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18th March 2023, 04:11 AM  #1081 
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18th March 2023, 05:04 AM  #1082 
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18th March 2023, 06:20 AM  #1083 
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All of that has been explained earlier.
I don’t have the time to look it up now, but I might find the links later. However, I am also slightly against doing your research for you in your own thread, and finding answers that you wilfully ignored the first time round. 
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18th March 2023, 07:53 AM  #1084 
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What is that you don't understand about the simple and oftenrepeated statement that the linear relationship between velocity and redshift (or negative blueshift in your case) is a first order approximation to a polynomial whose higher terms depend on the specific cosmological model chosen.
You've had your paper rejected for identical reasons to those explained to you several times here. Instead of thinking that there might be something in what people are telling you, and humbly accepting it, you are doing what crackpots do  giving their extremely limited knowledge more weight than those who know what they are talking about. For all the people here who have been patiently explaining things to you, the rejection note comes as no surprise at all. We might as well have been explaining it to our cats. 
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18th March 2023, 08:26 AM  #1085 
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18th March 2023, 09:32 AM  #1086 
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Let's reconsider just one example of evidence that has already been mentioned repeatedly within this thread.
Observations of type 1a supernovae tell us that, at the time corresponding to z=1.5, the value of the Hubble parameter was approximately 2.7 times as large as H_{0} (which is, by definition, the current value of the Hubble parameter). That observed fact that the Hubble parameter has been decreasing counts as strong evidence for the concordance ΛCDM model.
Originally Posted by Wikipedia
According to Helland physics, however, the value of the Hubble parameter never changes. That misprediction counts as strong evidence against the Helland model. Which is why Mike Helland has consistently refused to pay any attention to that evidence. And that is just one of many examples of actual evidence that Mike Helland has refused to consider within this thread. You "derived" your redshiftdistance equation by a combination of (1) equivocating (defining b to be one thing, but later pretending b is "equivalent" to something quite different), (2) performing an obviously incorrect (because of the equivocation) change of variable in a first order approximation that, even in its correct form, was known to be a useful approximation only at redshifts much less than 1, (3) graphing both the correct first order approximation and your bogus first order approximation on a time scale that went up to z=9, and (4) pretending the Helland equation you had derived via mistakes (1) and (2) should be taken seriously. ETA: The preceding paragraph is a summary of what you have been told, repeatedly, within this thread. The referee's report on your paper says pretty much the same thing as that paragraph. 
18th March 2023, 10:38 AM  #1087 
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18th March 2023, 10:56 AM  #1088 
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18th March 2023, 11:19 AM  #1089 
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18th March 2023, 11:20 AM  #1090 
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18th March 2023, 11:29 AM  #1091 
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Thanks for the reference.
Quote:
It's in post #896. Came up with it a few days after I submitted the paper. Here it is: Both the traditional and alternative redshiftdistance equations can be derived from Hubble's law and the traditional redshift equations. For the traditional redshiftdistance equation, start with the definition of redshift in terms of wavelength: 1+z = w_o / w_e Now multiply both sides by f_e / f_e: 1+z = w_o / w_e * f_e / f_e The product of w_e and f_e will be c, and the product of w_o and f_e will be a velocity greater than c. 1+z = w_o * f_e / c To reason what w_o * f_e might be, consider as a toy model, a Newtonian analog of a photon, its source, and an observer. The source will be stationary, and the observer will be moving away from the source at velocity v = H_0 * D, as per Hubble's law. The photon is emitted at a velocity of c, however, due to the expansion of space, the photon moves with the Hubble flow, giving it a velocity relative to its source c + H_0 * d. Any observer it encounters will also be moving at H_0 * d, so the photon's speed will be c relative to the observer. This increased velocity of the photon in the toy model represents an elongation of the wavelength combined with its original frequency, and this velocity can be substituted in for w_o * f_e, making: 1+z = (c + H_0 * d) / c 1+z = c/c + H_0 * d / c z = H_0 * d / c d = cz / H_0 To derive the alternative redshiftdistance equation start with the definition of redshift in terms of frequency: 1+z = f_e / f_o And this time multiply both sides by w_e / w_e. 1+z = c / (f_o * w_e) Once again, f_e * w_e = c, but now there is the term f_o * w_e, which is a velocity less than c. Consider another toy model similar to the previous one, with both the source and the observer stationary. This time, the photon has a velocity of v = c  H_0 * d. Due to the deceleration of the photon, the light travel time of the photon increases equal to the light travel time of a photon in the toy expanding universe. (See Appendix A.) If the photon's drop in velocity corresponds to a reduction of its frequency, while maintaining its original wavelength, then we can say f_o * w_e = c  H_0 * d, therefore: 1+z = c / (c  H_0 * d) 1/(1+z) = (c  H_0 * d) / c 1/(1+z) = c/c  H_0 * d / c 1/(1+z)  1 =  H_0 * d / c z/(1+z) =  H_0 * d / c d = c/H_0 * z/(1+z) 
18th March 2023, 11:36 AM  #1092 
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18th March 2023, 12:09 PM  #1093 
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I was summarizing the derivation in your paper.
