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11th November 2022, 08:21 PM  #201 
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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 

11th November 2022, 08:23 PM  #202 
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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 

11th November 2022, 10:08 PM  #203 
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Adding another checkpoint shouldn't be a big deal, and might help describe what's going on. Code:
7 A B C 2.334.66 A B X C 2.33 First photon A (d=0, z=0, E=12 eV) B (d=2.33 Gly, z=?, E=? eV) X (d=4.66 Gly, z=?, E=? eV C (d=7 Gly, z=1, E=6 eV) Second photon B (d=0, z=0, E=9 eV) X (d=2.33 Gly, z=?, E=? eV) C (d=4.66 Gly, z=0.5, E=6 eV) 
12th November 2022, 07:44 AM  #204 
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an important correction
Yesterday, I wrote:
Astute observers will also note that the highlighted word is inconsistent with the parenthesized notations λ(t_{B}) and λ(t_{C}). λ(t) is the wavelength of the photon at time t, not its frequency. The wavelength determines the frequency, but they are inversely proportional. Here is an equivalent of the original equation, to which I have added the ratio of frequencies f(t): 1 + z = a(t_{1}) / a(t_{0}) = λ(t_{1}) / λ(t_{0}) = f(t_{0}) / f(t_{1})We can use that equation to correct some of Mike Helland's miscalculated numbers. Before doing so, I must once again point out that Mike Helland has been computing his distances by using an equation he derived using Helland physics, not mainstream physics: d = (z / (1+z)) (c/H_{0})The H_{0} in that equation is the presentday value of the Hubble parameter H(t), which is defined by H(t) = ȧ(t) / a(t)where a(t) is the scale factor (of an FLRW model for the expanding universe) and ȧ(t) is the derivative of a(t) with respect to time in FLRW coordinates with spatial coordinates centered on earth. Mike Helland rejects the idea of an expanding universe, so he rejects the idea that FLRW models for an expanding universe can approximate the universe in which we live, so it is somewhat amusing that Mike Helland's equation for d involves a Hubble parameter whose definition already assumes the validity of FLRW models as approximations to the universe in which we live. But it is even more amusing to take the Helland physics equation for d seriously enough to consider what that equation would predict as the Hubble parameter changes over time. The value of the Hubble parameter is decreasing, but mainstream physics predicts the Hubble parameter's value is likely to converge toward a particular asymptotic value while the scale factor a(t) continues to grow. The convergence of the Hubble parameter toward its asymptote means the generalized Helland physics equation for d also converges toward an asymptotic maximum value for d, even as the scale factor increases. It is therefore freaking obvious that the Helland physics equation for d is incompatible with mainstream physics. No matter how vehemently Mike Helland insists that his d values are computed using mainstream physics, they are not. Those d values come from Helland physics, which is why we should just ignore Mike Helland's "calculations" of those d values. With that out of the way, we can use the mainstream physics equation for 1+z to fill in two of the values for z and eV that Mike Helland challenged us to supply in the following table: Here is that table with two of the missing values as calculated using mainstream physics, omitting the d values Mike Helland calculated using Helland physics: Mike Helland hasn't given us enough information about event X to calculate a red shift or energy at X. (He gave us a dvalue for X, but that's a number that comes from Helland physics and therefore has no useful meaning in mainstream physics.) I have highlighted the values I added. In my highlighted additions to the table, I have preserved Mike Helland's convention of showing z values that are computed by comparing the energy of a photon at an event to the energy of that photon at the first event shown for that photon in the table. That is a confusing and misleading convention, but it is Mike Helland's convention so I stuck with it. Someone who tries to compute red shifts by summing or subtracting the z values calculated using Mike Helland's misleading convention might be misled into thinking there is some kind of contradiction between the first photon's zvalues at B and C and the second photon's zvalues at those events. Before I say more about that, I will let Mike Helland tell us whether he thinks cumulative red shifts can be computed by summing or subtracting the z values calculated using Mike Helland's misleading convention. It is, after all, possible that Mike Helland's confusion derives from some other mistake. I will, however, offer this hint. 
