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Old 23rd November 2022, 07:08 PM   #281
W.D.Clinger
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computing lookback times from redshifts

ReferencesThe equations and notations that appear below are from Cappi's short paper. The Peebles book was Cappi's primary reference. Cappi's paper is rather terse, even cryptic in a couple of spots, so I used the Peebles and Weinberg books to check my understanding and calculations.
Cappi's notational conventions are somewhat different from the conventions used by Peebles and Weinberg, whose notations are fairly similar. The following remarks might help someone who is trying to understand the correspondences between those three references.

Peebles assumes natural units that allow him to omit the speed of light from most of his equations. Cappi, being more concerned with number crunching, makes the speed of light explicit in his equations.

Peebles' equation (4.10) is missing a minus sign. That doesn't matter because dw is squared in equation (4.11), which appears to be the only place equation (4.10) is used. I'm mentioning this to remind you that my own calculations are likely to contain considerably more errors than can be found in the works of these two Nobel Prize winners.

Cappi's R is the same as Peebles' a(t)R, and is probably the same as Weinberg's a(t). For Peebles, R is a constant, but Cappi's R is not. Both are a radius of curvature of space. Peebles can fix R as the radius of curvature at the present day, which makes a(t0)=1 where t0 is the present day.

(In most of my previous posts in this thread, I wrote t1 for the present day and t0 for the earlier time at which a photon was omitted. Almost all authors do the opposite; with this post, I am falling in line with the consensus notation.)

Cappi's Ωk is the same as Peebles' ΩR and the same as Weinberg's ΩK. Cappi writes Ωi for the ordinary density fractions, which I (following Weinberg) will write as ΩM, ΩΛ, and ΩR. (Note that Peebles' ΩR is completely different from Weinberg's ΩR.) Cappi writes Ωtot for the sum of the density parameters without the curvature parameter Ωk, but Peebles writes Ω to mean the same thing. (Note that some authors use Ω to mean the critical density, or write Ω=1 to remind readers that the critical density, taken as a fraction, is 1, or possibly to mean something else.)

Consider, for example, Peebles equation (5.56):
ΩR = 1/ (a0H0R)2
Translated into Cappi's notation, that becomes
Ωk = 1 / (H0R0)2)
Peebles often, but not always, treats pressure as negligible. Cappi doesn't speak of pressure explicitly, but it is present in the derivations of some of Cappi's equations as you can see by reading Peebles or Weinberg.

Peebles and Weinberg write out the formula for E(z), whereas Cappi got cute with the wi so he could use a summation notation instead.

Peebles and Weinberg usually give separate equations for k=+1 and k=-1, leaving it to the reader to obtain the equations for k=0 via continuity. As explained in the next spoiler, Cappi tried to give equations that covered all three situations at once, but two of those equations don't work for k=0.

Peebles equation (13.9) is essentially the same as Cappi's equation (7), and that equation is the main focus of my remarks here.


Cappi's Equations

Cappi's Equation (1)

The Robertson-Walker metric can be written as
ds2 = c2dt2 - R2(t) [ dr2 + Sk2(r) dΩ]
where
  • Sk(r) = r for k = 0 (flat space)
  • Sk(r) = sin(r) for k = +1 (positively curved space)
  • Sk(r) = sinh(r) for k = -1 (negatively curved space)
  • dΩ = dθ2 + sin2θ dΦ2
Cappi doesn't actually use that dΩ notation, which has absolutely nothing to do with the density fractions Ωi, Ωk, and Ωtot. I'm using that abbreviation to state equation (1) because many other authors use it, and I wanted to warn you about it so you won't make the mistake of thinking it is related to a density fraction.

On the other hand, Cappi's Sk(r) notation actually appears in the paper, and probably contributed to the divide-by-zero error in equation (6).

Density Fractions

Cappi writes Ωi for the first three fractions below, with i ranging over the subscripts in those three fractions, but his equations are easier to understand if written out (as in what follows).
  • ΩM = ((8πG)/(3H2)) ρM
  • ΩR = ((8πG)/(3H2)) ρR
  • ΩΛ = ((8πG)/(3H2)) ρΛ
  • Ωk = - kc2 / (HR)2
ΩM is the mass density, as a fraction of the critical density that separates an open universe from a closed universe.

ΩR is the radiation or relativistic mass density, as a fraction of the critical density.

ΩΛ is the dark energy density, as a fraction of the critical density.

Ωk = 1 - ΩM - ΩR - ΩΛ is the so-called curvature parameter. For flat space (k=0), Ωk = 0. For positively curved (closed, k=+1) space, Ωk < 0. For negatively curved (open, k=-1) space, Ωk > 0.

Equations (4) and (6) are problematic, so I won't discuss them further outside of the following spoiler.
For flat space, k=0 and Ωk = 0. According to Cappi's equation (4), that makes r=0, which is something of a coordinate singularity. It also creates a division by zero in equation (6).

Equation (4) is used only in equation (6), and I haven't figured out what the dc(z) of equation (6) means, so I'm just going to ignore equations (4) and (6) outside of this spoiler.

I do know, however that dc(z) is not equal to the lookback time multiplied by c.

As for how Cappi messed up these equations, it seems pretty clear that he got too cute as he tried to cram three separate cases (k=0, k=+1, k=-1) into single equations.

It isn't hard to fix the errors, because equation (4) involves a multiplication by sqrt(abs(Ωk)), while equation (6) involves a division by that same number. Combining equations (4) and (6) into a single equation, those factors cancel out and the combined equation makes sense. I have used the combined equation to calculate some values for dc(z), but I don't know what to make of those numbers. Perhaps some reader can help me out here.

Cappi's Equation (5)

Unlike Cappi, I'm writing this out in full:
E(z) = sqrt (Ωk(1+z)2 + ΩM (1+z)3 + ΩR(1+z)4 + ΩΛ)
Cappi's Equation (7)

The lookback time is
t(z) = (1/H0) ∫0z dz' / [(1+z) E(z')]
Cappi put 1 in the numerator instead of dz'.

When faced with integrating the reciprocal of a square root of a polynomial in (1+z), I usually fall back on numerical integration. For several unrealistically simple models, however, it's easy to find a closed form for t(z).

Lookback Time for Unrealistically Simple Models

Completely Empty Universe with Negative Curvature

With parameters
  • ΩM = ΩR = ΩΛ = 0
  • Ωk = 1 (implied by the above)
  • k = -1 (implied by the above)
applying an easy bit of algebra and calculus to equation (7) yields
c t(z) = (c/H0) (z/(1+z))
That is Mike Helland's equation relating distance to redshift, for the model he referred to as "LCDM in a default state".

Note, however, that space is negatively curved in this model. From Cappi's
Ωk = 1 = k c2 / (HR)2
and a bit of algebra, we get
R0 = c / H0
as the present-day radius of curvature for this model. With H0 approximately 70 km/s/Mpc, that radius of curvature is about 14 billion light years. If space were really that curved, we'd have noticed.
In a previous post, I miscalculated somehow to get a radius of 140 billion lightyears. My remarks concerning the incompatibility of Ωk = 1 with the Planck measurements were correct, however.

Ωk=1 is hundreds of times more curvature than would be consistent with the Planck mission's observations:
Originally Posted by Wikipedia
Final results of the Planck mission, released in 2018 show the cosmological curvature parameter, 1 – Ω = ΩK = –K c²/a²H², to be 0.0007±0.0019, consistent with a flat universe.[18] (i.e. positive curvature: K = +1, Ωκ < 0, Ω > 1, negative curvature: K = −1, Ωκ > 0, Ω < 1, zero curvature: K = 0, Ωκ = 0, Ω = 1).

Einstein-de Sitter Universe

With parameters
  • ΩM = 1
  • ΩR = ΩΛ = Ωk= 0
  • k = 0 (implied by the above)
we get the Einstein-de Sitter model of the universe, which was proposed in 1932, became popular in the 1980s, but fell out of fashion when better upper bounds for ΩM were obtained by Peebles and others.

Once again, applying a tiny bit of algebra and calculus to Cappi's equation (7) yields
t(z) = (2/(3H0)) [1 - (1+z)-3/2]
which implies t(z) < 2/(3H0) for all finite redshifts. With H0 ≈ 70 km/s/Mpc, that means the universe could not be more than about 9.33 billion years old.

Radiation Universe

With parameters
  • ΩR = 1
  • ΩM = ΩΛ = Ωk= 0
  • k = 0 (implied by the above)
we get a universe awash in radiation, with no matter and no dark energy. ΩR is the only density parameter we can measure directly at this time, so we know ΩR is very close to zero in today's universe, but that would have been different in the very early universe so this model deserves some attention. Using this model to calculate lookback times is rather silly, however. Regardless, plugging its parameters into equation (7) yields
t(z) = (1 / (2 H0)) [z(1+z) / (1+z)2]
implying such a universe could not be more than about 7 billion years old.

