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27th June 2023, 02:48 AM  #321 
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In a simply expanding space, comoving distance is:
Proper distance is: And luminosity distance is: The author seems to have that straight, unless I'm missing something. ETA, read it a couple more times. When he says "the proper distance has expanded by a factor of (1+z)", he's referring to the proper distance now, aka comoving distance.
Quote:
This is one of the big muddy spots I've brought up before. In the expanding model, luminosity distance is: In my nonexpanding model it's based on the light travel time distance: What the author's nonexpanding model is, I'm still figuring out. It all depends on the "d" used in the fluxluminositydistance relationship. The question I have for my model is, what effect, if any, does time dilation have on angular size. I'm not sure on that right now. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

27th June 2023, 07:49 AM  #322 
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No, the author doesn't have that straight.
From the last equation you wrote above, the luminosity distance is greater than the proper distance by a factor of (1 + z)^{2}. But the author says: Redshift and time dilation cause a luminosity distance greater than the proper distance by (1 + z).Now that might just be another example of careless/sloppy wording, as in Figure 3 and its caption. But the author goes on to say The expanding metric makes the angular diameter distance smaller than the proper distance by (1 + z).According to Wikipedia, however: d_{A} = d_{M} / (1 + z)where d_{M} is not the proper distance, but is instead the transverse comoving distance, which is equal to the comoving distance d_{C} if space is flat. From your second equation, and assuming flat space, the proper distance is d_{P} = d_{M} / (1 + z)so d_{A} = d_{P}In other words, the angular distance should be the same as the proper distance (for flat space). The author's equation (11) is derived from the author's belief (which I quoted above) that (for an expanding universe) the angular distance is "smaller than the proper distance by (1 + z)." As I have just shown, however, using your equations and those of Wikipedia, the angular distance is actually equal to the proper distance (assuming flat space). If that is the error it appears to be, then the entire paper is worthless. And it does appear to be some kind of error. After writing the above, I consulted Weinberg's Cosmology. Weinberg's equation (1.4.11) says the angular distance is d_{A} = a(t_{1})r_{1}For flat space, the right hand side of that equation is the proper distance (as given by Weinberg's equation (1.1.15)). At the very least, it seems the author of that paper is writing "proper distance" when he should be writing "comoving distance" or "transverse comoving distance". But if he really believes the angular distance differs from the proper distance by a factor of (1 + z), and derives his equation (11) by removing that factor, as appears to be the case, then I think that's a fatal error. If he's referring to the comoving distance, he should say so. By writing "proper distance" when, on your reading, he means the proper distance today, i.e. the comoving distance, he confuses readers such as myself who know just enough to check what he wrote but do not know enough to intuit what he really meant. At the very least, it's a sloppy paper. That much is obvious from Figure 3 and its caption. The author completed his PhD (in astronomy) at Case Western Reserve University in 2020, and his BS (in Engineering) at Huazhong University of Science and Technology in 2012. He is currently a postdoc at Case Western Reserve University. A young researcher who is probably not a native speaker of English can be forgiven some sloppy prose, but there may be a real question here as to whether his sloppiness carried over into his calculations. 
27th June 2023, 07:56 AM  #323 
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ETA: When sketching a proof that metric form 1 describes the same metric as metric form 2, via a simple coordinate transformation, I omitted the highlighted factor I am now adding to this equation: The wrong guesses I snipped are wrong guesses. Yes. 
27th June 2023, 01:54 PM  #324 
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The comoving distance is the proper distance now.
The angular distance is the proper distance then. In my "paper", I say comoving distance, and proper distance when the light was emitted. Adding "when the light was emitted" to every single instance of "proper distance" is kind of annoying, but necessary to avoid the nitpicks. It seems his convention is to use angular distance (proper distance when light was emitted) and proper distance (now, aka, comoving distance). It's a bit more concise. But otherwise yeah, it confused me too for a bit. ETA: he discusses it in a tweet thread: https://twitter.com/PengfeiLi0606/st...23586709274624 I mean, the dashed line shows the turnaround, so that has to be the expanding model. I asked him on twitter. I'll let you know. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