12th November 2022, 08:17 AM  #205 
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To calculate LCDM values, I use a standard cosmo calculator:
Code:
// from http://www.bo.astro.it/~cappi/cosmotools /* Written by Alberto Cappi (2000); updated November 2005. / Email: alberto.cappi@oabo.inat.it / Cosmological formulae */ //  function fun(v1, Omega_M, Omega_L, Omega_k) { v2 = v1 * v1 v3 = v1 * v1 * v1 f = Math.sqrt(Omega_M * v3 + Omega_k * v2 + Omega_L) return 1. / f }; function simpson(x0, x2) { h = (x2  x0) / 2. x1 = x0 + h igr = h * (fun(x0, Omega_M, Omega_L, Omega_k) + 4. * fun(x1, Omega_M, Omega_L, Omega_k) + fun(x2, Omega_M, Omega_L, Omega_k)) / 3. return igr }; function sumint(z1) { integrale = 0, zone = 1, deltaz = 0.001 while (zone <= (z1  deltaz)) { zini = zone zfin = zone + deltaz integrale += simpson(zini, zfin); zone += deltaz } return integrale }; //  function lookfun(v1, Omega_M, Omega_L, Omega_k) { v2 = v1 * v1 v3 = v1 * v1 * v1 f = v1 * Math.sqrt(Omega_M * v3 + Omega_k * v2 + Omega_L) return 1. / f }; function timeint(z1start, z1end) { s = 0, a = z1start, b = z1end s = 0.5 * (b  a) * (lookfun(a, Omega_M, Omega_L, Omega_k) + lookfun(b, Omega_M, Omega_L, Omega_k)) n = 2 while (n <= 11) { n2 = n  2 it = Math.pow(2, n2) tnm = it del = (b  a) / tnm x = a + 0.5 * del sum = 0. j = 1 while (j <= it) { sum = sum + lookfun(x, Omega_M, Omega_L, Omega_k) x = x + del j += 1 } s = 0.5 * (s + (b  a) * sum / tnm) n += 1 } return s }; //  function sinh(x) { s = (Math.exp(x)  Math.exp(x)) / 2. return s }; function zToD(z) { // From redshift to distance z1 = 1. + z; h = H0 / 100.; Tnorm = 9.77810945 / h; cvel = 299792.458 ch0 = cvel / H0; pig = 3.1415926536; rad = pig / 180.; q0 = Omega_M / 2.  Omega_L; Omega_k = 1.  Omega_M  Omega_L; age = (timeint(1., 50.)) * Tnorm; if (Omega_L > 0. && Omega_k == 0.) { DC = ch0 * sumint(z1); DL = DC * z1 } if (Omega_L > 0. && Omega_k < 0.) { curv = Math.sqrt(Omega_k) r = sumint(z1); DC = ch0 * Math.sin(r * curv) / curv DL = DC * z1 } if (Omega_L > 0. && Omega_k > 0.) { curv = Math.sqrt(Omega_k) r = sumint(z1); DC = ch0 * sinh(r * curv) / curv DL = DC * z1 } if (Omega_L == 0. && q0 > 0) { q0sq = q0 * q0 a = 1.  q0 + q0 * z + (q0  1.) * (Math.sqrt(2. * q0 * z + 1.)) DL = ch0 * a / q0sq DC = DL / z1 } if (Omega_L == 0. && q0 == 0) { DL = ch0 * z * (1. + z / 2.) DC = DL / z1 } // Lookback time lookback = timeint(1., z1) * Tnorm // Angular distance DA = DL / (z1 * z1) // Lunghezza in primi corrispondente a 1 Mpc. angle = (60. / rad) * z1 * z1 / DL; // Length in Mpc corresponding to 1 degree on the sky R = rad * DL / (z1 * z1); // Display result in the form. /* form.q0.value = q0.toFixed(2); form.Omega_k.value = Omega_k.toFixed(2); form.dlum.value = DL.toFixed(1); form.dcom.value = DC.toFixed(1); form.dang.value = DA.toFixed(1); form.lsep.value = R.toFixed(1); form.asep.value = angle.toFixed(1); form.look.value = lookback.toFixed(1); form.age.value = age.toFixed(1); */ return lookback } Code:
ztest = (1 / (1 + dp.z)  1) * c / H0h * pc2ly / 1000
Quote:

12th November 2022, 08:36 AM  #206 
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12th November 2022, 09:42 AM  #207 
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So the Helland physics equation of your "code" was obtained by curvefitting to a universe devoid of matter. And you think I should be impressed?