Dark Energy Universe

With parameters
  • ΩΛ = 1
  • ΩM = ΩR = Ωk= 0
  • k = 0 (implied by the above)
we get a universe crammed full of dark energy and nothing else. Equation (7) yields
t(z) = (1/H0) log (1+z)
where log(1+z) is the natural logarithm of 1+z. As will be seen, that signifies a rapidly expanding universe.

More Realistic Models of the Universe

It looks as though the class of models considered in Cappi's paper best fit the universe in which we live with parameters such as these:
  • ΩM ≈ 0.3
  • ΩΛ ≈ 0.7
  • ΩR ≈ Ωk ≈ 0
With those parameters, the integral in Cappi's equation (7) is more daunting, so I resort to numerical integration. We can use the closed form solutions for the unrealistically simple models to estimate the magnitude of error in my numerical integrations.
Simpson's rule would have been appropriate, but I used Runge-Kutta because I wanted to figure out how to apply it to a straightforward definite integral. Hey, I deserve to learn something from all this.


A Table of Lookback Distances

This table shows distances obtained by multiplying the speed of light times lookback times for various models and red shifts, taking H0=70 km/s/Mpc. Distances are stated in billions of light years. Rows marked with (*) were calculated using the closed form solutions for simple models; all other rows were calculated using numerical integration.

Code:
ΩM                 0       1         0        0        0.2      0.3      0.4
ΩΛ                 0       0         1        0        0.8      0.7      0.6
ΩR                 0       0         0        1        0        0        0
Ωk                 1       0         0        0        0        0        0

z = 0.1           1.27    1.24      1.33     1.21     1.31     1.30     1.29
z = 0.2           2.32    2.22      2.54     2.13     2.46     2.42     2.39
z = 0.3           3.22    3.03      3.66     2.85     3.49     3.42     3.35
z = 0.4           3.99    3.69      4.70     3.43     4.41     4.28     4.18
z = 0.5           4.66    4.25      5.67     3.89     5.22     5.05     4.90

z = 1 (*)         7.00    6.03      9.70     5.25
z = 1             7.00    6.03      9.70     5.25     8.19     7.73     7.36
z = 2             9.46    7.65     15.6      6.32    11.3     10.4      9.75
z = 3            10.7     8.29     19.7      6.67    12.7     11.6     10.8
z = 4            11.4     8.63     22.9      6.83    13.4     12.2     11.3
z = 5            11.7     8.70     25.1      6.80    13.6     12.3     11.4

z = 10           12.8     9.18     33.6      7.08    14.5     13.0     12.1
z = 20           13.4     9.34     42.6      7.13    14.9     13.3     12.3
z = 30           13.6     9.38     48.1      7.14    15.0     13.4     12.4
z = 40           13.7     9.40     52.0      7.14    15.0     13.5     12.4
z = 50           13.8     9.41     55.1      7.14    15.0     13.5     12.4

z = 100          13.9     9.43     64.6      7.14    15.1     13.5     12.4
z = 1000         14.1     9.43     96.7      7.14    15.1     13.5     12.5
z = 1000 (*)     14.0     9.33     96.7      7.00

z = 10000 (*)    14.0     9.33    128.9      7.00

Last edited by W.D.Clinger; 23rd November 2022 at 07:35 PM. Reason: added missing row to table
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Old 23rd November 2022, 11:35 PM   #282
steenkh
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W.D.Clinger, thanks for this huge and interesting post!
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Old 25th November 2022, 01:08 PM   #283
Mike Helland
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Originally Posted by W.D.Clinger View Post
References
The equations and notations that appear below are from Cappi's short paper. The Peebles book was Cappi's primary reference. Cappi's paper is rather terse, even cryptic in a couple of spots, so I used the Peebles and Weinberg books to check my understanding and calculations.
Cappi's paper isn't anything special. It just explains his cosmo calculator:

http://www.bo.astro.it/~cappi/cosmotools

Which I made an interactive version of here:

https://mikehelland.github.io/hubble...other/lcdm.htm


Quote:
Equation (4) is used only in equation (6), and I haven't figured out what the dc(z) of equation (6) means, so I'm just going to ignore equations (4) and (6) outside of this spoiler.

I do know, however that dc(z) is not equal to the lookback time multiplied by c.
dc is comoving distance.

Quote:
As for how Cappi messed up these equations, it seems pretty clear that he got too cute as he tried to cram three separate cases (k=0, k=+1, k=-1) into single equations.
Well, here is the code he used:

Code:
        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
        }
Quote:
applying an easy bit of algebra and calculus to equation (7) yields
c t(z) = (c/H0) (z/(1+z))
That is Mike Helland's equation relating distance to redshift, for the model he referred to as "LCDM in a default state".
Yep. Had that never been discovered before?

FWIW, H0 never changes, so the 0 isn't actually necessary.

Quote:
This table shows distances obtained by multiplying the speed of light times lookback times for various models and red shifts, taking H0=70 km/s/Mpc.
H0 is measured to be 74 km/s/Mpc.

Why do you use 70? Is it because FLRW doesn't hold up with the measured value?

Quote:
Taken at face value, these observations are at odds with the Universe being described by the FLRW metric. Moreover, one can argue that there is a maximum value to the Hubble constant within an FLRW cosmology tolerated by current observations, H0 = 71 ± 1 km/s/Mpc, and depending on how local determinations converge, this may point to a breakdown of the FLRW metric in the late universe, necessitating an explanation beyond the FLRW metric.
https://en.wikipedia.org/wiki/Friedm...3Walker_metric

Does Hubble Tension Signal a Breakdown in FLRW Cosmology?

https://arxiv.org/abs/2105.09790
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Old 25th November 2022, 02:58 PM   #284
W.D.Clinger
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Originally Posted by Mike Helland View Post
Quote:
As for how Cappi messed up these equations, it seems pretty clear that he got too cute as he tried to cram three separate cases (k=0, k=+1, k=-1) into single equations.
Well, here is the code he used:
I had not looked at Cappi's code or calculator at all. In the code you quoted, he has three separate calculations for the three cases, so his code does not actually match the equations in his paper. That is a good thing, because he messed up his equations (4) and (6) by trying to cram all three cases into a single equation.

Originally Posted by Mike Helland View Post
FWIW, H0 never changes, so the 0 isn't actually necessary.
H is the Hubble parameter, which change with time. H0 is the value of the Hubble parameter at the present day, which is a constant. The subscript is necessary so readers will know whether I'm talking about the Hubble parameter (which changes with time) or the Hubble constant.

Originally Posted by Mike Helland View Post
Quote:
This table shows distances obtained by multiplying the speed of light times lookback times for various models and red shifts, taking H0=70 km/s/Mpc.
H0 is measured to be 74 km/s/Mpc.

Why do you use 70? Is it because FLRW doesn't hold up with the measured value?
I used 70 km/s/Mpc because there is still a lot of uncertainty even in recent estimates of the Hubble constant, and 70 is a nice round number that lies within the range of uncertainty for many of those estimates.

Furthermore, H0 ≈ 70 km/s/Mpc was implied by Mike Helland's computations in which his computed distances converge to 14 billion light years as the redshift z increases without bound. As for why Mike Helland assumed H0 ≈ 70 for his own calculations, but is now making an issue of my adoption of that same estimate, readers are free to draw their own conclusions.

Cappi's equations are based upon straightforward FLRW models, and all calculations compatible with Cappi's equations and calculator (such as Mike Helland's own calculations) also assume FLRW models. As I have said, mainstream cosmologists are willing to consider effects that elaborate upon the basic FLRW models. One example of that willingness is the preprint cited by Mike Helland in his most recent contribution to this thread.
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Old 25th November 2022, 08:45 PM   #285
Mike Helland
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Originally Posted by W.D.Clinger View Post
I had not looked at Cappi's code or calculator at all.
Since the paper was merely documentation for his code, I think you should have.

I posted it in full in post 205:

http://www.internationalskeptics.com...&postcount=205

Apparently you like to not read things and then judge them.

Quote:
H is the Hubble parameter, which change with time. H0 is the value of the Hubble parameter at the present day, which is a constant. The subscript is necessary so readers will know whether I'm talking about the Hubble parameter (which changes with time) or the Hubble constant.
It changes in your formula. But not mine.

Read. Think. Understand.
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Old 26th November 2022, 06:58 PM   #286
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Note: In several previous posts, I wrote t1 for the present day and t0 for the earlier time at which redshifted photons were emitted. That was inconsistent with the standard convention, in which t0 is the present day and t1 the earlier time at which redshifted photons were emitted. In what follows I am following the standard convention, in which t1 < t0.

