (again)==

Joshua, in the section "]" above, ] 22:41, 9 November 2005 mentions that "The "Wolf Effect .. can produce red and blue shifts .. holds for *any* wavelength". How do you interpret his statement? --] 00:05, 16 November 2005 (UTC)

:The user apparently doesn't understand that the redshift applies to light other than optical. ] 01:16, 16 November 2005 (UTC)

::So you are biased against purely optical redshifts, is that it? --] 03:25, 16 November 2005 (UTC)

:::There is no such thing as a "purely optical redshift". Redshift is defined as on the page for all frequencies of electromagnetic radiation. ] 06:05, 16 November 2005 (UTC)

::::Nice circular reasoning there. You are using your limited definition of redshift to conclude that only your redshift constitutes a valid definition. "Redshift" is literally a phenomenon where the wavelength of light is increased by some external influence. This encompasses all mechanisms including Wolf effect, Doppler Shift, etc. Even the definition as it appears in the article does not preclude the Wolf effect, "Redshift describes a change in the wavelength of light, in which the wavelength is longer, or redder, than when it was emitted at the source." Your reluctance on this issue is not supported by the evidence. I would also appreciate a response to my cosmological bias analysis above. --] 01:59, 16 November 2005 (UTC)

:::::The definition given on the page is the definition of redshift. It has to apply over all frequencies, not just optical frequencies. Your cosmological bias "analysis" is based on a lot of hot air. ] 19:50, 16 November 2005 (UTC)

:Joshua, so when ] writes "holds for *any* wavelength", and you say "The user apparently doesn't understand that the redshift applies to light other than optical", are you saying that one of you is wrong, or there is another way that I should interpret both statements? --] 09:06, 16 November 2005 (UTC)

::The effect holds for any optical wavelength. It is impossible for it to hold to all wavelegths as delineated above. ] 13:14, 16 November 2005 (UTC)

:::The ] seems to say otherwise. --] 01:59, 16 November 2005 (UTC)

::::We must be reading different articles. ] 14:53, 16 November 2005 (UTC)

:::::Why not try reading the papers. Replies to the issues I raised above is also suggested. --] 16:25, 16 November 2005 (UTC)

::::::Stop being argumentative and think about the fact that redshifts apply to more than just optical wavelengths. ] 19:50, 16 November 2005 (UTC)

My paper with Emil Wolf in Physics Letters A vol.188, pp. 239-244 (23 May 1994) dealt with this issue in detail and at length. I stand by the conclusion stated there: "the frequency shift will be the same for every line present in the spectrum of the incident light". The term "light" should be interpreted in a very broad sense of anything that obeys the E/M wave equation, not just that with wavelengths between 400 and 700 nanometers. The expression for the frequency shift depends solely on geometrical factors which are the same for all wavelengths. The Wolf effect is a universal phenomena for all types of wave: indeed one of the earliest tests was for sound waves at a kHz frequencies.
] 21:45, 16 November 2005 (UTC)dfvjames

:So, for example, in your studies this holds equally true for GeV &gamma;-rays and GHz radio waves? &ndash;] 22:11, 16 November 2005 (UTC)

:The analysis only applies for apparent reasonance spectra. It doesn't apply to individual sources (lasers for example) nor does it apply in the same way for high frequency waves as it does for low frequency waves according to your paper. ] 13:56, 17 November 2005 (UTC)

::'''Ian:''' "The Wolf Effect is another cause of redshift .. that distinguishes itself by its application to reasonance spectra and interaction of pairs of sources. It also applies differently to low and high frequency". (based on Joshua's interpreation).

::'''Other:''' "You'll find no substandard or partial redshifts on my page, only genuiine Doppler, gravitational and cosmological redshifts here. If you thought you could find out about other kinds of redshifts you may have read about, then you're wasting your time, because I won't even tell you what they're about. Best you live in ignorance because us "scientists" know best. Transverse redshift? Yes, I know it's really obscure, but it's one of ours really!
::--] 15:21, 17 November 2005 (UTC)

So, are we ready to add the Wolf Effect to the list of causes? --] 17:36, 20 November 2005 (UTC)

:No, since the Wolf Effect doesn't apply over all frequencies in the same manner. ] 18:56, 20 November 2005 (UTC)