We know how mistaken you are. You think mainstream physics predicts the first photon's energy is 10 eV at event B and 6 eV at event C, even though you stipulated that the second photon has energy 9 eV at event B and 6 eV at event C. That alleged 10 eV energy for the first photon at B is not what mainstream physics predicts, as shown by the mainstream equation in my remarks earlier this morning. Ziggurat and many others have been telling you what's wrong with your calculations. In my remarks earlier this morning, I even gave you a spoiler that shows you the numbers of a correct calculation using the mainstream equation, and also shows why the energy I gave for the first photon at B is consistent with your stipulated z values for both photons at events A, B, and C. Distances are coordinatedependent, and the relationships between distances that hold at different times is modeldependent, so "All the same lengths" is meaningless unless you tell us what coordinate system you're using and the model you're assuming. From one of your remarks quoted above, it seems you are assuming a model in which the universe contains essentially no matter. Which seems silly, but no matter.^{*} The reason that doesn't matter is because distances do not show up at all in the mainstream equation that states the relationship between z and ratios of scale factors, wavelengths, frequencies, and energies. You tell us the value of z at two events and the energy at one of those events, and we can use mainstream physics to tell you the energy at the other event. That is where you went wrong and persist in being wrong. There's no reason at all to drag coordinate and modeldependent distances into this discussion, unless of course you are attempting a Gish gallop to obfuscate your fundamental error. ^{*}Pun intended. 
12th November 2022, 10:01 AM  #208 
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No, it was derived by inverting the redshift formulas.
And if redshifts are caused by motion, then gravity and thus matter would have an effect on them. If they aren't caused by motion, then gravity and matter don't have an effect on them.
Quote:
The situation is that a photon leaves some point A, and after 2.33 million years, where ever it is you can call that point B, and after another 2.33 million years, that's point X, and after another 2.33 million years, then its at point C. The actual distance of these points at any time changes due to expanding space, but the events are 2.33 million years apart.
Quote:

12th November 2022, 10:10 AM  #209 
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12th November 2022, 10:18 AM  #210 
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W.D.Clinger  wish you'd been my lecturer when I was doing my A level pure and applied maths! Thanks for the lessons.

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12th November 2022, 10:20 AM  #211 
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I'm not obscuring anything.
Code:
 A B C D E F G 14 Gly A z=0 12 ev 9 ev B z=0.2 10 7.5 C z=0.5 8 6 D z=1 6 4.5 E z=3 4 3 F z=5 2 1.5 G z=∞ 0 0 Ok, let's try it your way: Code:
A z=0 12 ev B z=0.33 9 C z=? ? D z=1 6 E z=? ? F z=? ? G z=? ? 
12th November 2022, 10:51 AM  #212 
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Outright lying can be part of a Gish gallop. For example...