Originally Posted by Mike Helland View Post
Quote:
H is the Hubble parameter, which change with time. H0 is the value of the Hubble parameter at the present day, which is a constant. The subscript is necessary so readers will know whether I'm talking about the Hubble parameter (which changes with time) or the Hubble constant.
It changes in your formula. But not mine.

Read. Think. Understand.
Your very own equation contradicts you.

Your equation relating distance to redshift is
d = (c/H0) (z / (1+z))
Equivalently, since you obtain the distance by multiplying the lookback time t by the speed of light c,
t = (1/H0) (z / (1+z)) = t0 - t1
The redshift z is defined by the equation
1 + z = a(t0) / a(t1) = λ(t0) / λ(t1) = f(t1) / f(t0)
where
  • t0 is the present time, at which the redshifted photons are received
  • t1 is the time at which those photons were emitted
  • a(t0) is the FLRW scale factor at the present day
  • a(t1) is the FLRW scale factor for the time at which the photons were emitted
  • t = t0 - t1 is the lookback time
  • λ(t0) is the redshifted wavelength of the photons emitted at time t1, which is known because it is measured
  • λ(t1) is the wavelength of the photons when they were emitted at t1, which is known because it is the same as the wavelength of those emission/absorption lines as measured in laboratories today
  • f(t1) is the frequency of the photons when they were emitted at t1, which is known because it is the same as the frequency of those emission/absorption lines as measured in laboratories today
  • f(t0) is the redshifted frequency of the photons emitted at time t1, which is known because it is measured
The Hubble parameter H(t1) is defined by
H = (da/dt1) / a(t1)
I'm being careful to write t1 instead of t in that equation, because it is easy to get confused between the time t1 (reckoned from an arbitrary origin) and the lookback time t defined by t = t0 - t1. If you get those two confused, you'll probably get a minus sign wrong in your derivatives.

Those three equations imply
da/dt1 = H0 a(t0)
(which is, surprisingly, a constant) which implies in turn that the value of the Hubble parameter is given by
H(t1) = H0 (1 + z)
where
  • H0 = H(t0) is the value of the Hubble parameter at the present day
  • z = H0 t / (1 - H0t) = H0 (t0 - t1) / (1 - H0 (t0 - t1)) = (a0 - a1) - 1
From the fact that
H(t1) = H0 (1 + z)
it is obvious that the value of the Hubble parameter changes over time in Mike Helland's model.

I found it surprising that, according to Mike Helland's equation, the Hubble parameter was greater in the past and is decreasing at the present day. That is a consequence of Mike Helland's selection of a very peculiar FLRW model in which the universe is entirely devoid of matter, radiation, and dark energy, but space is strongly curved in the negative direction.

It should be noted that I am not accusing Mike Helland of being aware that his equation implicitly assumed that model. He was aware that his equation relating distance to redshift assumed ΩM = ΩΛ = 0, which was already unrealistic, but his recent posts suggest he was at least as surprised as anyone else to learn that his equation assumed an FLRW model with a substantial amount of negative spatial curvature.
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Old 26th November 2022, 08:09 PM   #287
Mike Helland
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Originally Posted by W.D.Clinger View Post
From the fact that
H(t1) = H0 (1 + z)
it is obvious that the value of the Hubble parameter changes over time in Mike Helland's model.

I found it surprising that, according to Mike Helland's equation, the Hubble parameter was greater in the past and is decreasing at the present day. That is a consequence of Mike Helland's selection of a very peculiar FLRW model in which the universe is entirely devoid of matter, radiation, and dark energy, but space is strongly curved in the negative direction.
The Hubble term does not change in my model.

The universe is also not absent of matter.

It's just that matter doesn't effect redshift. You must know that (about my equation). But you choose to pretend otherwise.

Is everything ok with you?
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Old 26th November 2022, 08:23 PM   #288
Mike Helland
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Originally Posted by Mike Helland View Post
Yep. Had that never been discovered before?
How is it this equation had never been discovered before?

I will tell you. WWII

In the 1920's cosmological redshift was discovered. But it was very very small.

Now, you could say an electron has -1 charge, and a proton has a +1 charge. Inherently, we would assume charges can be arbitrarily negative or positive.

Let's say the same about redshifts. Red being positive and blue being negative is arbitrary.

But it isn't.

The entire domain in the positive equals, reversed, only equal up to -1.





In the 1920's and 1930's this would have been prudent. The redshifts aren't that large. No one expected them to be z=1, much less z=10.

In December of 1941, Hubble announced to the world that the expanding universe idea was wrong. But this was a week after Pearl Harbor. The word's most well known astronomer was assigned to a wind tunnel to study ballistics for the war effort.

Years later, no one questioned the expanding universe, much less than quantification of redshift.

The steady state universe was an expanding one, btw, if anyone thought that would be worth bringing up.

Last edited by Mike Helland; 26th November 2022 at 08:48 PM.
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Old 27th November 2022, 07:28 AM   #289
W.D.Clinger
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In my previous post, I wrote:
Originally Posted by W.D.Clinger View Post
I found it surprising that, according to Mike Helland's equation, the Hubble parameter was greater in the past and is decreasing at the present day. That is a consequence of Mike Helland's selection of a very peculiar FLRW model in which the universe is entirely devoid of matter, radiation, and dark energy, but space is strongly curved in the negative direction.
I shouldn't have been surprised by that.

As explained by Wikipedia, with italicized "not" as in the original:
Originally Posted by Wikipedia
Another common source of confusion is that the accelerating universe does not imply that the Hubble parameter is actually increasing with time; since H ( t ) ≡ ȧ ( t ) / a ( t ), in most accelerating models a increases relatively faster than ȧ, so H decreases with time. (The recession velocity of one chosen galaxy does increase, but different galaxies passing a sphere of fixed radius cross the sphere more slowly at later times.)

This is madness:
Originally Posted by Mike Helland View Post
The Hubble term does not change in my model.
(ETA: In the context of that sentence, Mike Helland is saying the Hubble parameter H does not change over time in his model. In the past, Mike Helland has often appeared to be confused about the distinction between the Hubble parameter H and the Hubble constant H0, and it is possibly that he was confused when he wrote that sentence or is hoping the possibly deliberate ambiguity of "the Hubble term" will confuse others.)

It is a mathematical fact that, when we combine the Helland equation
d = (c/H0) (z/(1+z))
with the two mainstream physics equations that define the redshift z and the Hubble parameter H, we find that the value of the Hubble parameter changes with time in whatever model Mike Helland thinks he's using.

We don't need to discuss the details of Mike Helland's model, because the time-varying Hubble parameter follows directly from the Helland equation and the mainstream definitions of z and H.

By saying "The Hubble term does not change in my model", Mike Helland is telling us that he rejects at least one of these three equations:
  • d = (c/H0) (z/(1+z))
  • z = a(t0) / a(t1)
  • H ≡ ȧ ( t ) / a ( t )

By rejecting one or more of those equations, Mike Helland is abandoning at least one of these three claims:
  1. the Helland equation tells how to calculate distance d from redshift z
  2. Mike Helland's equations and calculations are consistent with mainstream physics
  3. "The Hubble term does not change in my model."
To my great surprise, it has been established that claims 1 and 2 are tenable in the following sense: The Helland equation really does describe the relationship between distance d and redshift z in a completely unrealistic FLRW model where ΩM = ΩΛ = ΩR = 0, and ΩΛ = 1 (which is hundreds of times larger than would be consistent with observation).

Because claims 1 and 2 are tenable in that sense, Mike Helland could have declared victory. With claim 3, however, his second claim collapses. Regardless of the details of Mike Helland's model, claims 1 and 2 support a mathematical proof that claim 3 is false.

Mike Helland doesn't have many options here. He can abandon claim 1, he can abandon claim 2, or he can abandon claim 3. If he persists in claiming all 3, then Mike Helland is arguing with high school algebra and calculus.

Originally Posted by Mike Helland View Post
The universe is also not absent of matter.

It's just that matter doesn't effect redshift. You must know that (about my equation). But you choose to pretend otherwise.
"Matter doesn't [a]ffect redshift" is not consistent with mainstream physics.

It seems therefore that Mike Helland is abandoning his claim 2 above.

Despite his recent repetitions of claim 2:

Originally Posted by Mike Helland View Post
My calculations are standard mainstream stuff.
Originally Posted by Mike Helland View Post
There are no Helland physic here. Just standard redshift and lookback calculations.

Last edited by W.D.Clinger; 27th November 2022 at 07:33 AM. Reason: added ETA
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Old 27th November 2022, 08:23 AM   #290
Mike Helland
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Originally Posted by W.D.Clinger View Post
By saying "The Hubble term does not change in my model", Mike Helland is telling us that he rejects at least one of these three equations:
  • d = (c/H0) (z/(1+z))
  • z = a(t0) / a(t1)
  • H ≡ ȧ ( t ) / a ( t )
2 and 3. Since space isn't expanding in my model, anything with the scale factor is abandoned.