::Joshua, I have three researchers in the field who say otherwise, all of whom have produced peer-reviewed articles, and two of which are professors. Isn't this in accord with the "scientific method"? Surely you can produce a paragraph that fits with the peer-reviewed evidence and satisfies your opinion?
::*Prof. Emil Wolf confirms his peer-reviwed articles and emails me that "it is virtually impossible to distinguish between the cosmological redshift and a noncosmological one because shifts in the spectral lines can be the same in both cases."
::::This is an example of conflation of redshift with the optical phenomenon. Appraently Prof. Wolf is not familiar with the fact that shifts of spectra lines have been witnessed across more than just optical wavelengths. ] 21:31, 20 November 2005 (UTC)
::*Daniel James () confirms his peer-reviewed articles, and writes above, based on his article, that "the frequency shift will be the same for every line present in the spectrum of the incident light".
::::Apparently denying the fact that the effect as they outline it will be different for different frequencies coming from the same source. --] 21:31, 20 November 2005 (UTC)
::*Sisir Roy, Professor, Theoretical Physics () confirms his peer-reviewed articles, and wrote to me that "under appropriate conditions, Wolf effect is frequency independendent and indistinguishable from Doppler effect.
::--] 21:02, 20 November 2005 (UTC)
::::Those conditions being that you don't have a spectrum that starts in the radio and goes to gammawaves, for example.

::::You haven't made the case, and neither has these references. --] 21:31, 20 November 2005 (UTC)

All I've ever had from you Joshua, is your opinions, and your definitions, I have three peer reviewed authors and their papers contradicting you. Give me something more than your interpretation. You've demanding it from me, now me from you. Give me two peer reviewed paper that falsify the Wolf Effect as a redshift. --] 00:29, 21 November 2005 (UTC)

:Ian, you have completely missed the point, and I am not sure how to explain it to you any more clearly than this: a coherent source of light from gamma rays to radiowaves would be redshifted at all frequencies coherently as described in the article. The Wolf Effect as you have cited it does not provide for this. There is no coherent frequency shift that is predicted at all frequencies. To put it another way: there is no mathematical model that predicts the shift as illustrated in the introduction to this article. Therefore the Wolf Effect is rightly excluded. --] 00:39, 21 November 2005 (UTC)


Joshua, at least three peer-reviewed papers, two professors and a researcher, have all written and confirmed that the Wolf Effect produces a redshift. It says so in their papers in black and white; they use the term 'redshift' specifically and deliberately to describe what they mean. But anyone who subsequently comes to Misplaced Pages looking for 'redshift' will discover a very strange ommission, and an inability to described 'redshift' as used in these papers.

::From the paper "Correlation-induced spectral changes" by Emil Wolf and Daniel F V James (1995):
*p.778: Figure 2. '''Redshifts''' and blueshifts of a spectral line as predicted by (3.4),
*p.778: .. when the source correlations give rise to '''redshifted''' field spectrum,
*p.778: It will be shifted towards the lower frequencies ('''redshifted''')..
*p.778: ...which is a '''redshifted''' line,...
*p.779: The line is seen to be '''redshifted''' with respect...
*p.779: In one of the experiments the observed spectrum C was '''redshifted'''...
*p.780: Figure 5. .. '''Redshifted''' spectrum, ..
*p.780: It is seen that with appropriate orientations of the beamsplitter, a '''redshifted''' spectral line (curve (A)) or a blueshifted spectral line (curve (B)) were produced.
*p.789: As is common in astronomy, .. a positive value of z is associated with shifts towards lower frequencies, and one then speaks of a '''redshift'''.
*p.792: Fig.17... The peak spectral intensity measured at the off-axis point exhibits a '''redshift''',
*p.797: Since z > 0, this mechanism produces only '''redshifts''' of spectral lines.
*p.806: This expression shows that the relative frequency shift is '''independent of the central frequency''' of the incident light and thus imitates the Doppler effect. Evidently when &theta; < &theta;0 the spectral line of the scattered light is '''redshifted'''...
*p.807: The possible 'excess' '''redshift''' observed in the spectrum of the quasar in such a galaxy-quasar pair may perhaps be induced by the mechanism that we have just discussed.

::So I ask again, why are you excluding this redshift? --] 09:24, 21 November 2005 (UTC)

Yes, Ian, I read the papers. They use the term all the time, but it doesn't have a model that is translatable to our opening point. Look at all the other examples of redshift, they all have a mathematical form that directly relates the phenomenon to the shift in frequency listed at the top of the page. The Wolf Effect doesn't have such a model that I can see which works independent of frequency. It appears that the effect is medium dependent (reliant on the index of refraction). Since there is absolutely no medium which has a frequency-independent index of refraction, how can you say that this effect is frequency independent? The citations themselves seem to indicate that it is not.

Moreover, the researcher who came by here didn't answer the basic points brought up. Just because we derive an effect from Maxwell's Equations doesn't make the effect frequency indepedent. It just means we can see a similar effect over all frequencies, but not necessarily the same one. Their papers even point to this.

So in short, this doesn't qualify as a redshift.