I have not said the numbers shown in that particular table are impossible. You have not shown that particular table of numbers before, so it would not have been possible for me to say those numbers are impossible. Upon seeing that table for the first time, just moments ago, I confirmed that the numbers in that table are correct. ETA: Readers should note that, unlike Mike Helland's previous tables, the table above is not showing any single event at which the two photons have the same energy, and is also not showing any one event at which the photons have energies 10 eV and 9 eV, respectively. Here are the facts Mike Helland is hoping to obscure: I have highlighted the sentence that explains how I was able to confirm that the numbers in Mike Helland's brand new table above are correct. The fact that distances do not appear within the rows of that brand new table, and the one distance given (14 Gly) is irrelevant to the correctness of the numbers in that table, can be taken as Mike Helland's tacit admission (finally!) that we don't need to talk about distances to find the error(s) in Mike Helland's previous tables. 
Last edited by W.D.Clinger; 12th November 2022 at 11:01 AM. Reason: added ETA and other text in gray 

12th November 2022, 11:19 AM  #213 
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ETA: Readers should note that, unlike Mike Helland's previous tables, the table above is not showing any single event at which the two photons have the same energy, and is also not showing any one event at which the photons have energies 10 eV and 9 eV, respectively.
[/quote] Ok, so we have: Code:
 A B C D E F G 14 Gly A z=0 12 ev B z=0.2 10 C z=0.5 8 D z=1 6 E z=3 4 F z=5 2 G z=∞ 0 Now let's say a 10 eV photon was emitted from B. Since the photons must act identically, them both being at point B with the same energy, then: Code:
A   B z=0 10 C z=? 8 D z=? 6 E z=? 4 F z=? 2 G z=∞ 0 That's wrong. The only thing that makes sense is: Code:
A   B z=0 10 eV C z=0.2 8.33 D z=0.5 6.66 E z=1 5 F z=3 2.5 G z=5 1.66 
12th November 2022, 12:23 PM  #214 
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12th November 2022, 12:40 PM  #215 
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Here is the mainstream equation Mike Helland is finding so difficult to apply correctly:
1 + z = a(t_{1}) / a(t_{0}) = λ(t_{1}) / λ(t_{0}) = f(t_{0}) / f(t_{1})That much is okay. Readers should note that the photon whose energies are listed in that table is not either of the photons whose energies were shown in Mike Helland's correct table of a few minutes ago. If we fill in the question marks with z values computed using the mainstream equation, we get the following table for this third photon, which was emitted at event B: Code:
A   B z=0 10 C z=0.25 8 D z=0.67 6 E z=1.5 4 F z=4 2 G z=∞ 0 Readers should note that those added values for z are different from the z values for the first photon at those events, because the red shifts for this new photon tell how far its energy/frequency/wavelength has been shifted from the energy/frequency/wavelength this new photon had when it was emitted. The red shifts Mike Helland calculated for the first photon tell how far it had been shifted from when that first photon was emitted. In other words, the z values for the first and new photons are not directly comparable (although someone who actually knows what he or she is doing can use the mainstream equation to show exactly how and why those differing z values are related, as I did in the spoiler I offered as a hint earlier this morning). When all else fails, you can say something silly by relying on fallacious reasoning about infinity. Both photons have positive energy at all finite distances from the events at which they were emitted. The last rows, with z=∞ and an energy of 0 eV, are said to correspond to an event G, but there is no actual event G within the spacetime manifold at which z=∞ and the photons have zero energy. I don't know what Mike Helland might think he means by "5/6th of Hubble's distance", but the context suggests he thinks he can get a reliable finite distance by subtracting things from infinity. Or maybe he's relying on a fallacy that involves dividing by zero. If you examine the mainstream equation at the top of this post, you'll see that the z=∞ in the table is a mathematically suspect but common informal way of indicating the undefined result of dividing a positive number by zero. Here we have f(t_{1}) = 0, which appears in the mainstream equation as a divisor. Mike Helland might be reasoning as follows: ∞=x/0 and also ∞=y/0, so x=y. That reasoning is fallacious. Regardless of how Mike Helland made his mistake here, he made a mistake. When all else fails, you can fall back on equivocation. Mike Helland is once again using exactly the same letter to mean completely different things, this time in consecutive tables. Event G of this new table, at which a photon has positive energy and a red shift of z=5, cannot be the same as event G of any previous table that appears in Mike Helland's post, because all of the other rows for G show an infinite red shift and zero energy. (As noted above, however, there is no event G at which the red shift of any photon is actually infinite and its energy is actually zero. What is true is the red shift can increase without bound as the energy converges toward zero, but neither value ever actually reaches those limits.) It is possible that Mike Helland intends for events B through F to be different as well, but his calculations and exposition have been so riddled with errors that there's no point to trying to guess exactly where he is equivocating and where he is not. 
