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


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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)
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Science edit now complete. If anybody sees any errors or ambiguities, let me know. --] 18:03, 1 December 2005 (UTC)
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By the way, no scattering processes are included anymore. They are not agreed upon in the scientific community to allow for full-band redshifts and therefore should not be included. --] 18:03, 1 December 2005 (UTC)
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:I've reverted your changes Joshua. I'm sorry you didn't like the changes to the article.
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:*Your description of me as a "nonscientist layman" is childish.
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:*I have not made any "claims" as you put it. Every statement I have included is taken from peer-reviewed articles as required by the scientific process, and as suggested by Misplaced Pages policy. I suggest that you read it more thoroughly.
|action7date=20:31:53 18 October 2006 (UTC)
:*Redshift, as described by this article, is far more inclusive than your narrow viewpoint.
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:*"Redshift is well-established in intro astronomy texts"<br>
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::I suggest that you get you head out of your as-tronomy text book, and read further afield.
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:--] 19:35, 1 December 2005 (UTC)
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== Redshift of gravitational waves ==
:::We need to write this article so that, say, a secondary school student wishing to learn about the subject will be properly informed about the consensus on the subject. As the article stands as you have it, it is full of errors, innuendo that are external to the subject, and general bad science. The article will be reverted.


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)
:::I strongly suggest you read an introductory astronomy text currently in use at the secondary, college, or graduate level and see what it has to say about redshift. That is our bellweather and our standard.


== Charts and age/lookback calculation ==
:::I stand by my assertion that you are a non-scientist layman who is inappropriately editting the article. I do not mind comments or edits by you, but I will continue to make sure no errors or NPOV problems creep into the article.


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.
:::Thanks,
:::--] 22:24, 1 December 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.


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)
*"I strongly suggest you read an introductory astronomy text"<br>
:Your astronomy point of view, Joshua, is indeed ''one'' POV, and as such is not a neutral point of view. I am delighted to include that point of view in the article.


: Seconded. I too would like to understand why this revision makes sense. ] (]) 15:56, 16 November 2023 (UTC)
*"I will continue to make sure no errors..."<br>
:I note that you have not highlighted any errors to date, except to point out that certain redshifts mentioned are not Doppler-like redshifts. I am pleased that we agree, that the non-Doppler redshifts were excluded.


: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 ] 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>.
*As evidence of the use of the term ''redshift'' elsewhere, and in peer-reviewed articles, I submit:
:*Redshift as used in Brillouin scattering
:*Redshift as used in Compton scattering
:*Redshift as used in Raman scattering
:*Redshift as used in Wolf Effect
:*Non-cosmological Redshift
:*Non-Doppler redshift
:*Intrinsic redshift
:*Tired-light redshift


:<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>
*I think you need to provide some peer-reviewed articles to suggest that these 500-odd peer-reviwed articles are using the term ''redshift'' incorrectly in their fields.
--] 23:02, 1 December 2005 (UTC)


::<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>
:::Ian, your POV pushing is out of control. Your refusal to read introductory astronomy texts means that you refuse to address the real concerns about the article representing consensus in the field. I encourage you to read the Italian article for an example of a good redshift article, for example. Your insertion of nonsense does not deserve inclusion in the article. --] 23:06, 1 December 2005 (UTC)


Or in Python,


<syntaxhighlight lang="python">
::::*I have already said that I am quite happy with your ''astronomical'' definition and use of the word 'redshift'. I have read some text books, and I believe that your point of view is quite accurate.
from scipy.special import hyp2f1 # hypergeometric function 2F1 is in integral solution


H0 = 69.32 # Hubble parameter, median of disparate approxiamations
::::*"Your insertion of nonsense..."<br>
Om = 0.317 # Density parameter for matter Omega_mass from arxiv:1406.1718.pdf p. 8
:::::500 peer-reviewed articles are nonsense? Surely I misunderstand you?
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,
::::*Thanks for the message on my ]. You mention that I am "getting all information from very biased sources"<br>
def age_at_z(z): # ...which is 27 times faster than the original numeric integration
:::::My source is the . How is that biased?
hypergeom = hyp2f1(0.5, 0.5, 1.5, -OL / (Om * (z + 1)**3))
:::::--] 23:25, 1 December 2005 (UTC)
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:
::::::When you claim that you are getting your information from adsabs, I know this to be false because there is no way you read all the articles you purported to read. More than that, you have not demonstrated a cursory understanding of the subject and instead are content to naysay and bring in irrelevent material. You haven't made a thorough evaluation of the sources you wish to consider, nor have you taken the advice of myself and others to read the Italian page which is a featured article. Instead you are insisting that there are many points of view about redshifts, a claim that is not backed up even by the papers you cite and do not read. As such, I can only say that your sources are indeed the many "intrinsic redshift" "Arp" and nonstandard cosmology websites which make a big to-do about what is or isn't phenomenologically sound. Please, research standard definitions before you go charging on into redefining a page on a very standard subject. --] 16:45, 2 December 2005 (UTC)