--] 13:13, 21 November 2005 (UTC)


*"but it doesn't have a model that is translatable to our opening point"

:It is not OUR opening point. It is YOUR opening point. Why are you excluding the Wolf Effect redshift, from YOUR opening point? Why do you exclude other uses of "redshifts" from YOUR definition? --] 16:25, 21 November 2005 (UTC)

*"Moreover, the researcher who came by here didn't answer the basic points brought up"

:Irrespective of whether the researcher answers the questions, the Wolf Effect will redshift spectral lines, as the word is commonly used.

:If a spectral line is redshifted, can you tell whether it is due to Doppler, Cosmological, or Einstein redshifts? Could you tell if it was Wolf Effect redshifted, or Compton-redshifted?
--] 16:25, 21 November 2005 (UTC)


:My apologies to Prof. Daniel F.V. James, who is not just a researcher as I mentioned earlier, but a professor at the University of Toronto.

:So we have three professors saying that the Wolf Effect will redshift, and many peer-reviewed papers supporting them. And Joshua, you're saying that your definition is not compatible with theirs? --] 17:54, 21 November 2005 (UTC)


Ian, the article gives the standard definition of redshift in the opening paragraph. Discordant changes in spectra may be due to things that are not characterizable by a simple formulation illustrated in the opening paragraph, but they do not belong in this article as other sources for redshift since they are not defined in the way the article (rightly) defines it. --] 18:29, 21 November 2005 (UTC)


:So if a paper on the Wolf Effect paper mentions "The 21-cm line at high redshift" it means what? --] 20:48, 21 November 2005 (UTC)

::It means that the 21-cm line in the radio was shifted to higher wavelengths. --] 20:52, 21 November 2005 (UTC)

:::In which case the Wolf Effect could redshift a spectral line? --] 21:16, 21 November 2005 (UTC)

::::The Wolf Effect, according to your cited papers, can shift an emission line to a different wavelength. The shifting of individual lines, however, is not the definition of redshift which applies to the entire spectrum. ] 21:18, 21 November 2005 (UTC)

:::::Since redshift of a spectral line is intimitely related to your defintion of redshift, then it should be included in the article. Isn't the more general use of the word used extensively in astronomy? And if so, why has an astronomer excluded this common use of the word? --] 21:38, 21 November 2005 (UTC)

:::::::We measure spectral lines, but redshift applies across the entire E-M spectrum. As to your other questions, I don't understand them. Which astronomer excluded which "common use" of the word? And what do you assume is the more "general use" of the word? Whenever astronomers talk of redshift, they are talking about what is defined in the opening paragraph of this article. ] 22:29, 21 November 2005 (UTC)

You've mentioned that "The 21-cm line at high redshift", refers to a different use of the word "redshift". ie. it means "an increase in wavelength", and not necessarily "an increase in wavelenth due to Doppler, Cosmological or Graviational redshift". Both uses of the word are used extensively by astronomers? --] 23:35, 21 November 2005 (UTC)

:It means "an increase in wavelength of the type that takes all wavelengths and shifts them by a fractional amount up the spectrum dependent on normalization to an inertial-frame wavelength (as for, example, seen in a controlled laboratory setting)". --] 01:55, 22 November 2005 (UTC)


:*"Redshift" means "an increase in wavelength" over ONE or more frequencies. "The 21-cm line at high redshift", tells you NOTHING of the mechanism causing the redshift, unless it is derived from the context of the article. You can't possibly infer that this is due to a full-spectrum redshift, that is an unstubstantiated assumption.

::No, redshift means what I wrote above. It doesn't mean just an increase in wavelength. It has to be a proportional increase. --] 15:43, 22 November 2005 (UTC)

:*"Doppler redshift" infers an increase in wavelength over all frequencies (as does "Cosmological redshift" and "Gravitational redshift")

::No, Doppler redshift refers to the mechanism. Namely, it refers to a redshift due to a line-of-sight velocity. Cosmological redshift refers to a redshift due to metric expansion and gravitational redshift refers to a redshift due to the curvature of space. --] 15:43, 22 November 2005 (UTC)

:*The term "redshift", depending on the context, may refer to any of these kinds of redshift.
:: --] 08:40, 22 November 2005 (UTC)

The term redshift is defined above. It is not just an increase in wavelength. It must be proportional over the entire spectrum as described in the article. --] 15:43, 22 November 2005 (UTC)

:So you're suggesting that other than in the context of Doppler, Cosmological and graviational redshifts, any use of the term "redshift" to described an increase in wavelength of an emission line is incorrect? --] 16:01, 22 November 2005 (UTC)

::No, I'm suggesting that the increase in wavelength of an emission line needs to be of the form described in the intro of this article in order for it to be correctly described as a "redshift". --] 17:32, 22 November 2005 (UTC)

:::Implying that the use of "redshift" to describe just "an increase in wavelength" is incorrect --] 18:00, 22 November 2005 (UTC)

:::The keyword in the above sentence being "just". --] 18:31, 22 November 2005 (UTC)