12th November 2022, 01:23 PM  #216 
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Even 1 trillion light years?
Not all finite distances. Just those less than c/H_{0}.
Quote:
Divide that into 6 pieces., AB, BC, CD, DE, EF, FG. The first photon travels from A to G. 6/6th of Hubble's length. The second photon starts at B and goes to G. 5/6 of Hubble's length. If both photons have 10 eV at point B, the first photon will burn out at G. The second photon will burn out H (not pictured). 
12th November 2022, 01:24 PM  #217 
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12th November 2022, 01:27 PM  #218 
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Your answer to my question should have simply been "yes" and then you should have used to that open your mind to the stuff that W.D. Clinger said about infinity.

12th November 2022, 01:32 PM  #219 
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12th November 2022, 01:50 PM  #220 
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Ok, so we have:
Code:
 A B C D E F G 14 Gly A z=0 12 ev B z=0.2 10 C z=0.5 8 D z=1 6 E z=3 4 F z=5 2 G z=∞ 0 Code:
E z=2 4 So this needs to be: Now let's say a 10 eV photon was emitted from B. Code:
A   B z=0 10 eV C z=0.2 8.33 D z=0.5 6.66 E z=1 5 F z=2 3.33 G z=5 1.66 
12th November 2022, 02:35 PM  #221 
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Code:
Ω_{M}=0, Ω_{Λ}=0 ΛCDM(Ω_{M}=0.3, Ω_{Λ}=0.7 B= z=0 t=0 t=0 C z=0.25 t=2.799 t=2.9 D z=0.67 t=5.616 t=6.1 E z=1.5 t=8.4 t=9.3 F z=4 t=11.2 t=12 G z=? t=? t=? If you'll notice, the first t column, the times go up by about ~2.79 and the second t column goes by about ~3.1. That means at G, t=14 and t=15.1 Gly. But if you look at the first photon, going from A to B with 12 eV, its lookback time goes up by 2.333 Gyr. Times that by 6, and you get 14 Gyr. A photon traveling from A to G at c takes 14 billion years. A photon traveling to B to G at c takes 14 billion years. Doesn't add up. 
12th November 2022, 03:01 PM  #222 
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If a photon travels for 1/6th the age of the universe, it loses 1/6th of its original energy.
If a photon travels for 1/2 the age of the universe, it loses 1/2 of its original energy. If a photon travels for 1/6th the age of the universe, and then again, and then again, it loses 3/6 of its original energy. I know that seems hard to believe. I didn't expect it either. But that's the only way jonesdave116's problem works out. 
12th November 2022, 03:32 PM  #223 
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photon1 leaves point A toward point G. Check its z and energy every 2.33 Gyr.
Code:
A z=0 12 ev 0 Gyr B z=0.2 10 2.33 C z=0.5 8 4.66 D z=1 6 7 E z=2 4 9.33 F z=5 2 11.66 G z=∞ 0 14  A B C D E F G 14 Gyr As it passes point D, photon2 leaves point D with 6 eV: Code:
A x B x C x D z=0 6 0 E z=0.5 4 4.66 F z=2 2 9.33 G z=∞ 0 14 It takes photon2 14 billion years to get do the same thing. That is not correct. This is correct: Code:
A x B x C x D z=0 6 0 E z=0.2 5 2.33 F z=0.5 4 4.66 G z=1 3 7 
13th November 2022, 01:05 AM  #224 
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Those were very good.