:<math>\text{lookBackTime}(z) = \text{ageAtRedshift}(0) - \text{ageAtRedshift}(z)</math>
:::::::If you click on any of the links to the references I gave above, you will find a list of search results, from the Astrophysics Data System. A very simple check:


::::::Better? ] (]) 18:59, 21 November 2023 (UTC)
:::::::*Redshift as used in Brillouin scattering (Click link)
:::::::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?
:::::::*The very first search result is "Structure-dependent electronic properties of nanocrystalline cerium oxide films" (Click for the Abstract)
:::::::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)
:::::::*An extract reads: We investigate the electronic properties of nanocrystalline cerium oxide The fundamental gap Eg of CeOx is due to the '''Brillouin''' zone explaining the '''redshift''' of Eg in nanostructured CeOx... (my emphasis)


== simultaneous ==
:::::::Unless you are suggesting that cerium oxide films are subject to Doppler, Cosmological or Gravitational redshifts, then I would suggest that the author's use of redshift is not included in your exclusive astronomy-related definition.


is not the right word for two descriptions of the same thing changing correspondingly. ] (]) 03:06, 12 December 2023 (UTC)
:::::::There are lots of other examples from the search results, such as the explicit "The origin of the redshift in Brillouin spectra"
: Agreed. I removed it as unnecessary. ] (]) 04:51, 12 December 2023 (UTC)

:::::::To summarise: I have provided 500 peer-reviewed references that seem to use redshift in a non-astronomy-related manner, and you have rubbished then all. You have balls. I'm still waiting for ONE peer-reviewed reference from yourself.
:::::::"Nonscientist layman" --] 17:46, 2 December 2005 (UTC)

All you need to do to show me your POV deserves inclusion is cite one example where someone applies any of the formulae in this article to a cause not cited in the article. Any of the five formulae will do. Until then, you haven't demonstrated that they are talking about the same thing. -] 21:51, 2 December 2005 (UTC)

==Ian's demonstartion of understanding==

Ian, please before you start inserting your POV into the article answer the following questions:

#If an object has an observed wavelength of 600 nm and an emission wavelength of 400 nm, what is the redshift?
#What recessional velocity does a redshift of z=1 correspond to? (HINT: it is not c).
#A spectroscopic binary shows a recessional velocity of 30 km/sec. What is its redshift?
#What is the Doppler broadening of a line refer to? Can Doppler broadening of a line be said to be due to redshift?

These will give us an indication of how familiar you are with the subject you wish to completely overhaul with your supposed "neutral" POV.

We need to have an article that will help students, for example, answer these questions with as little clutter as possible.

Thanks,

:--] 23:14, 1 December 2005 (UTC)


::I'm not jumping through any hoops for you Joshua. If I have made any errors in my additions, besides your non-acceptance of 500 peer-reviewed, non-Doppler-like redshifts, then I am happy to be corrected. --] 23:25, 1 December 2005 (UTC)

:::::See the article, the corrections have been made. --] 23:28, 1 December 2005 (UTC)

== Can't we just be friends? ==

Sarcastic title aside, sometimes I worry that people on Misplaced Pages like arguing more than improving articles. If we use Google scholar, and search for "redshift" we get 187,000 hits. If we exclude the litany of astrophysical words : "cosmology cosmological star stars stellar galaxy galaxies galactic extragalactic nebula quasar quasars QSO supernova supernovae forest CfA IRAS astrophysics astrophysical GRB" (forest is to exclude the Lyman-&alpha; forest without excluding other mentions of hydrogen) we get a little less than 6,000 hits, and probably about half of them are still astrophysical uses. This clearly indicates that the astrophysical usage predominates. So why not write, "redshift is primarily used by the astrophysical community to indicate a proportional increase in the wavelength of light across the spectrum ... the only known causes are relativistic effects such as the Doppler shift, Hubble redshift and gravitational redshift. Atomic, condensed matter and other physicists occasionaly use redshift to indicate a ''frequency dependent'' effect, in which the wavelength of a given spectral line is reduced. This is usually accompanied by other effects, such as the broadening or splitting of the spectral line, and can be caused by the ], ], the ], etc..." &ndash;] 18:23, 2 December 2005 (UTC)

:Yes, I agree that (a) something like this should be added to the list of causes (b) and also a note that redshift means "shift", as in spectral shift due to any of the numerous possible causes.