::::And all the peer-reviewed papers that use "redshift", other than referreing to Doppler, Cosmological, and gravitational redshifts, are ALL using the word incorrectly? --] 19:23, 22 November 2005 (UTC)

:::::You haven't shown that there are peer-reviewed papers that use the word "redshift" to refer to something different than that which is defined in the introduction of this article. By the way, the introduction of the article is not about mechanisms for redshift but just a description of the phenomenon itself. --] 19:57, 22 November 2005 (UTC)


From this :-
*1932: Jackson, C. V., The wave-lengths of the H and K lines of calcium in the arc in vacuo and their red shifts in the solar spectrum
*1936: Evershed, J., The red shift of the iron lines at the edge of the Sun
*1937: Evershed, J., The problem of the red shift in the solar spectrum
*1938: Evershed, J., The red shift of the D lines of sodium in the Sun
*1938: Sulaiman, S. M., The problem of the red shift in the solar spectrum (with reply by J. Evershed)
*1956: Freundlich, Erwin; Forbes, Eric G., On the red shift of the solar lines
*1960: Higgs, L. A., The Solar Red-Shift
*1962: Brault, James William, The Gravitational Red Shift in the Solar Spectrum.
*1964: Forbes, E. G., On the red shift of the solar lines IV
*1965: Gillieson, A. H., The solar and extragalactic red shifts
*1968: Kierein, J. W.; Sharp, B. M., Compton Effect Interpretation of Solar Red Shift
*1968: Pasachoff, Jay M.; Silk, Joseph I., The Interpretation of the Absorption-Line Red-Shifts in the Solar Spectrum
*1988: Missana, M., Variations of the Generalized Compton Red Shift in the Sun
*1988: Zarro, D. M.; Canfield, R. C., The Dependence of Hα Redshifts on Coronal Heating in Solar Flares
*1989: Zarro, Dominic M.; Canfield, Richard C., H-alpha redshifts as a diagnostic of solar flare heating
*1989: Marmet, Paul, Red shift of spectral lines in the sun's chromosphere
*1991: Samain, D., Is the ultraviolet spectrum of the quiet sun redshifted?
*1991: Samain, D., Photospheric lines redshift from balloon ultraviolet spectra of the quiet Sun
*2005: Gallo, Charles, Our Sun's Center-to-Limb Redshift: A Puzzle

From this :-
*1977: Narlikar, J. V., Non-Cosmological Redshifts
*1977: Burbidge, G., Arguments and evidence concerning non-cosmological redshifts
*1980: Burbidge, G., Evidence for non-cosmological redshifts - QSOs near bright galaxies and other phenomena
*1999: Chu, Y.; Zhu, X., New Evidence for Non-Cosmological Redshift
*2004: López-Corredoira, M.; Gutiérrez, C. M., The field surrounding NGC 7603: Cosmological or non-cosmological redshifts?
*2005: Zackrisson, E., On quasar host galaxies as tests of non-cosmological redshifts

While some of the peer-reviewed solar redshift articles could arguable refer to gravitational redshift, a number do not. And there should be little doubt that the peer-reviewed articles on non-cosmological redshifts do not also refer to Doppler, nor gravitational redshifts.

So it seems that there are peer-reviewed articles that commonly use the term "redshift" in a way that you exclude from your definition.

How long did ? --] 21:15, 22 November 2005 (UTC)

:The articles you quote above do not pretend that the definition in the intro is incorrect. However, claiming that the Wolf Effect as a mechanism is inappropriate for already stated reasons.

:I didn't say how long I have been a professor.

:] 21:22, 22 November 2005 (UTC)


::But (most of?) the articles above all use the term redshift in way that is not defined in your introduction, ie. redshift as applied to a single spectral line, with no assumption of cause. This seems to be a common use of the word, even among the astronomy community. Why do no we not features this common definition in the article?
::So what subject are you a professor of? --] 22:31, 22 November 2005 (UTC)

:::Redshift of a single spectral line applies when the entire spectrum is shifted. When someone measures a "redshift" it means that they are measuring a change in the wavelength and then they ''assume'' that the introduction definition applies. When someone measures a redshift they report it as ''z'' which is defined in the introduction of the article. It's not just a "change" in wavelength. It is a proportional one of a particular variety defined in the introduction. This is ''always'' the case (even in the sources you cite). ] 22:53, 22 November 2005 (UTC)


::::So when Evershed, J. wrote in 1938 "The red shift of the D lines of sodium in the Sun", we assume that his use of the words "red shift" applies to the whole spectrum being shifted, frequency-independent, as defined by your definition? I suggest that Evershed's spectrum showed ONLY a change in the wavelength of the D line, and NOTHING ELSE. It does not and can not imply the change in wavelength of ANY other fequency since it was not measured.