What do you think are the differences with this: http://www.bo.astro.it/~cappi/cosmotools.pdf It looks good too. *edit*Not to take away from WDC. That was thorough. Christoffel symbols? That's how you know you're getting in there. 
13th November 2022, 06:02 AM  #225 
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Blessed are they who set out to learn nothing, for they shall surely succeed.Mike Helland has been treating us to a Gish gallop of numerical distances, even though Ziggurat and I and others have shown that the relationship between red shift and photon energy is measured and calculated without any knowledge of distance. Mike Helland computed most of his numerical distances using an equation based upon Helland physics instead of mainstream physics. Mike Helland stubbornly insists his equation is based upon mainstream physics, even after I have given a proof that it isn't (and will give two more proofs below of its incompatibility with mainstream physics). This may be a good time to remember how red shifts are actually measured and computed. Mainstream physics and chemistry tell us that certain elements and molecules have emission and absorption lines at definite fixed frequencies. When we examine the spectrum of light emitted by a distant source, we can easily measure the displacement of those lines from their original frequencies. We do that without having to know anything about our distance from the source, and without having to form any opinion about how those red or blue shifts came to be. From those measured shifts, mainstream astrophysics defines a parameter z via the equation 1 + z = a(t_{1}) / a(t_{0}) = λ(t_{1}) / λ(t_{0}) = f(t_{0}) / f(t_{1})where t_{0} is the time at which the photons were emitted, t_{1} the time at which the spectrum was observed, λ(t) is the wavelength at time t, f(t) the frequency at time t, and a(t) the FLRW scale factor at time t. Note first of all that distances are completely absent from that equation. Note also that we can use that equation to calculate z without knowing the times t_{0} and t_{1}. The reason we don't have to know t_{0} is that λ(t_{0}) and f(t_{0}) are simply the wavelength and frequency of unshifted photons at the emission/absorption lines we are using to compute the shift, and we know those wavelengths and frequencies because they have been measured in modern laboratories and published in the research literature. The reason we don't have to know a numerical value for t_{1} is that λ(t_{1}) and f(t_{1}) are simply the wavelength and frequency of the shifted emission/absorption lines we are seeing in the spectrum. Finally, note that the scale factor a(t) is the only thing in that equation that might appear to require us to form an opinion about the cause of the shifts. In use, however, we don't use the a(t) part of that equation to measure or to compute red/blue shifts. We use the wavelength or frequency parts when measuring or computing shifts. The a(t) part of that equation is there because mainstream physics attributes much of the red shift seen in spectra from distant sources to expansion of the universe as predicted by certain FLRW models, and we use the a(t) part of the equation to relate the red shift we measure and compute (without using the a(t) part) to those FLRW models. From the above, it should be easy to understand why Mike Helland's obsession with numerical distances is unhelpful to anyone who truly wishes to understand the relationship between red shift and photon energy. The energy of photons corresponding to emission/absorption lines is known
Distances become a concern only when we want to develop a theory that explains the correlation of red shift with distance. Expansion of space, as in the FLRW models for an expanding universe, is the mainstream theory that explains that correlation. The James Webb telescope will provide new data to help us test that mainstream theory, and also help us to calculate better estimates for the parameters of that mainstream theory. And so the mainstream equations that relate distance to red shift are based upon expansion of space, as predicted by the FLRW models. Those FLRW models have several parameters, but for any choice of those parameters we can use the FLRW model to derive equations that relate distance to the part of the red shift that is caused by expansion of space. Note that, in mainstream physics, the relationship between distance and red shift is modeldependent. In particular, it depends upon the parameters of an FLRW model, and those parameters show up in the mainstream equations for estimating distance from red shift. Mike Helland's equation for calculating distance from red shift does not involve any of the FLRW parameters, which was an extremely strong clue that the Helland equation is