27th June 2023, 03:31 PM  #325 
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That wouldn't be right either, because the angular distance coincides with proper distance only for flat space, and he claims to make no assumptions about the model. ETA: This seems like too obvious a mistake for the author to make, but Mike Helland might not be entirely right about what the author is thinking. 
27th June 2023, 03:39 PM  #326 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

27th June 2023, 04:08 PM  #327 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

27th June 2023, 04:13 PM  #328 
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That seems to be a valid criticism to me (I added the bit in parenthesis).
ETA: FWIW, this means his conclusion applies to all flat models, but not open or closed models. From that image we looked at showing levels of confidence for SNe 1a models for different cosmological parameters, we can see that an open FLRW is a better fit to the data. My own SSE calculations show that the luminosity distance ct(1+z), which is the same is Melia's, is a better fit to that data than all flat models. But I also calculated SSE values for open FLRW models, after seeing that image, and universes with Ω_{Λ} > 1 show an improvement over d_{L}=ct(1+z). So it appears to be model independent in the sense that as long as Ω_{Λ} + Ω_{M}=1, the model is covered. This avoids drawing a conclusion specific to Ω_{Λ}=0.68 or 0.72, for example. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th June 2023, 01:01 PM  #329 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

29th June 2023, 07:38 PM  #330 
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Here's one idea for a geometrical foundation. You have a hyperboloid:
Place stationary clocks around its "neck". The worldlines of the clocks are hyperbolas that go up and down. As time passes, these clocks don't actually move along their worldlines. We usually think of them as moving up. We'll say instead that the events representing clock ticks move down the worldline instead, into the past. It's an equivalence principle for time, of sorts. Who says we're moving forward in time? Maybe we're standing still and time is moving against us? This means the distances between the clocks never changes, but the space and time between their events does as they move to the past. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

30th June 2023, 10:51 AM  #331 
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"As long as it is admitted that the law may be diverted from its true purpose  that it may violate property instead of protecting it  then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and allabsorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious."  Bastiat, The Law 

30th June 2023, 09:32 PM  #332 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

2nd July 2023, 12:49 PM  #333 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

3rd July 2023, 11:03 AM  #334 
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As human right is always something given, it always in reality reduces to the right which men give, "concede," to each other. If the right to existence is conceded to newborn children, then they have the right; if it is not conceded to them, as was the case among the Spartans and ancient Romans, then they do not have it. For only society can give or concede it to them; they themselves cannot take it, or give it to themselves. 

3rd July 2023, 01:52 PM  #335 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

3rd July 2023, 02:03 PM  #336 
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I wish I knew how to quit you 

3rd July 2023, 03:07 PM  #337 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 12:48 AM  #338 
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4th July 2023, 01:42 AM  #339 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 07:31 AM  #340 
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Modern galaxies are really very different to high redshift ones.
Probably the most powerful test is chemical abundances, unlike sizes or masses they don't depend on the assumed cosmology. It has been known for decades that higher redshift galaxies have less heavy elements, and that has been further confirmed to higher redshift by JWST spectroscopy. Most z=610 galaxies studied by JWST are around a tenth solar, but some go much lower. This is not compatible with no evolution. The difference is so marked that some emission lines which can barely be detected in local galaxies are booming in highz ones. https://ui.adsabs.harvard.edu/abs/20.....89R/abstract https://ui.adsabs.harvard.edu/abs/20....425C/abstract https://ui.adsabs.harvard.edu/abs/20...8255M/abstract Under standard cosmology galaxies are also smaller and less massive at fixed galaxy abundance. They show bluer UV spectra which likely indicates less dust. The highest redshift objects appear to have basically zero dust. https://ui.adsabs.harvard.edu/abs/20...3582O/abstract https://ui.adsabs.harvard.edu/abs/20.....18P/abstract https://iopscience.iop.org/article/1...418213/acbfb9 There's also a lot of things which fall in line with predictions, such as the decline in metallicity and more detailed predictions. There some loud nonsense claims at the beginning, but those people did not formalise any analysis and very much cherry pick what results they look at. https://ui.adsabs.harvard.edu/abs/20...3755M/abstract https://ui.adsabs.harvard.edu/abs/20...3755M/abstract Another confirmed prediction is the time dilation thing, which is exactly what is predicted in an expanding universe. (1+z) time dilation. That result and others is incompatible with tired light models. 
4th July 2023, 08:04 AM  #341 
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As human right is always something given, it always in reality reduces to the right which men give, "concede," to each other. If the right to existence is conceded to newborn children, then they have the right; if it is not conceded to them, as was the case among the Spartans and ancient Romans, then they do not have it. For only society can give or concede it to them; they themselves cannot take it, or give it to themselves. 