The fact that you must come up with new derivations so often tells us something important about the typical quality of your derivations. No. As is perfectly clear from the section of that Wikipedia article you cited, Hubble's Law falls out of FLRW in the form v_{r} = HD, where H is the timevarying Hubble parameter that you persistently misread as the Hubble constant. As that section goes on to make perfectly explicit, the approximate form of Hubble's Law from which you allegedly "derived" whatever you think you derived is an approximation obtained by dropping all but the firstorder term of a Taylor series expansion. With my highlighting:
Originally Posted by Wikipedia

Last edited by W.D.Clinger; 18th March 2023 at 12:22 PM. Reason: expanded the quotation from Wikipedia 

18th March 2023, 12:19 PM  #1094 
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18th March 2023, 12:31 PM  #1095 
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18th March 2023, 12:34 PM  #1096 
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I understand the difference. It's relevant when the scale factor changes the ratio of densities of matter and energy, which changes how the scale factor changes.
Quote:
However, instead of making those approximations, I was able to derive them.
Quote:
We can approximate and say z ≈ v / c. But from my derivation, I say z / (1 + z) = v / c. Which also means b = v / c. Here's the thing though. d = cz / H_{0} doesn't fit the observational data. d = z/(1+z) * c / H_{0} does. Let's say z=1.5. It's either ~22 Gly, or ~9 Gly. Which one fits the evidence? 
18th March 2023, 12:37 PM  #1097 
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18th March 2023, 12:51 PM  #1098 
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So you plan to ignore this entire paragraph of your referee's report:
The subsequent discussion then appears to take a lowredshift approximation to the Hubble Law, using both the traditional $z$ definition and the new $b$ definition. The approximate behaviour is then extrapolated to high redshift where the two formulae give different outcomes. But both these options are wrong since the extrapolation rapidly becomes invalid, so the fact that two wrong answers differ from each other does not appear to be telling us anything useful.Both numbers are wrong, for the reason I highlighted in the above quotation from your referee's report. Evidence, however, is what you continue to ignore. 
18th March 2023, 01:20 PM  #1099 
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That's what I'm responding too.
The criticism as I see it has two parts: 1. the equations are approximations 2. they don't predict the right values for high redshift Those are the points I'm addressing.
Quote:
Here's your reference: https://iopscience.iop.org/article/1...384357/aaa5a9 In Table 2 we have: Code:
SN ID z CLH11Tra 1.520 ± 0.04 
18th March 2023, 03:00 PM  #1100 
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See, this is where you knowing calculus would help, because it is once again clear that you don't.