:::::You are incorrect in your suggestion. Accordingly, Evershed was predicting that every line in the sun would be redshifted in the same way the NaD lines were redshifted. ] 00:59, 23 November 2005 (UTC)

::::What subject are ? --] 00:09, 23 November 2005 (UTC)


Higgs, L. A. writes in his paper "The Solar Red-Shift" (1960, p.421) "This shift refered to as the "gravity shift", is however, independent of the point of observation on the Sun. Thus '''other physical processes must be invoked to described the observed variations in the red-shifts''' at the centre of the disk and for the very existence of the limb effect." (my emphasis).

Here Higgs is clearly stating a "red-shift" that involves another physical process other than the gravitational redshift. Since he has no idea what is causing the shift, he can not possible suggest that this redshift is full spectrum. As I have demonstrated and referenced several times now, in this case, 'redshift' means "an increase in wavelength" and NOTHING more. Why do you, and you alone, exclude this common definition from your article introduction?

How long have you been ? --] 09:33, 23 November 2005 (UTC)


You have jumped to conclusions that are not supported by the quote you use. There is no indication he doesn't believe the redshift isn't full spectrum. Variations in the redshift occur from one part of the disk to the other, but for any given parcel, it's the entire spectrum that is shifted. I do understand why other editors have left -- your insistence on your idea is beginning to be very tiresome especially because you can read the introduction of the article to see why you are incorrect. Nevertheless, I'll be responding for as long as it takes to help you understand that redshift is always a reference to a full-spectrum effect when it is used in astronomy. --] 14:24, 23 November 2005 (UTC)


:Any redshift of a spectral line indicates ONLY that that line was shifted. There is NO REASON to assume that any other part of the spectrum was shifted.

:Unless information is presented, nothing is assumed. In the quote above, we do NOT assume and can NOT assume that Higgs meants a full-spectrum redshift. The evidence does not support it. --] 15:04, 23 November 2005 (UTC)

::No, you don't assume that because you don't know what the definition of redshift is, despite it being clear in the introduction of this article. --] 17:24, 23 November 2005 (UTC)

:::Your narrow, exclusive definition of 'redshift' is incomplete. It does not include 'redshift' meaning "an increase in wavelength". I have shown beyond doubt, and with numerous peer-reviewed examples, that this latter meaning of redshift does not automatically assume a full-spectrum, distortion-free, frequency-independent redshift. --] 17:51, 23 November 2005 (UTC)

Ian, you have not shown that the definition of redshift you want is held by anybody. All you have done is blown a lot of hot air.

Let's put it another way. Redshift is a concept found in every introductory astronomy text. If you can find a citation in an introductory astronomy text proving that you are correct in your assertion, provide it here. You can go to whatever level of introductory text you want including those that are for graduate students, for example.

--] 18:04, 23 November 2005 (UTC)


:The following quotes use the term redshift in a way that is clearly not compatible with your narrow, exclusive defintiion. I have not exclusively chosen books from an astronomical point of view, since redshift is used in other disciplines too:
:* (Textbook, p.511) "The relaxation can be observed in the Raman spectra as a redshift of the LO frequency"
:* (Textbook, p.177): "This leads to a redshift of the characteristic Raman peak"
:* (Textbook, p.273): "... and that redshifts arise from a process called the Wolf effect"
:* (Textbook, p.323): "QSO's and non-Doppler related mechanisms (ie the Wolf effect), and proposed experiments related to the observed redshift anomalies are presented."
:* (Textbook, p.194): "Tired light is a common name for certain theoretical phenomena proposed for explaining the redshift"
:--] 18:57, 23 November 2005 (UTC)

Sorry Ian, you did not follow directions. Give me a '''definition''' of redshift which does not correspond with the opening definition in the article. Even Zwicky's tired light corresponds to a shift over the entire spectrum. You have failed in my request. If you don't believe me, maybe you should reinvigorate the RfC. Your inability to understand this most basic point is frustrating because you are basically asking to include a falsehood in the article. --] 19:03, 23 November 2005 (UTC)

:I have given you examples of the term "redshift" whose usage is different to your narrow, exclusive defintion. If the texts on Raman scatting, Tired Light, and the Wolf Effect are indeed using the term as per your definition, then we should add all these causes. If the use of the word "redshift" is different to yours, then we must add this common usage to the word to the article. --] 19:33, 23 November 2005 (UTC)

::You haven't shown that the definition on the page right now is incorrect. --] 19:50, 23 November 2005 (UTC)

:::Do you mean your definition of redshift on the main article page? --] 20:31, 23 November 2005 (UTC)

::::As I am not the only author of this article, that is not "my" definition. Check the edit history. --] 20:38, 23 November 2005 (UTC)

:::::In the sense that you've continually referred to it and indorsed it, it's "yours". However, do you mean the definition of redshift on the main article page? --] 21:08, 23 November 2005 (UTC)