My claim was that my equation predicts the same lookback times as an FLRW model where gravity doesn't counteract redshifts.

A little context would be helpful here. In 1915 Einstein came up with general relativity. It was around 1919 that he applied the theory to the universe as a whole. At the time, Babe Ruth played for the Red Sox, and galaxies hadn't been discovered yet.

So he was applying GR to a field of stars. He noted this would collapse. Where does it collapse? Toward us? Seems a bit anti-Copernican.

In any case, we're making an assumption here. Let me elaborate.

Imagine you're watching a play, and the actors say their lines and make their motions.

Now imagine the same play where the stage is expanding, and the actors are all moving away from each other. Do the actors still say their lines and move about as they did before? Or do they realize they are moving away from each other, and then move toward each other to try to stay where they were?

Applying GR to the universe as a whole assumes the latter. Space isn't just expanding, but the things in it are counteracting the expansion.

If we assume the former, that space expands, and the actors (which include gravity and electromagnetism) play their roles with this new dynamic of spacetime rather than against it, you get a universe that always expands and will never collapse (negative curvature). And you eliminate the need for dark energy entirely.

In FLRW models, gravity does counter act redshifts, assuming the matter density is greater than zero. I'm not advocating any FLRW model. In those models, we don't exist:

Quote:
In a strictly FLRW model, there are no clusters of galaxies, stars or people, since these are objects much denser than a typical part of the universe. Nonetheless, the FLRW model is used as a first approximation for the evolution of the real, lumpy universe because it is simple to calculate, and models which calculate the lumpiness in the universe are added onto the FLRW models as extensions. Most cosmologists agree that the observable universe is well approximated by an almost FLRW model, i.e., a model which follows the FLRW metric apart from primordial density fluctuations.
https://en.wikipedia.org/wiki/Friedm...3Walker_metric

Here's a quick recapp of my position.

Redshift is traditionally quantified as:
1+z = Eemit / Eobs
And its relation to distance is:
d = cz / H0
But this is only valid when z<<1 (much less than one).

So we can invert it:
1+b = Eobs / Eemit
And then:
d = -bc / H
Since 1+b=1/(1+z), then b=1/(1+z)-1=-(z/(1+z)), so:

d = z/(1+z) * c/H

This stands separate from GR and FLRW. But the lookback times are identical to FLRW when the matter density of the universe doesn't counteract its expansion.
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Old 27th November 2022, 02:31 PM   #291
W.D.Clinger
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We have witnessed the collapse of Mike Helland's claim that Helland physics is consistent with mainstream physics.
The fact that Mike Helland's claim has collapsed does not preclude the possibility that Mike Helland will continue to repeat the claim that now lies in ruins.


Originally Posted by W.D.Clinger View Post
By saying "The Hubble term does not change in my model", Mike Helland is telling us that he rejects at least one of these three equations:
  • d = (c/H0) (z/(1+z))
  • z = a(t0) / a(t1)
  • H ≡ ȧ ( t ) / a ( t )

By rejecting one or more of those equations, Mike Helland is abandoning at least one of these three claims:
  1. the Helland equation tells how to calculate distance d from redshift z
  2. Mike Helland's equations and calculations are consistent with mainstream physics
  3. "The Hubble term does not change in my model."

Mike Helland has abandoned claim 2:

Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
By saying "The Hubble term does not change in my model", Mike Helland is telling us that he rejects at least one of these three equations:
  • d = (c/H0) (z/(1+z))
  • z = a(t0) / a(t1)
  • H ≡ ȧ ( t ) / a ( t )
2 and 3. Since space isn't expanding in my model, anything with the scale factor is abandoned.

By rejecting two of the most important mainstream equations concerning the relationship between redshift and the expansion of space, Mike Helland has abandoned his claim that Helland physics is consistent with mainstream physics.

I'm glad we were finally able to put an end to that charade.
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Old 27th November 2022, 05:46 PM   #292
Mike Helland
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Originally Posted by W.D.Clinger View Post
By rejecting two of the most important mainstream equations concerning the relationship between redshift and the expansion of space, Mike Helland has abandoned his claim that Helland physics is consistent with mainstream physics.

I'm glad we were finally able to put an end to that charade.
I think you're getting two conversations mixed up. We were talking about my equation in one. We were talking about the internal consistency of an expanding universe in the other. The latter was irrelevant to my equation.
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Old 1st December 2022, 08:04 PM   #293
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Originally Posted by W.D.Clinger View Post
To my great surprise, it has been established that claims 1 and 2 are tenable in the following sense: The Helland equation really does describe the relationship between distance d and redshift z in a completely unrealistic FLRW model where ΩM = ΩΛ = ΩR = 0, and ΩΛ = 1 (which is hundreds of times larger than would be consistent with observation).
I did find this:



https://arxiv.org/abs/astro-ph/9306002

I think what's interesting about that is:
1 + z = Eemit / Eobs
t = z / H0

where z << 1
But, if they had chose to quantify redshift as negative blueshift, they would have found:
1 + b = Eobs / Eemit
t = -b / H0

since:
1 + b = 1 / (1 + z)
b = 1 / (1 + z) - 1
b = -(z / (1 + z))
t = H0-1 (z / (1+z))
I think the best way to quantify it though would be as an energy scalar Q:
Q = Eobs / Eemit
The 1+z and 1+b formulas give valid result between -1 and infinity.

On the other hand Q is always positive, and is directly related to the energy of a photon. Seems to more closely follow nature than arbitrarily preferring redshift or blueshift to be positive or negative.
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Old 2nd December 2022, 08:49 AM   #294
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correcting an editing error

I just now noticed this error because Mike Helland quoted it:
Originally Posted by W.D.Clinger View Post
To my great surprise, it has been established that claims 1 and 2 are tenable in the following sense: The Helland equation really does describe the relationship between distance d and redshift z in a completely unrealistic FLRW model where ΩM = ΩΛ = ΩR = 0, and ΩΛ = 1 (which is hundreds of times larger than would be consistent with observation).
The highlighted parameter should have been Ωk.
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Old 2nd December 2022, 08:53 AM   #295
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Originally Posted by W.D.Clinger View Post
I just now noticed this error because Mike Helland quoted it:

The highlighted parameter should have been Ωk.
You've mentioned the "hundreds of times of larger" a half dozen times now.

Where do you get that number?
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Old 2nd December 2022, 09:57 AM   #296
W.D.Clinger
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Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
I just now noticed this error because Mike Helland quoted it:

The highlighted parameter should have been Ωk.
You've mentioned the "hundreds of times of larger" a half dozen times now.

Where do you get that number?

If you'd been paying attention, you'd have read this ten days ago:
Originally Posted by W.D.Clinger View Post
Ωk=1 is hundreds of times more curvature than would be consistent with the Planck mission's observations:
Originally Posted by Wikipedia
Final results of the Planck mission, released in 2018 show the cosmological curvature parameter, 1 – Ω = ΩK = –K c²/a²H², to be 0.0007±0.0019, consistent with a flat universe.[18] (i.e. positive curvature: K = +1, Ωκ < 0, Ω > 1, negative curvature: K = −1, Ωκ > 0, Ω < 1, zero curvature: K = 0, Ωκ = 0, Ω = 1).

And you'd have read this five days ago:
Originally Posted by W.D.Clinger View Post
Ωk=1 is hundreds of times more curvature than would be consistent with the Planck mission's observations:
Originally Posted by Wikipedia
Final results of the Planck mission, released in 2018 show the cosmological curvature parameter, 1 – Ω = ΩK = –K c²/a²H², to be 0.0007±0.0019, consistent with a flat universe.[18] (i.e. positive curvature: K = +1, Ωκ < 0, Ω > 1, negative curvature: K = −1, Ωκ > 0, Ω < 1, zero curvature: K = 0, Ωκ = 0, Ω = 1).

And just last night, you could have found the excerpt quoted immediately above by following the link in this paragraph you quoted:
Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
To my great surprise, it has been established that claims 1 and 2 are tenable in the following sense: The Helland equation really does describe the relationship between distance d and redshift z in a completely unrealistic FLRW model where ΩM = ΩΛ = ΩR = 0, and ΩΛ = 1 (which is hundreds of times larger than would be consistent with observation).
ETA: As I noted earlier this morning, the highlighted parameter should have been Ωk.

Last edited by W.D.Clinger; 2nd December 2022 at 10:00 AM. Reason: added the last sentence
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Old 2nd December 2022, 10:07 AM   #297
Mike Helland
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Originally Posted by W.D.Clinger View Post
If you'd been paying attention
I am. And I'm wondering, why do you keep saying "hundreds"?

Are you comparing 0.0007±0.0019 to zero?
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Old 2nd December 2022, 11:50 AM   #298
W.D.Clinger
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Mike Helland needs some help with arithmetic.