First off, what they describe as Hubble's Law isn't z = (D/c)H, but v_{r} = HD. That's a very important distinction, BTW, because THAT equation isn't an approximation. But H in that equation also ISN'T A CONSTANT, but varies with time. The problem, though, is that we can't measure v_{r} directly, but we can measure z. Which brings us to a second problem. At that point in the derivation, there is no connection between redshift and any other quantities, including v_{r}. This is important, because if your universe expands but then stops expanding, then when it has stopped expanding v_{r} = 0 and H = 0, but you still have left over redshifts. The connection between v_{r} and z is going to be model dependent, and that derivation actually hasn't specified a model. We aren't working with an R(t) derived from FLRW. OK, so how then do they connect Hubble's constant to redshifts? It's not by plugging in an R(t) from FLRW, because again, they didn't specify anything about R(t). Rather, they do exactly what I said: they make an approximation to an exact AND model independent equation for z. What approximation do they make? A first order approximation, using the first derivative of R(t) with respect to t, which is how H makes its way into an equation for z. Which is exactly what I described before. z = (D/c) H doesn't come from FLRW, it comes from making a first order approximation. And that approximation is still model independent, because the derivation still never specified what R(t) is. So no, it's not a coincidence at all. It's just basic calculus, and it's model independent. It has essentially NOTHING to do with the specifics of the expansion function, which is why you'll find that section never specifies what the expansion function is. You are out of your depth here. This is calculus 101 stuff, and you're missing it completely. 
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18th March 2023, 03:01 PM  #1101 
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Sorry, I thought you were still comparing your own approximation's predicted distance to the distance obtained from your bogus extrapolation of the correct first order approximation far beyond its domain of usefulness.
According to the mainstream concordance ΛCDM model, z = 1.5 corresponds to approximately 9 Gly, as can be seen in your own graph. As can be seen in your own graph, your Helland equation says z = 1.5 corresponds to a bit over 8 Gly. So there's almost a billion light years of difference between the ΛCDM model's distance (with Ω_{M} = 0.3 and Ω_{k} = 0) and the Helland model's distance (which happens to coincide with the distance predicted by an FLRW model with the absurd parameters Ω_{M} = 0 and Ω_{k} = 1). We should not be surprised that the modeldependent equation for distance we get by assuming the concordance ΛCDM model yields results that disagree with results predicted by the Helland model. To determine which result is more accurate, we have to look beyond the modeldependent equations by considering which of the models is more consistent with evidence. That's really easy. The concordance ΛCDM model fits the evidence quite well, which is why it is the concordance model. The Helland model predicts a wide variety of things that don't fit the evidence at all, while failing to predict much of anything really. Here's an example, which is very much relevant here because the main result of the paper you and I have most recently been citing is its improved estimate for H(z=1.5) / H_{0}. 
18th March 2023, 03:29 PM  #1102 
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Yup.
So which one is right? Let's check the evidence. In the paper you've referenced: https://iopscience.iop.org/article/1...384357/aaa5a9 Tables 1 through 4 have data on 15 supernovae. There isn't a table that has their calculated distances, though Table 6 has "Measurements of E(z)", and for z=1.5 it has E(z)=2.69 +0.86 0.52. So I take it we plug that into Equation 1, and we get a Luminosity distance. Do I have that right? 
18th March 2023, 03:40 PM  #1103 
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18th March 2023, 04:05 PM  #1104 
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If the criticism is:
1. the equations are approximations 2. they don't predict the right values for high redshift I've already shown that they are not approximations, but can be derived from the standard redshift definitions and Hubble's law. Next just show it does have the right values for high redshift. 
18th March 2023, 05:03 PM  #1105 
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18th March 2023, 05:33 PM  #1106 
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18th March 2023, 06:03 PM  #1107 
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18th March 2023, 07:52 PM  #1108 
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If you say so.
It looks to me like we have two predictions, which are close enough to be within the error margin and uncertainty, and different enough that future measurements should prefer one over the other. AFAICT, there is no modelindependent distance measurement for the z=1.5 supernovae detailed in your reference. 