4th July 2023, 08:31 AM  #342 
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There is no Antimemetics Division. 

4th July 2023, 08:44 AM  #343 
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Caption from and old New Yorker cartoon  Why am I shouting? Because I'm wrong!" 

4th July 2023, 09:07 AM  #344 
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Thanks for that.
Doesn't that follow a pretty obvious general trend though? https://www.nature.com/articles/nature14164
Quote:
Don't we always notice the easiest ones to notice first? Isn't that to be expected? Sure we see some metal poor galaxies out there. But we also see exceptions. Which shouldn't be there is the early universe was actually different. JWST was supposed to show Pop III stars. Maybe it will. Some might even say it has. We'll have to let the dust settle on that. But we notice metal poor stars right here in our own galaxy too: https://en.wikipedia.org/wiki/HD_140283 So it's not like those conditions are unique to the early universe. If visible light is, just say, between 800 nm and 400 nm, then at z=9, those wavelengths would be between 80 nm and 40 nm. Doesn't that make absorption lines harder to see? And, if the theory were right, shouldn't we notice at some distance elements like Oxygen completely disappearing?
Quote:
If phenomena are time dilated because of their speed away from us, and if the expansion of universe also stretches wavelengths while light from those distances as it travels, it seems the oscillations of EM waves should be redshifted by two factors of (1 + z), one for the time dilation at the beginning, one for the stretching during the trip. So if photons are redshifted by (1 + z) shouldn't supernovae be time dilated by (1 + z)^{1/2}? 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 09:46 AM  #345 
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No.
Quote:
Quote:
Quote:
Quote:
Quote:
Quote:

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Gulielmus Princeps Haroldum Principem in catino canino impulit 