Originally Posted by Mike Helland View Post
I am. And I'm wondering, why do you keep saying "hundreds"?

Are you comparing 0.0007±0.0019 to zero?

No. I am comparing the observed value of Ωk = 0.0007±0.0019 to your assumption that Ωk = 1.

0.0007 + 0.0019 = 0.0026
0.0007 - 0.0019 = -0.0012
1 / 0.0026 ≈ 384.6
1 / -0.0012 ≈ -833.3

To be clear, I am not accusing you of being aware that your Helland equation, like the values you calculated using Cappi's calculator with ΩM = ΩΛ = ΩR = 0, assumed Ωk = 1. To the contrary, I think it's pretty clear that you have been more or less completely clueless concerning Cappi's paper (which you cited repeatedly and quoted) and concerning Cappi's calculator (which you relied upon repeatedly, as its agreement with your Helland equation was the entire basis for your claim that your equation matched calculations based on mainstream physics). You didn't realize you were assuming Ωk = 1, so you didn't realize you were assuming a model with hundreds of times more curvature than is consistent with observation.

But your cluelessness does not excuse the fact that your equation and calculations assumed a degree of negative curvature that is hundreds of times greater than would be consistent with observations made by the Planck mission.
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Old 4th December 2022, 03:36 PM   #299
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Originally Posted by W.D.Clinger View Post
No. I am comparing the observed value of Ωk = 0.0007±0.0019 to your assumption that Ωk = 1.

0.0007 + 0.0019 = 0.0026
0.0007 - 0.0019 = -0.0012
1 / 0.0026 ≈ 384.6
1 / -0.0012 ≈ -833.3
That's pretty funny. If you use 0.0007 its thousands of times off. And if you use 1 * 10-45 its 45 orders of magnitude off, and then there's also a vertical asymptote in the domain too, which is actually what its expected to be. That's why I wondered about the hundreds thing. It's a pretty arbitrary claim.

Quote:
But your cluelessness does not excuse the fact that your equation and calculations assumed a degree of negative curvature that is hundreds of times greater than would be consistent with observations made by the Planck mission.
Ignoring your insults, yes, I'm perfectly aware of that. That's my point.

Here is an expanding universe with no matter to counteract it (red line).



That's Pure Expansion.

Here's the same universe with matter and gravitation that counteracts expansion (red line):



That's Expansion + Attraction.

We know the universe must be older than 9 billion years, so that's clearly wrong. We can add dark energy to sort of right the wrong there (red line):



That's Expansion + Attraction + Repulsion.

In order, you have negative curvature, then positive curvature, and then none (or very very little).

However, since my equation (black line) is not based on GR, and since I doubt the universe is expanding, and I doubt that gravity affects redshifts, and thus I doubt the need for dark energy, you get this universe:



This universe has light that redshifts. No curvature or FLRW necessary. (edit: and I don't mean it has zero curvature. I'm mean the concept is absent in this treatment of redshift.)

As distance measurements continue to advance further out, the slight differences between the predictions of my equation, and those of the mainstream LCDM (ΩM=0.3 and ΩΛ=0.7) will be testable by observation.

I get that most people believe in the CMB because its evidence of the big bang. But since I doubt all that, why should I believe it?

Do you know specifically how measurements of the CMB are made, and how you arrive at Ωk = 0.0007±0.0019? Seems about akin to looking at the coals of campfire, and proclaiming you can tell what stories were told around it.

Last edited by Mike Helland; 4th December 2022 at 04:41 PM.
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Old Yesterday, 06:22 AM   #300
W.D.Clinger
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Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
No. I am comparing the observed value of Ωk = 0.0007±0.0019 to your assumption that Ωk = 1.

0.0007 + 0.0019 = 0.0026
0.0007 - 0.0019 = -0.0012
1 / 0.0026 ≈ 384.6
1 / -0.0012 ≈ -833.3
That's pretty funny. If you use 0.0007 its thousands of times off. And if you use 1 * 10-45 its 45 orders of magnitude off, and then there's also a vertical asymptote in the domain too, which is actually what its expected to be. That's why I wondered about the hundreds thing. It's a pretty arbitrary claim.
My statement was conservative, not arbitrary. The Ωk = 1 you assumed when using Cappi's calculator is at least several hundred times any curvature that would be consistent with the Planck observations.

Originally Posted by Mike Helland View Post
Quote:
But your cluelessness does not excuse the fact that your equation and calculations assumed a degree of negative curvature that is hundreds of times greater than would be consistent with observations made by the Planck mission.
Ignoring your insults, yes, I'm perfectly aware of that. That's my point.

Here is an expanding universe with no matter to counteract it (red line).



That's Pure Expansion.
It is the spatial expansion predicted by mainstream physics for a universe totally devoid of matter and energy, but with negative spatial curvature that is hundreds of times (at least!) greater than would be consistent with observations.

It is not the spatial expansion predicted by Helland physics, because Helland physics rejects the concept of spatial expansion.

Originally Posted by Mike Helland View Post
However, since my equation (black line) is not based on GR, and since I doubt the universe is expanding, and I doubt that gravity affects redshifts, and thus I doubt the need for dark energy, you get this universe:



This universe has light that redshifts. No curvature or FLRW necessary. (edit: and I don't mean it has zero curvature. I'm mean the concept is absent in this treatment of redshift.)

That's Helland physics. As indicated by the phrases I highlighted both above and below, Helland physics is based on one person's personal incredulity and ignorance of mainstream physics, including his rejection of general relativity.

Originally Posted by Mike Helland View Post
As distance measurements continue to advance further out, the slight differences between the predictions of my equation, and those of the mainstream LCDM (ΩM=0.3 and ΩΛ=0.7) will be testable by observation.

I get that most people believe in the CMB because its evidence of the big bang. But since I doubt all that, why should I believe it?
You are the world's foremost authority on Helland physics, so you can make up whatever stories you like.

You have yet to suggest a reason for anyone else to pay the slightest attention to Helland physics.

Originally Posted by Mike Helland View Post
Do you know specifically how measurements of the CMB are made, and how you arrive at Ωk = 0.0007±0.0019? Seems about akin to looking at the coals of campfire, and proclaiming you can tell what stories were told around it.

That may be what mainstream science looks like to Mike Helland, but that's not the impression I get from reading papers such as this:
Planck Collaboration: N. Aghanim, Y. Akrami, [etc; the 181 co-authors are listed in alphabetical order]. Planck 2018 results. VI. Cosmological parameters. Astronomy & Astrophysics special issue, Volume 641, A6, September 2020. https://doi.org/10.1051/0004-6361/201833910
Originally Posted by Planck Collaboration
ABSTRACT

We present cosmological parameter results from the final full-mission Planck measurements of the cosmic microwave background (CMB) anisotropies, combining information from the temperature and polarization maps and the lensing reconstruction. Compared to the 2015 results, improved measurements of large-scale polarization allow the reionization optical depth to be measured with higher precision, leading to significant gains in the precision of other correlated parameters....The joint constraint with BAO [baryon acoustic oscillation] measurements on spatial curvature is consistent with a flat universe, ΩK = 0.001 ± 0.002....

1. Introduction

Since their discovery..., temperature anisotropies in the cosmic microwave background (CMB) have become one of the most powerful ways of studying cosmology and the physics of the early Universe....Our first results....were based on temperature (TT) power spectra and CMB lensing measurements...combined with the Wilkinson Microwave Anisotropy Probe (WMAP) polarization likelihood at multipoles ℓ ≤ 23...to constrain the reionization optical depth τ....Planck Collaboration XIII...reported substantial improvements in the characterization of the Planck beams and absolute calibration....The focus...was on temperature observations, though we reported preliminary results on the high-multipole TE and EE polarization spectra. In addition, we used polarization measurements at low multipoles from the Low Frequency Instrument (LFI) to constrain the value of τ.
That introduction goes on for one and a half pages, relating the continuing improvements in such measurements. Section 2, which explains the methodology, goes on for ten and a half pages. Section 3, which states consequent constraints for the base ΛCDM model, goes on for five and a half pages. And so on. The entire paper is 67 pages long.
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Old Yesterday, 11:50 AM   #301
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Originally Posted by W.D.Clinger View Post
That's Helland physics. As indicated by the phrases I highlighted both above and below, Helland physics is based on one person's personal incredulity and ignorance of mainstream physics, including his rejection of general relativity.
I don't reject GR.

GR predicts an accurate orbit for Mercury and GPS satellites, using metrics that are not FLRW.

When Einstein and Friedmann were applying GR to the universe as a whole, galaxies had not yet been discovered. It was a field of stars.

For FLRW to work, there can be no empty space and there can be no bodies (rocks, planets, stars, galaxies, etc). Clearly it does not represent reality.