18th March 2023, 09:41 PM  #1109 
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The primary modelindependent result of the paper we've been discussing for the past day or two is that observations of type 1a supernovae tell us H(z=1.5) / H0 ≈ 2.7, with the uncertainty in that measurement given by 2.17 ≤ H(z=1.5) / H0 ≤ 3.55That modelindependent measurement of H(z=1.5) / H0 is consistent with the concordance ΛCDM model. It is not consistent with Helland physics, however, which predicts H(z=1.5) / H0 = 1. So Helland physics is incompatible with the evidence. Which is why you continue to ignore that evidence.
Originally Posted by Riess et al.

18th March 2023, 10:45 PM  #1110 
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I'm not ignoring it. I'm trying to dig in to it.
It says the luminosity distance as a function of z is: Is that specific to a flat universe? If E(z) = 1, then: d_{L} = c / H_{0} * (1 + z) * F Where F is the integral (from 0 to z) of just dz, right? I notice that E(z) ≈ 2.69 which is ≈1+z, when z=1.5. It's within the error of margin. 
18th March 2023, 11:01 PM  #1111 
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Nothing personal.
Just a comment on the obvious lack of knowledge, concerning calculus. As shown in your question regarding that reviewers remark. And all your questions in your posts since. The obvious route would be to address that lack of knowledge to see for yourself where you did go wrong. 
19th March 2023, 03:59 AM  #1112 
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19th March 2023, 06:03 AM  #1113 
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19th March 2023, 07:05 AM  #1114 
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ETA: The main result of the the paper discussed below, authored by Adam Riess (2011 Nobel Prize in Physics) and others, is an improved modelindependent measurement of the dimensionless Hubble parameter E(z) ≡ H(z)/H_{0}.
In the paper, that equation (1) lies within the middle of a complete sentence. You should read the first four words of that sentence. That's true if E(z) = 1 independent of z, as in Helland physics, which would reduce equation (1) to the Helland equation for distance. But the whole point of the paper is to obtain a more precise modelindependent estimate for E(z), which is most certainly not equal to 1 at z=1.5. E(1.5) ≈ 2.69, but Helland physics requires E(1.5) = 1, which is far outside the margin of error. Because you have so obviously missed/ignored/evaded the point, I repeat these facts, with highlighting: 
Last edited by W.D.Clinger; 19th March 2023 at 07:13 AM. Reason: added ETA (the very first sentence of the edited post) 

19th March 2023, 08:15 AM  #1115 
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19th March 2023, 08:18 AM  #1116 
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I did. It's for a flat universe.
As such it wouldn't apply to an empty universe with negative curvature.
Quote:

19th March 2023, 08:23 AM  #1117 
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19th March 2023, 08:30 AM  #1118 
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19th March 2023, 09:07 AM  #1119 
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My mistake. Your screenshot of the equation didn't display properly in my browser, and I made the mistake of guessing at what it was saying instead of looking at the equation in the paper.
Quoted from your "derivation": Because you have so obviously missed/ignored/evaded the following evidence, I repeat these facts, with highlighting: 
19th March 2023, 09:48 AM  #1120 
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Replace "photon" with "projectile".
If f_e * w_e = c, then a reduction in frequency or increase in wavelength will lead to a velocity less than c, or greater than c respectively. That's just math. The step of the derivation you're referring to just multiplies both sides by 1.
Quote:
This all relates to the questions I asked in post #616: http://www.internationalskeptics.com...&postcount=616 So I'm certainly not ignoring it. Figure 1 has some data points compared to E(z) / E(z)_{fid}. It straight up misses 2 of the 6 datapoints there. It does say: "By eye, the set of E(z) measurements may appear somewhat discrepant with the fiducial ΛCDM model, but the overall ${\chi }^{2}$, which includes the moderate correlations, is 6.7 for the 6 degrees of freedom." I think I can use the cosmo calculator code I've been using to plot E(z)_{fid} by itself. Then, assuming my equation actually predicts E(z)=1, I can plot my equations results there. But like I said, I don't think equation 1 from the paper applies to the empty FLRW model with negative curvature. 
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