::::::That is what I have been refering to ''all along''. -] 22:34, 23 November 2005 (UTC)


Redshift due to Doppler, Cosmological and Gravitational effects, as described in the Wiki article is fine, and I've never had any problems with it. But this definition provides an exclusive and narrow astronomical point of view, and is incomplete. Where a text writes (and quoted from a textbook above): "Tired light is a common name for certain theoretical phenomena proposed for explaining the redshift", either the use of the term redshift is as defined in the article, in which we add Tired Light as a proposed cause of redshift, or, the term redshift is not defined as in the article, in which case we need to add the definition. In this case, redshift refers to "an increase in wavelength", as in an emission line in a spectrum. --] 23:05, 23 November 2005 (UTC)

Redshift is independent of mechanism. It is defined thusly:

In general, redshift (and ], the observation of shorter wavelength light than emitted) is quantified by
<center><math>z = \frac{f_{\mathrm{emitted}} - f_{\mathrm{observed}}}{f_{\mathrm{observed}}} = \frac{\lambda_{\mathrm{observed}} - \lambda_{\mathrm{emitted}}}{\lambda_{\mathrm{emitted}}}</math></center>
where ''f'' is frequency and &lambda; is wavelength. This quantity is unitless.

Tired light works as a cause for redshift because Zwicky's proposal could have (if there really was such a phenomenon) produced the above relationship. The Wolf effect produces a different ''z'' for different frequency ranges. Therefore it is not a redshift as given by the definition. --] 23:29, 23 November 2005 (UTC)


:Great, I agree. If the Wolf Effect, (or Raman scattering), produces a redshift that is not given by the definition as described above, then we need to add a definition for this use of the term. Namely that it means "an increase in wavelength". This use of the term "redshift" is in use and is found in peer reviewed articles (as I have provided and shown previously). Shall I draft the text, or will you? --] 23:37, 23 November 2005 (UTC)

:I also have that tell me that Brillouin scattering will cause a redshift. They use the term redshift consistently. Are you able to define this use of "redshift" for the article?

:I refered to over a dozen uses of the term "redshift" in Daniel James' article above. Since the article definition does not include this use of the word, shall I draft the text, or will you? --] 00:04, 24 November 2005 (UTC)


'''Joshuaschroeder:''' It appears that Joshua Schroeder was subjected to a 24-hour ban from another admin for his alledged Point of View activities in another article. See ]. Subsquently he appears to have changed his username from Joshuaschroeder to ] in an attempt to dissociate his name from his posts. It was noted by the banning admin that "He appears determined to keep out of Misplaced Pages any information related to POVs which he disagrees with"

Of course I wouldn't be surprised to see some anonymous contributions from him, or under a different Username. His style should not be too difficult to identify. --] 22:21, 25 November 2005 (UTC)

==Introduction dummed down==

I've dummed down the introduction in an attempt to explain redshift to a wider audience. And I've added a pretty picture. --] 22:21, 25 November 2005 (UTC)

== Redshift ==

Could someone who knows what they're talking about ] add some info about how scientists determine f-emitted and λ-emitted? With the example of stars, why do they say a star's light is redshifted rather than saying the star is just redder than other stars naturally? --] 08:00, 28 November 2005 (UTC)

:As far as I can tell, f-emitted is measured in the laboratory. Just point as spectrometer at a glowing tube of hydrogen gas, and you can get a spectrum showing several absorption lines. Then do the same with a distant star, and you'll find f-observerd, and the spectral lines (which are like a fingerprint), have moved. Bingo.

::Why assume that the redness of the f-emitted light in the lab is the same as that of the star to begin with? --] 05:10, 29 November 2005 (UTC)

:::Universiality of physical laws is tested. See ]. --] 17:48, 1 December 2005 (UTC)

==Redshift and the POV of nonscientist layman Iantresman==

As things have settled down a bit, I popped over here to see a terrible change to this article. Ian, claiming that the nonstandard redshift explanations are "non-Doppler" and the others are "Doppler" is not only incorrect, it belies an inordinate ignorance of the physics involved. You need to cut out your POV-pushing. Redshift is well described as the article stands right now. All that really needs to be done is relegate the non-standard explanations to POV-related articles. Redshift is well-established in intro astronomy texts as the four causes listed up front. The remaining ideas are outside of the mainstream and do not belong in the article. --] 17:47, 1 December 2005 (UTC)

Latest revision as of 23:30, 4 January 2024

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Redshift of gravitational waves

The lead says, "Gravitational waves, which also travel at the speed of light, are subject to the same redshift phenomena." But then it would be true that gravitational waves are subject to redshifting by gravitational potentials. Is this true? Praemonitus (talk) 18:07, 28 October 2023 (UTC)

Charts and age/lookback calculation

Hi @Parejkoj: regarding , could you please give me more actionable criticism than "not sure these are a good fit"? I worked hard to make charts the lay readership can actually use when interpreting the groundswell of very early JWST observations filling the news these days. The existing proper distance plot you favor goes to z=10,000 so fully half of it will almost certainly never correspond to any observations, and the log scale axes aren't at all layperson friendly. My charts are designed to do what laypeople readers are most likely going to want to do when they read a z number, and do it clearly and easily. I am most interested in learning how you think they may be improved.