Quote:
You have yet to suggest a reason for anyone else to pay the slightest attention to Helland physics.
It's a testable alternative treatment of redshifts to LCDM, and here are the problems with LCDM:

https://en.wikipedia.org/wiki/Lambda...del#Challenges

Code:
    5.1 Lack of detection
    5.2 Violations of the cosmological principle
        5.2.1 Violations of isotropy
        5.2.2 Violations of homogeneity
    5.3 El Gordo galaxy cluster collision
    5.4 KBC void
    5.5 Hubble tension
    5.6 S8 tension
    5.7 Axis of evil
    5.8 Cosmological lithium problem
    5.9 Shape of the universe
    5.10 Violations of the strong equivalence principle
    5.11 Cold dark matter discrepancies
        5.11.1 Cuspy halo problem
        5.11.2 Dwarf galaxy problem
        5.11.3 Satellite disk problem
        5.11.4 High-velocity galaxy problem
        5.11.5 Galaxy morphology problem
        5.11.6 Fast galaxy bar problem
        5.11.7 Small scale crisis
    5.12 Missing baryon problem
    5.13 Unfalsifiability
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Old Yesterday, 01:12 PM   #302
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Originally Posted by Mike Helland View Post
For FLRW to work, there can be no empty space and there can be no bodies (rocks, planets, stars, galaxies, etc). Clearly it does not represent reality.
No, this is wrong. The universe must be uniform above some scale and above, but non-uniformities at smaller scales are fine.

Quote:
It's a testable alternative treatment of redshifts to LCDM
Helland physics has already failed multiple tests. Have you forgotten? I have not.
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Old Yesterday, 01:45 PM   #303
W.D.Clinger
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Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
That's Helland physics. As indicated by the phrases I highlighted both above and below, Helland physics is based on one person's personal incredulity and ignorance of mainstream physics, including his rejection of general relativity.
I don't reject GR.
You don't realize you're rejecting general relativity. Not realizing that you are rejecting GR is not the same as not rejecting GR.

Originally Posted by Mike Helland View Post
GR predicts an accurate orbit for Mercury and GPS satellites, using metrics that are not FLRW.
Yes, the Schwarzschild model is an exact solution of the Einstein field equations, just as the FLRW models are exact solutions of those same equations.

Scientists understand that a model that serves as a suitable idealization for one set of circumstances may not be a suitable idealization for other sets of circumstances.

Originally Posted by Mike Helland View Post
When Einstein and Friedmann were applying GR to the universe as a whole, galaxies had not yet been discovered. It was a field of stars.

For FLRW to work, there can be no empty space and there can be no bodies (rocks, planets, stars, galaxies, etc). Clearly it does not represent reality.
Scientists understand that the FLRW models are idealized models, and are quite willing to consider perturbations, extensions, and other tweaks that may improve the usefulness of those models.

More generally:
Originally Posted by W.D.Clinger
Scientific models are simplified descriptions of messy reality.

Depending on our purposes, some models may be better than others. Good models are abstract enough to be tractable, yet accurate enough to draw conclusions matching the aspects of reality we hope to understand.
Mike Helland does not understand the nature of scientific models.

Originally Posted by Mike Helland View Post
Quote:
You have yet to suggest a reason for anyone else to pay the slightest attention to Helland physics.
It's a testable alternative treatment of redshifts to LCDM,
Here are a couple of the more obvious tests we might apply when trying to decide between mainstream and Helland physics:
  • Expansion/contraction of the universe.
    • General relativity says universes that are neither expanding nor contracting are unstable, with minor perturbations leading to local or global expansion or contraction.
    • Helland physics says the universe is neither expanding nor contracting.
  • Hubble-Lemaitre Law
    • In 1927, Georges Lemaître used the family of FLRW models to derive what is now known as the Hubble-Lemaitre Law, and was the first to publish an estimate of the so-called Hubble constant that was based on astronomical observations. This was two years before Hubble published anything on the subject.
    • Helland physics has no coherent explanation for the Hubble-Lemaitre Law.
  • Big Bang
    • In 1927, Lemaître used the family of FLRW models to suggest the universe began with a "primordial atom", now known as the Big Bang.
    • Helland physics does not contemplate a primordial atom or Big Bang.
  • Cosmic microwave radiation and nucleosynthesis
    • In a series of papers between 1946 and 1956, George Gamov and others (notably Ralph Alpher and Hans Bethe, if only because of the pun in their authorship of the Alpher/Bethe/Gamov paper) predicted the Big Bang would produce a cosmic temperature (i.e. background radiation) they ultimately estimated at 6 K, and also explained/predicted the abundance of light elements in the early universe.
    • Helland physics has no explanation for the cosmic microwave background radiation, and does not predict anything about the abundance of light elements in the early universe.

Originally Posted by Mike Helland View Post
and here are the problems with LCDM:

https://en.wikipedia.org/wiki/Lambda...del#Challenges

Code:
    5.1 Lack of detection
    5.2 Violations of the cosmological principle
        5.2.1 Violations of isotropy
        5.2.2 Violations of homogeneity
    5.3 El Gordo galaxy cluster collision
    5.4 KBC void
    5.5 Hubble tension
    5.6 S8 tension
    5.7 Axis of evil
    5.8 Cosmological lithium problem
    5.9 Shape of the universe
    5.10 Violations of the strong equivalence principle
    5.11 Cold dark matter discrepancies
        5.11.1 Cuspy halo problem
        5.11.2 Dwarf galaxy problem
        5.11.3 Satellite disk problem
        5.11.4 High-velocity galaxy problem
        5.11.5 Galaxy morphology problem
        5.11.6 Fast galaxy bar problem
        5.11.7 Small scale crisis
    5.12 Missing baryon problem
    5.13 Unfalsifiability
Real scientists welcome challenges, and (as I stated above) are quite willing to consider perturbations, extensions, and other tweaks that may improve the usefulness of idealized models that succeed in predicting/explaining the gist of observed phenomena but may fall short when it comes to more specialized details.

With regard to the challenges cited above, Helland physics has nothing to offer. Mike Helland has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.

Last edited by W.D.Clinger; Yesterday at 01:48 PM.
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Old Yesterday, 01:58 PM   #304
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Originally Posted by W.D.Clinger View Post
Yes, the Schwarzschild model is an exact solution of the Einstein field equations, just as the FLRW models are exact solutions of those same equations.

Scientists understand that a model that serves as a suitable idealization for one set of circumstances may not be a suitable idealization for other sets of circumstances.
The general theory of relativity seems to be a bit special in this regard, that it's not a single equation, like Newton's law of gravity, but a 4 dimensional Pythagorean theorem in non-Euclidean geometry that acts almost like an operating system given a coordinate system and metric.

GTR itself does not rely on any particular metric, including FLRW, being accurate representations of reality.


Quote:
With regard to the challenges cited above, Helland physics has nothing to offer. Mike Helland has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
Simply being in disagreement with conventional wisdom is not a challenge.

Being in disagreement with observation is. And LCDM has that in spades.
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Old Yesterday, 02:03 PM   #305
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Originally Posted by Ziggurat View Post
No, this is wrong. The universe must be uniform above some scale and above, but non-uniformities at smaller scales are fine.
Ok. So what scale?

https://en.wikipedia.org/wiki/Lambda...ical_principle

The Giant Arc is 1 billion parsecs long.

So I'm guessing more than that?

Quote:
Helland physics has already failed multiple tests. Have you forgotten? I have not.
If you're referring to the equation where the speed of light changes and the least time theorem, that's one thing.

But the equation that W.D.Clinger has dubbed the Helland equation does not change the speed of light.
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Old Yesterday, 02:20 PM   #306
W.D.Clinger
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No one with any serious knowledge of science in general, or general relativity in particular, would have written this:
Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
Yes, the Schwarzschild model is an exact solution of the Einstein field equations, just as the FLRW models are exact solutions of those same equations.

Scientists understand that a model that serves as a suitable idealization for one set of circumstances may not be a suitable idealization for other sets of circumstances.
The general theory of relativity seems to be a bit special in this regard, that it's not a single equation, like Newton's law of gravity, but a 4 dimensional Pythagorean theorem in non-Euclidean geometry that acts almost like an operating system given a coordinate system and metric.

Maxwell's equations, as taught in freshman physics, consist of four equations:Those four equations were not unified into a single equation until Einstein's special theory of relativity showed how they could be regarded as a single equation. That single equation, however, is a tensor equation that, when written in coordinate-dependent notation, abbreviates 16 equations, of which only 6 are independent equations. (Just as Einstein's field equations are a single tensor equation that, when written in coordinate-dependent notation, abbreviates 16 equations, of which only 10 are independent equations.)

So Mike Helland is asserting his ignorance of Maxwell's equations as well as his ignorance of the fundamental equation(s) of general relativity.