not based upon mainstream physics. In a recent post, however, Mike Helland has said his equation assumes a universe devoid of matter, which establishes the value Mike Helland's equation assumes for one of the FLRW parameters. It is conceivable that Mike Helland will eventually tell us the values of other FLRW parameters he may want us to believe he took into account when deriving the Helland equation. With that background... "It looks good too." For flat spacetime, a simplifying assumption I made in the notes I posted to this forum's predecessor years ago, equation (6) of Cappi's paper simplifies to d_{c}(z) = (H(t)/H_{0}) a(t) rwhere d_{c}(z) is the comoving distance corresponding to red shift z, H(t) is the Hubble parameter (as a function of time), H_{0} is the value of H at the present time, a(t) (which Cappi writes as R) is the FLRW scale factor (also a function of time), and r is defined by Cappi's equation (4), which involves a rather nastylooking integral that probably has no simple closedform solution and would therefore have to be computed using routine numerical integration. To use that equation, you'd have to know what time t to use for the H(t) and a(t) factors; it appears to me that you'd use the lookback time given by Cappi's equation (7), which involves another nastylooking integral. From the comoving distance, you can compute the luminosity distance via d_{L} = d_{c} (1 + z). Now compare (my simplification of a special case of) Cappi's equation for distance to the Helland equation, which is d = (z/(1+z)) c/H_{0}(For some reason, Mike Helland stubbornly persists in writing a more complicated equivalent of that equation, perhaps because the more complicated way of writing the equation makes it harder to compare against mainstream equations such as Cappi's.) Now I ask you: Does the Helland physics equation for distance even resemble the mainstream physics equation? To close: As if Mike Helland had any idea what Christoffel symbols are about. 
13th November 2022, 11:03 AM  #226 
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13th November 2022, 11:34 AM  #227 
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I write it with one z on the right hand side because that's how I derived it, and it's easier to solve for z (at least to me) that way.
Cosmological calculators will give you, based on your z and cosmological parameters: Luminosity Distance (Mpc) Comoving Distance (Mpc) Angular Distance (Mpc) Length corresponding to 1 degree (Mpc) Angle corresponding to 1 Mpc (arcmin) Lookback time (Gyr) The one I'm interested in is lookback time. A photon that travels for 1 billion years at the speed of light. Lookback time * 1 light year per year = lookback time distance How far was the source from the destination when the photon was emitted? It was < lookback time * c. How far is the source from the destination now? It is > lookback time * c. How far did the photon actually travel? It is = lookback * c. 
13th November 2022, 12:39 PM  #228 
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13th November 2022, 07:17 PM  #229 
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13th November 2022, 09:44 PM  #230 
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13th November 2022, 09:58 PM  #231 
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14th November 2022, 12:55 AM  #232 
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Yes, I often wonder if I had become better at math if calculators and computers had existed when I was young.
I would definitely have been adept at doing the calculations, but I am not sure that it would have helped my inability to ‘read’ equations. It seems to me that Mike Helland is in much the same situation. 
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14th November 2022, 07:44 AM  #233 
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Yeah, teacher quality can make a really big difference, especially for kids who aren't naturally gifted.
I took to calculus like a fish to water, but linear algebra was the one I didn't connect with on the first pass. I'll give you an example of something that I should have been taught from the beginning, but didn't learn until well after graduate school: the determinant of a matrix measures how much the volume of an object changes when it's transformed by that matrix. It has a physical, intuitive meaning, which is actually really easy to connect to the math. And it makes certain properties of determinants really obvious without having to remember them separately (like the determinant of the product of multiple matrices is the product of the determinant of each matrix, or the fact that nonsquare matrices don't have determinants). But if you just focus on the formulas, it's easy to miss, and then it all becomes forgettable. 