As for the equations, there are already no fewer than thirty-six display equations in this article, including lengthy integral solution derivations which have nothing practical to do with redshifts. Let me ask you, if someone gives you a redshift value, and asks you to calculate something with it, the age of the universe or lookback time is likely to be pretty high up on the list of possibilities, right? None of the 36 display equations already in this article allow you to calculate those; mine do.

Can we agree to delete the AP calculus derivations instead of the math which is immediately useful for values of the subject of the article? Sandizer (talk) 02:24, 16 November 2023 (UTC)

Seconded. I too would like to understand why this revision makes sense. Praemonitus (talk) 15:56, 16 November 2023 (UTC)
I agree that the big derivation is unnecessary, and I have removed it. I'm not sure the resulting text is fully coherent; please help clean it up! In particular, we could use some links to articles that do said derivation; I don't have access to the textbooks linked at the end of the Expansion of Space section. There are probably other equations in this article that should be removed, as the article itself is quite bloated. That said, I'm not sure how those derivations are "AP calculus" while your integral is not.
If someone gives me a redshift value and asks me to calculate something from it, I'm going to use one of the various numerical integration tools provided by e.g. Ned Wright or astropy.cosmology to perform the calculation (unless I'm a student in a class being asked to write my own numerical integrator). All of the things one would want to calculate are derived from the integral for the FLRW scale factor; I'm not finding that integral written out on any of the obvious pages, so that might be a worthy addition, probably to Scale_factor_(cosmology) or Lambda-CDM_model). The version you added to Chronology of the universe is specific to the current best LCDM parameters, so is not general enough (and probably should be removed from that page, too).
I hadn't noticed that the existing proper distance vs. redshift plot went to z=10,000 (I had noticed that it has far too small of fonts). For its purpose--showing the scale of the universe to past the CMB--that's probably fine. I think two plots like that--one to large redshift, the other to z~15, both showing distance on one axis and lookback time on the other--would be useful, shown side by side. I'd remove the callout to a JWST galaxy: that's going to become outdated very quickly. I'd also remove the values written along the curve: they make it cluttered. I'll try to quickly put together something with astropy and matplotlib. - Parejkoj (talk) 18:56, 16 November 2023 (UTC)
@Parejkoj Thanks! There's source code on the chart file description on Commons. I used Wright's python code to set Omega_Lambda from Omega_mass for a flat cosmology. I really like the numbers along the curve for the more bendy graph, but as that is so uncommon these days I suspect there's a better way. I put in the furthest observation for the labeled current year to give laypeople readers an idea of how far we've come along the range JWST was designed for. Anyway, I can't wait to see what you come up with! Sandizer (talk) 19:07, 16 November 2023 (UTC)
As I said, unless you're in a class, it's almost never worthwhile to code up your own cosmology integrator. Just use astropy.cosmology, which has various cosmologies built-in (or you can set your own parameters directly). Here's my version, with both distance and time. - Parejkoj (talk) 20:04, 16 November 2023 (UTC)
Your graph is far better than the old one, but it is in no way near what layperson and pre-tertiary students might be expected to be able to use when interpreting redshift discussions in the news or their schoolwork, respectively. I replaced the old graph with yours, replaced my two graphs, and replaced the equations showing how to calculate age of the universe and lookback time directly as more immediately practical and useful than the vast majority of the remaining display equations. Sandizer (talk) 12:29, 20 November 2023 (UTC)
Most readers wouldn't be able to use your equations either: they'll need a computer to evaluate the gamma function, at which point they might as well do it properly with one of the available numeric integrators or, even better, one of the many online tools that do it for you. I've removed your expression from the Age of the Universe page as well. We should do a better job linking to the full expressions on Distance measure and Friedmann_equations#Detailed_derivation, but partial solutions to those for a particular choice of parameters don't really belong here.
I'm also skeptical that any lay reader would be able to interpret any of the redshift vs. X graphs we show, and certainly using a graph to get the value of something is not at all a common skill. Graphs are useful for showing the qualitative shape of things, not typically for quantitative analysis (especially when there are equations one can evaluate directly).
With your changes, we now have two graphs of lookback time covering roughly the same redshift range, which seems excessive. Yours I find to be very cluttered, due to all the numbers. Do you really expect readers to read numbers off a wikipedia graph to determine numerical values? Given the section you placed it in, I'd rather remake my plot to go out to at least the CMB (~1000), but then the lookback time isn't very informative (which is why it was a log plot before). I'm also not sure that there's much benefit of having separate lookback time and age plots, and if we do want them, they should probably be just made on the same graph. - Parejkoj (talk) 00:11, 21 November 2023 (UTC)
@Parejkoj: Suppose you read (the hilariously titled for popular treatment) , but not the title of the original paper, and you want to know the z values for the "teenage" (2 to 3 billion years after the big bang) galaxies. Which of the two lookback time graphs can you actually do what with? The reason the numbers look like clutter to you is because as a professional you have both the familiarity with tools and skill such that you don't need to depend on actually usable graphs to get answers to common questions. In any case, I'll try putting python alongside the age formulas and see if you like that. It is not an "approximate expression," it's the exact closed form of the integral in parameterized Lambda CDM cosmology, contrary to your edit summary.