As for the idea that Einstein's field equations are "a 4 dimensional Pythagorean theorem in non-Euclidean geometry", well, no. Even apart from the fact that Pythagoras died more than a century before Euclidean geometry became a thing, and a couple of thousand years before non-Euclidean geometry was recognized as legitimate, Einstein's field equations are not a theorem of any branch of mathematics. Einstein's field equations express a theory about the real world, not a theorem that can be proved from geometrical axioms.
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Old Yesterday, 02:21 PM   #307
Mike Helland
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Originally Posted by W.D.Clinger View Post
With regard to the challenges cited above, Helland physics has nothing to offer.
Helland physics (your name for it) resolves nearly every one of those issues except those related to dark matter.
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Old Yesterday, 02:23 PM   #308
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Originally Posted by W.D.Clinger View Post
No one with any serious knowledge of science in general, or general relativity in particular, would have written this:



Maxwell's equations, as taught in freshman physics, consist of four equations:Those four equations were not unified into a single equation until Einstein's special theory of relativity showed how they could be regarded as a single equation. That single equation, however, is a tensor equation that, when written in coordinate-dependent notation, abbreviates 16 equations, of which only 6 are independent equations. (Just as Einstein's field equations are a single tensor equation that, when written in coordinate-dependent notation, abbreviates 16 equations, of which only 10 are independent equations.)

So Mike Helland is asserting his ignorance of Maxwell's equations as well as his ignorance of the fundamental equation(s) of general relativity.
Maxwell had 20 equations. Heaviside made them into 4.

But go on. Tell me I am ignorant over and over.

Quote:
As for the idea that Einstein's field equations are "a 4 dimensional Pythagorean theorem in non-Euclidean geometry", well, no. Even apart from the fact that Pythagoras died more than a century before Euclidean geometry became a thing, and a couple of thousand years before non-Euclidean geometry was recognized as legitimate, Einstein's field equations are not a theorem of any branch of mathematics. Einstein's field equations express a theory about the real world, not a theorem that can be proved from geometrical axioms.
https://www.worldscientific.com/doi/...812814128_0030
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Old Yesterday, 02:31 PM   #309
W.D.Clinger
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Originally Posted by Mike Helland View Post
Maxwell had 20 equations. Heaviside made them into 4.
What part of "as taught in freshman physics" are you failing to understand?

Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
With regard to the challenges cited above, Helland physics has nothing to offer.
Helland physics (your name for it) resolves nearly every one of those issues except those related to dark matter.
So says the originator and, so far as I can tell, sole advocate of Helland physics.

Until evidence for such claims is provided, it is fair to note that the sole advocate of Helland physics has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
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Old Yesterday, 02:47 PM   #310
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Originally Posted by W.D.Clinger View Post
So says the originator and, so far as I can tell, sole advocate of Helland physics.

Until evidence for such claims is provided, it is fair to note that the sole advocate of Helland physics has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
What specific claims do you think I'm making?

I would say that quantifying redshift with a preference toward wavelength leads to different time and distance relationships than when you quantify redshit with a preference toward frequency and energy, making it a negative number with a limit at -1.

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Old Yesterday, 04:18 PM   #311
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Originally Posted by W.D.Clinger View Post
Until evidence for such claims is provided, it is fair to note that the sole advocate of Helland physics has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
For context, what you refer to Helland physics is something I came up with a month ago and introduced in this thread:

http://www.internationalskeptics.com...0&postcount=81

As for the problems with LCDM and how "Helland physics" resolves them (excluding dark matter issues):

Quote:
5.1 Lack of detection

Extensive searches for dark matter particles have so far shown no well-agreed detection; the dark energy may be almost impossible to detect in a laboratory, and its value is unnaturally small compared to vacuum energy theoretical predictions.
Since dark energy doesn't exist in my hypothesis, its lack of detection is a nonissue.

Quote:
5.2 Violations of the cosmological principle
5.2.1 Violations of isotropy

Data from the Planck Mission shows hemispheric bias in the cosmic microwave background in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies in the CMB are, in fact, statistically significant and can no longer be ignored.[28]
Only an issue if the CMB is the leftovers of a hot big bang.

Quote:
5.2.2 Violations of homogeneity

Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.[44] However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including

The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc
The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc,[45]
U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc
The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)[46]
The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc[47]
If the universe is indefinitely large and old, and we just see a small observable region, then there's no limit to how big things can be.

The size of things is a non-issue for my hypothesis.

Quote:
5.3 El Gordo galaxy cluster collision
5.4 KBC void
Same goes for those.

Quote:
5.5 Hubble tension

The Hubble tension in cosmology is widely acknowledged to be a major problem for the ΛCDM model.
The measured expansion rate is ~74 km/s/Mpc. Measurements of the CMB, when fed into LCDM predict an expansion rate of ~68 km/s/Mpc.

In my model, the CMB isn't what LCDM says it is, and it does not tell us the rate of expansion. So ~74 km/s/Mpc, the measured rate of expansion, is the only valid one, and thus there is no tension.

Quote:
5.6 S8 tension

Early- (e.g. from CMB data collected using the Planck observatory) and late-time (e.g. measuring weak gravitational lensing events) facilitate increasingly precise values of S 8 {\displaystyle S_{8}} S_8. However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy is called the S 8 {\displaystyle S_{8}} S_8 tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that the ΛCDM model may be incomplete or in need of correction.
Another non-issue if the CMB is not what you think it is.

Quote:
5.7 Axis of evil

The ΛCDM model assumes that the data of the cosmic microwave background and our interpretation of the CMB are correct. However, there exists an apparent correlation between the plane of the Solar System,[61] the rotation of galaxies,[62][63][64] and certain aspects of the CMB. This may indicate that there is something wrong with the data or the interpretation of the cosmic microwave background used as evidence for the ΛCDM model, or that the Copernican principle and cosmological principle are violated.
Says it right there. There may be something wrong with how we interpret CMB.
.
Quote:
5.8 Cosmological lithium problem

The actual observable amount of lithium in the universe is less than the calculated amount from the ΛCDM model by a factor of 3–4.[66][13] If every calculation is correct, then solutions beyond the existing ΛCDM model might be needed.[66]
LCDM predicts the amount of basic elements in the universe. And it can't get the 3rd element right.

My model doesn't predict how much H, or He, or Li is around. It predicts redshifts and distances and lookback times. So the chemical make up of the universe is a non-issue.

Quote:
5.9 Shape of the universe

The ΛCDM model assumes that the shape of the universe is flat (zero curvature). However, recent Planck data have hinted that the shape of the universe might in fact be closed (positive curvature), which would contradict the ΛCDM model.
My model is concerned with redshifts, distances and times. It isn't based on GR, so the shape of the universe is a non-issue.


Quote:
5.12 Missing baryon problem

Note that this value is much lower than the prediction of standard cosmic nucleosynthesis Ω b ≃ 0.0486, so that stars and gas in galaxies and in galaxy groups and clusters account for less than 10% of the primordially synthesized baryons. This issue is known as the problem of the "missing baryons".
There is no "primordial" period in my equation for redshifts, so, again, a non-issue for me.
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Old Yesterday, 08:44 PM   #312
W.D.Clinger
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Originally Posted by Mike Helland View Post
Helland physics (your name for it) resolves nearly every one of those issues except those related to dark matter.
Originally Posted by W.D.Clinger View Post
So says the originator and, so far as I can tell, sole advocate of Helland physics.

Until evidence for such claims is provided, it is fair to note that the sole advocate of Helland physics has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
Originally Posted by Mike Helland View Post
What specific claims do you think I'm making?
I was referring to your claim, quoted above, that "Helland physics...resolves nearly every one of those issues except those related to dark matter."

But that claim wasn't very specific, so I guess you have a point. Not the sort of point in which anyone should take pride, but I guess any kind of point would be a start.

Originally Posted by Mike Helland View Post
Originally Posted by W.D.Clinger View Post
Until evidence for such claims is provided, it is fair to note that the sole advocate of Helland physics has yet to articulate any reason for anyone to pay the slightest attention to Helland physics.
For context, what you refer to Helland physics is something I came up with a month ago and introduced in this thread:

http://www.internationalskeptics.com...0&postcount=81
For context, conspiracy theorists and crackpots like to pretend their "theory" is the only viable alternative to the windmill they're assaulting, so they gleefully point to every flaw in the finishing of that windmill as if that flaw were evidence for their "theory".

Mike Helland is doing a lot of that in what I'm quoting below, but he also goes beyond the usual nonsense by ignoring the purpose or, at times, the very existence of the windmill.

In his remarks I have highlighted in blue, Mike Helland wants us to think Helland physics is superior to mainstream physics because Helland physics doesn't even try to deal with empirical facts that have been predicted or explained, however imperfectly, by mainstream cosmology. We don't often see people come right out and say "my theory is better because it has so little to say", but that's pretty much what Mike Helland is saying here.