:I do not contest that the astronomical use predominates, but that's arguably because there are more researchers. There's also 200 million Americans, but that's no reason to exclude eskimos from an Encyclopedia. --] 18:40, 2 December 2005 (UTC)

::I have been in many discussions with atomic, condensed matter, and other physicists and have never seen them use "redshift" as it is used in this article to describe a frequency dependent shift. None of the resources Ian has pointed to do that either, instead there are some that make vague claims about polluting redshift in astrophysical conditions. Therefore, our disclaimer on the page is sufficient. --] 21:53, 2 December 2005 (UTC)

I don't know, how about or or or . These are all Greek to me, but they certainly don't seem to be talking about the redshifts I know and love. It seems to me that while the astrophysical usage overwhelmingly predominates, it is natural also to use it for a generic behavior in which some effect shifts to longer wavelengths. &ndash;] 22:05, 2 December 2005 (UTC)

Your first citation is to a poorly written (from the English standpoint) paper on the ]. It seems the authors and the reviewers could have done with some vocabulary adjustment, but I understand the idea of the frequency shift due to ] can be locally viewed as analogous to the gravitational redshift for certain lines. Not a good choice of wording, if you ask me, but I cannot find reference to someone else using that wording that wasn't translating into English. Maybe it's an issue of translation? The second paper I cannot make heads-or-tails of. The last two papers appear to be about redshifts that are at least superficially due to the mechanisms we post above. To that end, I'm not sure we've demonstrated that there are people who use redshift to mean something other than the definition we have here. --] 22:17, 2 December 2005 (UTC)

::Well done Joshua, "there are people who use redshift to mean something other than the definition we have here".
::Nonscientist layman --] 22:40, 2 December 2005 (UTC)

:::Yes, Ian, there are people who use "Redshift" to refer to a computer program. That should also not be included on this page. -] 02:23, 3 December 2005 (UTC)

==POV pushing section removed==

<blockquote>''===Frequency-dependent redshifts===
There are also a number of causes of frequency-dependent redshift of spectral lines. This use of the term 'redshift' is in less common usage, and will not be discussed further in this article. They include ] ,
] ,
]
] ,
and other theories such as ] theories
These redshift mechanisms are sometimes called non-Doppler redshifts , non-Cosmological redshifts , or intrinsic redshifts .
''
</blockquote>
This section was removed as the statements made about the citations are not verified. --] 02:30, 3 December 2005 (UTC)


==RfC: Request for Comments==

Myself, ] is having a content dispute with ] (previously User: Joshuaschroeder ) over whether to mention that some scientists use the term 'redshift' in a wider context than is used by that in astronomy to mean just Doppler, Cosmological or Gravitational redshift. I do not contest that the astonomical use of the term dominates. Details of the dispute may be read above, and on previous archive pages.

'''I propose''' that the article includes something to the effect that (a) a 'redshift' means 'a shift in frequency' (ie regardless of the cause, such as in 'the spectral line is redshifted') (b) under the section "Causes of redshift": Some scientists recognsied a number of causes of frequency-dependent redshift of spectral lines. This use of the term 'redshift' is in less common usage, and will not be discussed further in this article. They include ] ,
] ,
]
] ,
Neutrino redshift ,
and other theories such as ] theories
These redshift mechanisms are sometimes called non-Doppler redshifts , non-Cosmological redshifts , or intrinsic redshifts .

'''Evidence in support of the proposal''' (])
#] (see list above) using the term 'redshift' in a non-Doppler-like manner.
#5 votes out of 5 in the Discussion on the Bad Astronomy Universe Today Forum in the thread "", including supporting comments from Jet Propulsion Laboratory physicist Tim Thompson
#Confirmation from three professors of physics that they use the term 'redshift' in a non-Doppler-like manner, including ] , Prof. Emil Wolf , and Prof. Theoretical Physics, Indian Statistical Institute, Sisir Roy
#Contributing editors (a) ] ] regarding the ] "it certainly rates a mention" (b) ] (mentioned above) ] "The term "redshift" is not used just by astronomers. it refers to any process which increases the wavelength of light" (c) ] ] "the general "Redshift" phenomenon should in fact discuss all redshift (ie. all mechanisms of redshift,.." (d) ] ] mentioning non-Doppler-like redshifts.
#The Misplaced Pages page requires articles to be "representing all majority and significant-minority views fairly and without bias."

'''Evidence opposing the proposal''' (])

{to come}


Please '''Support''' or '''Oppose''', together with a comment, and sign and date by either adding "<nowiki>--~~~~</nowiki>" (if you have an account), or your name and date if you don't.

===Nominations===
<!--- Please Add your nomination below this line ---->
'''Support''' As proposed above, --] 12:20, 3 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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