4th July 2023, 09:57 AM  #346 
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We theorize what the early universe should look like, and then we go looking for it, and we find it. Later, we find things we didn't initially calibrate our telescopes specifically for. "ALMA reveals a stable rotating gas disk in a paradoxical lowmass, ultradusty galaxy at z = 4.274" https://arxiv.org/abs/2306.10450 Happens every time. ETA: https://arxiv.org/abs/2305.14418 Extremely red galaxies at z=5−9 with MIRI and NIRSpec: dusty galaxies or obscured AGNs? 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 10:32 AM  #347 
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The evolution in the beta slope is done using the same galaxy selection at lower redshift. It is a likeforlike comparison. The galaxy in the paper you cited is a Lyman break galaxy and would meet the criteria used to select these galaxies. Some very dusty objects were missed by HST, but JWST's extends beyond the restframe UV. These objects are rare, they are not normal galaxies.
That is completely backwards. It isn't some galaxies being metal poor, it is the bulk population. All the NIRSpec galaxies at z=610 are metal poor. There is no law in the standard model which forbids some massive galaxies enriching early, that is set by galaxy evolution and not cosmology. What cannot happen is in a tired light or static model, there can be no global evolution. And yet there is. A star which is formed in the early universe, 12 Gyr ago. They're not measuring absorption lines. JWST isn't working in visible light. The models predict much earlier times for the first enrichment. No. Time dilation and redshift are the same thing, one cannot be bigger than the other. Both can be derived from the FLRW metric to show they scale together, and not as you suggest. 
4th July 2023, 10:57 AM  #348 
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Ok. Well, they seem to becoming less rare, but I'm just an outside observer.
Quote:
https://arxiv.org/abs/2305.14418 Is there a handy image for what the global evolution might look like? Say at z=0, we call the dusttogas ratio X. Presumably at z=infinity, it should be zero. I would think there should be curve that shows the evolution of that percentage from X to 0. And I'm curious how that has changed over the last few years. Are we now saying the early universe is z>10? Because it used to be like z>2. Can we just change where the early universe ends everytime we observe a dusty galaxy? Again, outside observer. But that seems to be what's happened since the early 2000's.
Quote:
If the restframe duration of the event were 2 weeks, the light from the end of the event would have 1 lightfortnight farther to travel than light at the beginning of the event. (ETA, assuming z=1 and a simply expanding universe.) So all the time dilation happens because of that. Which means whatever was emitting light back then should be time dilated too. So a photon emitted at that distance should be time dilated (and thus redshifted). But the photon should also be redshifted by the stretching of its wavelength due to the expansion that occurs between emission and detection. Doesn't it seem logical that the photon would be redshifted by the time dilation at the beginning and also by the stretching during its travel? I think that's what this paper is getting at: https://www.frontiersin.org/articles...22.826188/full Although, I've pointed to it here before, and its been dismissed (without direct criticism, fwiw). 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 12:30 PM  #349 
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Wow.
That is not just wrong. It is staggeringly, stupendously, spectacularly, extraordinarily, amazingly, astonishingly, mindbendingly wrong. ETA: Here's a direct criticism of that paper: Its equation (B6) is incorrect. The incorrectness of equation (B6) should be obvious to anyone with minimal understanding of calculus. As written, that equation assumes the integral doesn't change during a translation by t_{0}, as would be the case if a(t) were a constant function. In FLRW models of an expanding universe, however, a(t) is a monotonically increasing function, so translation by t_{0} changes the value of the integral. 
4th July 2023, 01:04 PM  #350 
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Well, say a supernova happens at z=1, and let's just use a simply expanding universe, so the galaxy's recessional velocity is v=c.
The light paths are shown in yellow. The green path is the supernova's motion away from us at v=c. The red line is the duration of the supernova in the rest frame, and the blue line is the time measured by an observer at the origin. The blue line is twice as long as the red line, which is what you'd expect at z=1, since 1+z =2. You obviously can't just use relativistic time dilation, since the speeds are greater than or equal to c. Were we to be talking about the oscillation of an EM wave instead of a supernovae, that wave would be redshifted by z=1 right out of the gate. Since the universe expands between the emission time and the detection time, wouldn't it redshift further? 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 01:18 PM  #351 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 02:27 PM  #352 
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Mike Helland's struggles with calculus have been apparent throughout this thread and its predecessor, but he continues to remind us of his incompetence.
Nonsense. The scale factor doesn't change much during the interval Δt, but t_{0} is completely arbitrary and T is the time between emission and detection, which can be billions of years. Here's a concrete counterexample to both Vavryčuk's equation (B6) and Mike Helland's attempt to justify it. Take the "initial time" t_{0} (i.e. the time at which the first photon is emitted) to be 10 billion years in the past, so (for example) t_{0} = 10 Gy. Take its travel time T to be the 10 billion years from its emission to its detection in the here and now (t = 0). The scale factor a(t) increases over time, so a(t_{0}) might (for example) be 1/3 of a(t_{0}+T), which might (for example) be 1/4 of a(T). (Note that the time t=T is ten billion years from now.) Then ∫_{t0+T}^{t0+T+Δt} (c dt) / a(t) ≈ 4 ∫_{T}^{T+Δt} (c dt) / a(t)In that example, Mike Helland and Vavryčuk's equation (B6) are off by the highlighted factor of 4. Vavryčuk's equation (B6) is just plain wrong. That error invalidates his equation (B7) and the whole point of his Appendix B. His entire paper depends on the false conclusion he draws from Appendix B, so his entire paper is worthless. Worse than worthless, actually, because the existence of that worthless paper does positive harm by misleading the unskeptical and uninformed. 
4th July 2023, 02:52 PM  #353 
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Wouldn't t_{0}+T = 20 billion using your numbers? (ETA, ha, nope. Should equal 0, so t_{0}+T+Δt = Δt. If t_{0}=0 it makes sense.)
His conclusion in that appendix is: "Comparing Eqs B5, B7, we see that the proper distance between two successive photons is constant and independent of the scale factor a(t). Consequently, the wavelength of photons cannot change with the scale factor a(t) in the standard FLRW metric." Which obviously seems wrong. My point about photons redshifting due to the expansion of space while they travel having a "double dipped" redshift compared to the time dilation of supernova from an equal distance just seemed similar to one of his arguments. I'm not endorsing that paper by any means. 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 02:58 PM  #354 
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They do not measure metallicities. One of the objects is in this paper, which is metal poor.
https://arxiv.org/abs/2301.09482 Perhaps someone posted some papers on that already. No, these are the same thing. They are imprecise ways of describing metric expansion. They author doesn't actually demonstrate that there is a contraction in FLRW. The two equations he compares are not describing the same time variable, one is a differential the other is an integral relating different observers. Nor does he prove that there is real mathematical contradiction. The explanation for where he thinks the derivation fails is also absurd, that it is due to the microscopic expansion between wave crests of light. His alternative derivation fudges it so the traveling photons have the same light travel time, this is entirely circular, there is no redshift because that's his definition. The paper skims over the contradiction point. Most bizarrely if you follow the source for the "conformal metric", it is completely different in the citation. The time component is replaced by the "parametric time", which by definition depends on the scale factor. So this paper has rejected the FLRW metric because "time depends on scale factor" and adopted a new one where time depends on the scale factor. But the paper here has just dropped that and replaced it with the normal time coordinate, which is wrong. In a later section the author comes clean that he has redefined everything in a conformal time, which indeed depends on the scale factor. His metric is still wrong though as he does not use this conformal time. In the end his equation for redshift is identical to the standard one and hence changes nothing. I'd say it's pure sophistry, but it's not even clever. It's literally just rearranging the same equations and expecting a different result, if you do it correctly there won't. The bit a the Friedman equations and supernovae is just wrong, he uses the standard Friedmann equation derived with the standard metric. But I see these aren't the only errors. https://arxiv.org/pdf/1103.4743.pdf 
4th July 2023, 03:24 PM  #355 
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Ok. I took it to mean "dusty" means not metal poor.
I suppose it would be useful to define when the "early" universe was and what constitutes "metal poor". A curve from now to the big bang showing what the predicted dusttogas ratio is would be the best way to quantify that. Maybe I can find one.
Quote:
Can we take this to mean that if we describe the metric as time dilating EM waves at their source, that it would be "wrong", in that context, to describe them as being stretched by the expansion of space as they travel?
Quote:

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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

4th July 2023, 04:36 PM  #356 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

5th July 2023, 12:04 AM  #357 
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Steen  Jack of all trades  master of none! 

5th July 2023, 12:08 AM  #358 
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5th July 2023, 05:37 AM  #359 
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Meanwhile, back in the real world;
Spectroscopic verification of very luminous galaxy candidates in the early universe Arrabal Haro, P. et al https://arxiv.org/abs/2303.15431 Basically, as we all expected, they have now done some spectroscopic measurements to confirm, or otherwise, the early claims of very distant galaxies. And, as expected, not all of them were as distant as the first claims. For instance, a galaxy at a claimed z ~ 16 was, in fact, only at z ~ 4.9! To cut a long story short, the most distant spectroscopically confirmed galaxy is now at z ~ 13.2. 
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5th July 2023, 11:15 AM  #360 
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Of course not.
I think it's a curious situation. Take this situation: Now say that at the time where the last photon is emitted (SN end, the top of the green line) expansion were to stop and everything would be stuck exactly where it is. In this situation, the SN would be observed as fully time dilated, as if expansion never stopped. It's only the galaxy's motion between the start and end that determines the time dilation. The light could travel for 1 year, or 1 trillion years, in static or expanding space, and nothing would change. If expansion stopped and everything was fixed into a position, the time dilation would exist. But the last photon never travels through expanding space. The first photon would only travel through expanding space until the second is emitted. Are the photons redshifted? One of them never travels through expanding space, and the other only does for short time. The author of the paper seems to think so. Though I'm not sure. This is part of the Discussion section:
Quote:
But what about the photons? Do they redshift or not? 
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I'm not entirely sure what I'm talking about, but based on what little I know, the above seemed like a reasonable thing to say. Thank you in advance for any corrections. 

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