To derive the age of the universe from redshift, numeric integration or its closed-form solution involving the special Gaussian hypergeometric function 2F1 may be used. For early objects, this relationship is calculated using the cosmological parameters for mass Ωm and dark energy ΩΛ, in addition to redshift and the Hubble parameter H0.

ageAtRedshift ( z ) = ∫ z ∞ 1 ( 1 + z ′ ) ⋅ Ω Λ + Ω m ⋅ ( 1 + z ′ ) 3 d z ′ ⋅ 977.8 H 0 {\displaystyle {\text{ageAtRedshift}}(z)=\int _{z}^{\infty }{\frac {1}{(1+z')\cdot {\sqrt {\Omega _{\Lambda }+\Omega _{m}\cdot (1+z')^{3}}}}}\,dz'\cdot {\frac {977.8}{H_{0}}}}
= 2 F 1 ( 1 2 , 1 2 ; 3 2 ; − Ω Λ Ω m ⋅ ( 1 + z ) 3 ) ⋅ 2 ⋅ 977.8 3 ⋅ Ω m ⋅ ( 1 + z ) 3 / 2 ⋅ H 0 Gyr . {\displaystyle ={}_{2}F_{1}\left({\frac {1}{2}},{\frac {1}{2}};{\frac {3}{2}};-{\frac {\Omega _{\Lambda }}{\Omega _{m}\cdot (1+z)^{3}}}\right)\cdot {\frac {2\cdot 977.8}{3\cdot {\sqrt {\Omega _{m}}}\cdot (1+z)^{3/2}\cdot H_{0}}}\,{\text{Gyr}}.}

Or in Python, 

from scipy.special import hyp2f1  # hypergeometric function 2F1 is in integral solution
H0 = 69.32  # Hubble parameter, median of disparate approxiamations
Om = 0.317  # Density parameter for matter Omega_mass from arxiv:1406.1718.pdf p. 8
OL = 1.0 - Om - 0.4165/(H0**2)  # set parameter for dark energy density Omega_Lambda
    # to a flat curvature, from https://www.astro.ucla.edu/~wright/CC.python
    # (on https://www.astro.ucla.edu/~wright/CosmoCalc.html which see)
# Age of universe at redshift z as a closed-form solution to its integral definition,
def age_at_z(z):  # ...which is 27 times faster than the original numeric integration
    hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
    return (2/3) * hypergeom / (Om**0.5 * (z + 1)**1.5) * (977.8 / H0)  # 977.8 for Gyr

Lookback time is the age of the observation subtracted from the present age of the universe:

lookBackTime ( z ) = ageAtRedshift ( 0 ) − ageAtRedshift ( z ) {\displaystyle {\text{lookBackTime}}(z)={\text{ageAtRedshift}}(0)-{\text{ageAtRedshift}}(z)}
Better? Sandizer (talk) 18:59, 21 November 2023 (UTC)
No, there's no point to any of that. As I keep saying, if someone wants to know the age, comoving distance, or lookback time of a given redshift, they'd just use one of the many calculators we link to. Your python above is completely unnecessary, and doesn't allow for changing the cosmological parameters. Why would someone ever use that expression, when they could just call astropy.cosmology for whatever parameters they wanted?
If I wanted to know the lookback time for a JWST galaxy at a given redshift, I'd go to Ned Wright's calculator and just get the exact answer. A lay reader would be much better served by us providing more obvious links to such calculators, than providing ad hoc expressions that factor out multiple parameters. - Parejkoj (talk) 04:39, 23 November 2023 (UTC)

simultaneous

is not the right word for two descriptions of the same thing changing correspondingly. 184.97.176.97 (talk) 03:06, 12 December 2023 (UTC)

Agreed. I removed it as unnecessary. Praemonitus (talk) 04:51, 12 December 2023 (UTC)
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