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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 

15th November 2022, 08:07 AM  #234 
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This right here:
I can tell you that: And that d = ct, so... those equations must be pretty related Of course, only when matter doesn't affect redshift and there is no dark energy. So let's talk about that. Here are the two equations when Ω_{M} and Ω_{Λ} are 0. Alright. But, since redshifts are caused by the expansion of space, then they are counteracted by matter pulling on them. So we set Ω_{M} to 1.0: That can't be right based on observations, so we need to add dark energy to counteract the counteractions of gravity (Ω_{M}=0.3 and Ω_{Λ}=0.7): This kind of shifts it back into place, but not perfectly. But, if matter doesn't affect redshifts, then you don't need dark energy, and the "nasty looking integral" just becomes d = bc/H_{0}, where 1+b=1/(1+z). So t=b/H_{0}. 
15th November 2022, 10:10 AM  #235 
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A couple of days ago, I wrote:
I was unsure about the highlighted part, and it bothered me that Cappi placed equation (7) after equation (6) when he was so careful to place all of the other equations that you needed before performing the calculation implied by (6) before equation (6). I have now figured out how to calculate the lookback distance according to equation (6) without needing equation (7), and will explain in a few days when I have time to write it up. For now, however... Those equations are most certainly related, but if you think those equations imply d_{c}(z) = c t(z), then you're wrong. The definite integral in equation (7) has (1+z') in the denominator, whereas the integral in equation (4) does not, and the value of that integral shows up in equation (6) via S_{k}(r). If you are assuming matter doesn't affect redshifts, then you are assuming Helland physics rather than mainstream physics. That is part of why your Helland equation for the relationship between red shift and distance is far less complicated than the mainstream equations for that relationship. (The other reason your equation is less complicated is that it either doesn't take model parameters into account, or it assumes those parameters have whatever fixed values you think they have in Helland physics.) And because you derived your Helland equation using Helland physics instead of mainstream physics, any inconsistencies you may think you have uncovered using that equation represent a problem with Helland physics, not mainstream physics. 
15th November 2022, 10:20 AM  #236 
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d_{c} is the comoving distance, so not quite.
Quote:
It could be that it matches a universe where matter doesn't affect redshift is just a bizarre coincidence. But its kinda of funny that: 1. if you add matter, you need dark energy to reverse its affects 2. LCDM is in tension with observations 
15th November 2022, 10:57 AM  #237 
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It's kinda funny that the evidence says that dark energy does exist. It may help if you, or anybody else involved in nonstandard physics, would actually deal with that evidence, before inventing equations that don't work.
So, the integrated SachsWolfe effect on the CMB photons. As predicted. The baryon acoustic oscillation observations. The SN 1a time dilation measurements. Inventing wonky equations for tired light nonsense does not make that evidence disappear, even if you miraculously came up with an equation that matches the results from mainstream equations. That is where Lerner fails miserably. Not only is his equation wonky, but he cannot explain the evidence. You are going about this bass ackwards. 
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15th November 2022, 03:44 PM  #238 
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Of course it does. That's why we're talking about it.
Here inverted redshift and distance match a universe that redshifts as it expands without the affects of matter and gravity. Now add the matter and gravity. Wait. This gives a universe of 12 billion years old. Younger than the oldest stars. What does the Nobel prize winner that discovered this think about it? Here's a paper from last week.
Quote:
[Submitted on 8 Nov 2022] The Hubble Tension and Early Dark Energy Marc Kamionkowski, Adam G. Riess 
16th November 2022, 03:22 AM  #239 
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Why the James Webb Telescope rewrites/doesn't the laws of Physics/Redshifts
There is nothing new in the question of the Hubble constant. Is the paper offering tired light as a solution?

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16th November 2022, 08:03 AM  #240 
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It's a review paper, "intended to be fairly general and understandable to a broad audience." Looks like a solid review. Mike Helland should read it. No, the paper does not offer tired light as a solution. It discusses mainstream physics, and explains why mainstream cosmologists are looking into adding "early dark energy" (EDE) to refine the ΛCDM model further, which has already been refined by augmentation with expansion, dark matter, and dark energy. The title of the paper already gives a clue as to what it's about: The Hubble Tension and Early Dark Energy 
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