Originally Posted by Mike Helland View Post
As for the problems with LCDM and how "Helland physics" resolves them (excluding dark matter issues):

Quote:
5.1 Lack of detection

Extensive searches for dark matter particles have so far shown no well-agreed detection; the dark energy may be almost impossible to detect in a laboratory, and its value is unnaturally small compared to vacuum energy theoretical predictions.
Since dark energy doesn't exist in my hypothesis, its lack of detection is a nonissue.

Quote:
5.2 Violations of the cosmological principle
5.2.1 Violations of isotropy

Data from the Planck Mission shows hemispheric bias in the cosmic microwave background in two respects: one with respect to average temperature (i.e. temperature fluctuations), the second with respect to larger variations in the degree of perturbations (i.e. densities). The European Space Agency (the governing body of the Planck Mission) has concluded that these anisotropies in the CMB are, in fact, statistically significant and can no longer be ignored.[28]
Only an issue if the CMB is the leftovers of a hot big bang.

Quote:
5.2.2 Violations of homogeneity

Based on N-body simulations in ΛCDM, Yadav and his colleagues showed that the spatial distribution of galaxies is statistically homogeneous if averaged over scales 260/h Mpc or more.[44] However, many large-scale structures have been discovered, and some authors have reported some of the structures to be in conflict with the predicted scale of homogeneity for ΛCDM, including

The Clowes–Campusano LQG, discovered in 1991, which has a length of 580 Mpc
The Sloan Great Wall, discovered in 2003, which has a length of 423 Mpc,[45]
U1.11, a large quasar group discovered in 2011, which has a length of 780 Mpc
The Huge-LQG, discovered in 2012, which is three times longer than and twice as wide as is predicted possible according to ΛCDM
The Hercules–Corona Borealis Great Wall, discovered in November 2013, which has a length of 2000–3000 Mpc (more than seven times that of the SGW)[46]
The Giant Arc, discovered in June 2021, which has a length of 1000 Mpc[47]
If the universe is indefinitely large and old, and we just see a small observable region, then there's no limit to how big things can be.

The size of things is a non-issue for my hypothesis.

Quote:
5.3 El Gordo galaxy cluster collision
5.4 KBC void
Same goes for those.

Quote:
5.5 Hubble tension

The Hubble tension in cosmology is widely acknowledged to be a major problem for the ΛCDM model.
The measured expansion rate is ~74 km/s/Mpc. Measurements of the CMB, when fed into LCDM predict an expansion rate of ~68 km/s/Mpc.

In my model, the CMB isn't what LCDM says it is, and it does not tell us the rate of expansion. So ~74 km/s/Mpc, the measured rate of expansion, is the only valid one, and thus there is no tension.

Quote:
5.6 S8 tension

Early- (e.g. from CMB data collected using the Planck observatory) and late-time (e.g. measuring weak gravitational lensing events) facilitate increasingly precise values of S 8 {\displaystyle S_{8}} S_8. However, these two categories of measurement differ by more standard deviations than their uncertainties. This discrepancy is called the S 8 {\displaystyle S_{8}} S_8 tension. The name "tension" reflects that the disagreement is not merely between two data sets: the many sets of early- and late-time measurements agree well within their own categories, but there is an unexplained difference between values obtained from different points in the evolution of the universe. Such a tension indicates that the ΛCDM model may be incomplete or in need of correction.
Another non-issue if the CMB is not what you think it is.

Quote:
5.7 Axis of evil

The ΛCDM model assumes that the data of the cosmic microwave background and our interpretation of the CMB are correct. However, there exists an apparent correlation between the plane of the Solar System,[61] the rotation of galaxies,[62][63][64] and certain aspects of the CMB. This may indicate that there is something wrong with the data or the interpretation of the cosmic microwave background used as evidence for the ΛCDM model, or that the Copernican principle and cosmological principle are violated.
Says it right there. There may be something wrong with how we interpret CMB.
.
Quote:
5.8 Cosmological lithium problem

The actual observable amount of lithium in the universe is less than the calculated amount from the ΛCDM model by a factor of 3–4.[66][13] If every calculation is correct, then solutions beyond the existing ΛCDM model might be needed.[66]
LCDM predicts the amount of basic elements in the universe. And it can't get the 3rd element right.

My model doesn't predict how much H, or He, or Li is around. It predicts redshifts and distances and lookback times. So the chemical make up of the universe is a non-issue.

Quote:
5.9 Shape of the universe

The ΛCDM model assumes that the shape of the universe is flat (zero curvature). However, recent Planck data have hinted that the shape of the universe might in fact be closed (positive curvature), which would contradict the ΛCDM model.
My model is concerned with redshifts, distances and times. It isn't based on GR, so the shape of the universe is a non-issue.


Quote:
5.12 Missing baryon problem

Note that this value is much lower than the prediction of standard cosmic nucleosynthesis Ω b ≃ 0.0486, so that stars and gas in galaxies and in galaxy groups and clusters account for less than 10% of the primordially synthesized baryons. This issue is known as the problem of the "missing baryons".
There is no "primordial" period in my equation for redshifts, so, again, a non-issue for me.
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Old Yesterday, 11:44 PM   #313
Mike Helland
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Originally Posted by W.D.Clinger View Post
I was referring to your claim, quoted above, that "Helland physics...resolves nearly every one of those issues except those related to dark matter."
Ok.


Quote:
For context, conspiracy theorists and crackpots like to pretend their "theory" is the only viable alternative to the windmill they're assaulting, so they gleefully point to every flaw in the finishing of that windmill as if that flaw were evidence for their "theory".
Just so we are clear the "Helland equation" and "Helland physics" are your nomenclature.

I said the distance relationship is"
d = -(1/(1+z)-1) c/H0
You said I should write it as:
d = z/(1+z) c/H0
Which means to me, that's not the Helland equation. That's the Helland/Clinger equation.

Agree?
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Old Yesterday, 11:56 PM   #314
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Mike Helland, you blame Lambda-CDM for not being able to predict certain variations in the CMB, but Helland physics ignores the CMB completely. How can that be better?
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Old Today, 12:22 AM   #315
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Originally Posted by steenkh View Post
Mike Helland, you blame Lambda-CDM for not being able to predict certain variations in the CMB, but Helland physics ignores the CMB completely. How can that be better?
Not sure I get this. LCDM make predictions. They aren't all right.

That's an established fact.


Imagine you ordered a glass of water. When it arrived, the server tipped it over and spilled half of it on your lap. Then poked a few holes in the bottom of the cup before you received it.

That's the CMB (excess energy at the beginning) and redshift (photons leaking energy).

I doubt that's real. The photons redshift (empirical fact) and the energy lost is observed as the CMB.
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Old Today, 12:33 AM   #316
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Originally Posted by Mike Helland View Post
Not sure I get this. LCDM make predictions. They aren't all right.

That's an established fact.


Imagine you ordered a glass of water. When it arrived, the server tipped it over and spilled half of it on your lap. Then poked a few holes in the bottom of the cup before you received it.

That's the CMB (excess energy at the beginning) and redshift (photons leaking energy).

I doubt that's real. The photons redshift (empirical fact) and the energy lost is observed as the CMB.

That is your theory of the CMB?

Why does it have that exact temperature? Why are there fluctuations, and why are they so small?
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Old Today, 12:35 AM   #317
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Originally Posted by Mike Helland View Post
Not sure I get this.
It's not hard to grasp.

1. LCDM makes predictions about the CMB, some of which (though not all) have proved correct

2. Helland physics makes no predictions about the CMB whatsoever

That makes LCDM the superior description of the universe.

If you could use Helland physics to make more accurate predictions about the CMB than LCDM does you might have something worth examining more closely. But you can't, so you don't.
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Old Today, 02:11 AM   #318
Mike Helland
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Originally Posted by steenkh View Post
Mike Helland, you blame Lambda-CDM for not being able to predict certain variations in the CMB, but Helland physics ignores the CMB completely. How can that be better?
Blame?

It could be right.

It could be wrong.

I don't ignore the CMB. I think its the energy lost from redshifting.
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Old Today, 02:13 AM   #319
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Originally Posted by Pixel42 View Post
It's not hard to grasp.

1. LCDM makes predictions about the CMB, some of which (though not all) have proved correct

2. Helland physics makes no predictions about the CMB whatsoever

That makes LCDM the superior description of the universe.

If you could use Helland physics to make more accurate predictions about the CMB than LCDM does you might have something worth examining more closely. But you can't, so you don't.
Well, I get that.
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Old Today, 02:21 AM   #320
Mike Helland
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Originally Posted by steenkh View Post
That is your theory of the CMB?

Why does it have that exact temperature? Why are there fluctuations, and why are they so small?
I don't claim to have a theory of the CMB.

It is either the echo of a hot big bang, or it's not.

I do have a conjecture however. The CMB energy is the energy lost when photons redshift.
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