Poor Sylas;
Poor Tensor.
All excited over nothing at all.
I see we all agree that f_2 varies between 0 and 1 for hydrogen?
Good, Now Sylas here is all excited because at high energies the photoabsorption cross section is 'zero' because f_2 is zero.
But this is the whole point, unless we are at resonance the photon is not 'photoabsorbed' it is re-emitted. None of the photons are retained they all all re-emitted.
Sylas et al are forgetting how light travels through a transparent medium, See my references to French Feynman etc.
When light travels through a transparent medium, the photons are constantly absorbed and re-emitted.
If we are near an energy level, the photon is absorbed never to return. The photoabsorbtion cross section is '2rλ' and the photore-emission cross section is zero.
When the photon energy is remote from the resonant energy, the photon is absorbed and re-emitted. The photoabsorption cross section is zero but the photore-emission cross-section is 2rλ.
Since Sylas is able to refer us to values of f_2 for single electron Hydrogen they must be published.
Cheers,
Lyndon.
PS in retrospect, the last link I gave was probably given in haste in an attempt to find something simple for Sylas. My paper and theory do not use this reference at all.

Alright, this does it. I'm calling it Bain's law: If you wait long enough, Sylas will post your reactions and do a much better job discussing it and proving your points than you would. (Maybe the possessive means that it only applies to me. :-k )

My point is that I saw all of that myself. It seems that Lyndon is the only one who doesn't see how he's misapplying his refs, for whatever reason. There's probably a snowball's chance in Illinois in August that he'll realize this in any decent amount of time. :roll:

Non of the refs are misapplied.
The trouble is that several of you have invested so much in learning the Big Bang theory that you cannot even contemplate that you have wasted your time and it is wrong. I think that your 'Bains Law' (why Bain?) can be summarised as "any post is good if it confirms your own preconceived ideas". Doesn't sound very scientific to me!
Some will grasp at any straw to hold onto the 'old' and reject the new - even though the 'new' is far better.
Cheers,
Lyndon

Sylas is not forgetting anything. He just disagrees that Lyndon describes it correctly.

Photo-absorption is a particular form of interaction of light with matter; one of several possible interactions. The transmission of light in a transparent medium is a different form of interaction, with no relation to photo-absorption cross section.

French does not consider how light travels through a transparent medium in any detail, except a brief comment (page 57) on how slow down of light was used as disproof of the classical particle model and support for the wave model.

Feynman explains transparent transmission with characteristic clarity and quantified models. He does not use photo-absorption. He uses his Nobel prize winning technique of integration over paths, with cancellation and reinforcement of the wave. It is not done by adding up delays in collisions along a single path.

Lyndon may use 2rλ, and he but cannot find anyone who has published anything so silly. A look at the actual numbers in all cases confirms that photo-absorption cross section is nowhere near 2rλ, except a very tiny window where f2 is close to 1. His descriptions of travel in a transparent medium are way outside the mainstream, and do not correspond to anything by French or by Feynman.

Here is a tabulation of Henke form factors and cross sections. Data obtained with this query from NIST. I tabulate photon energy in eV, wavelength in Angstroms, f1 and f2, Lyndon's cross section as 2rλ, the photo-absorption cross section from NIST, and the coherent+incoherent cross section from NIST, all converted to barns (1 barn is 1e-28 m^2).
A glance at this shows why Lyndon never quantifies his alleged cross sections and delays. His model fails to match actual numbers.

But Lyndon's claim goes even further. He claims that 2rλ is the published photo-absorption cross-section, rather than his own invention. We've already seen a number of publications in the thread that use 2rλ.f2. Will Lyndon ever give a reference to any paper or publication that uses the formula 2rλ for a cross section? Any cross section? Will he ever grasp that the claim he needs to back up concerns publication? Stay tuned...

Cheers -- Sylas

Thanks Tobin! That's high praise.

I'm enjoying this because I'm learning. A lot of this is quite new to me. Lyndon is right to call me an armchair physicist. It's often an armchair in the Uni library!

My major outstanding question at the moment concerns form factors and cross sections for Hydrogen at energies of 10eV to 13.6eV (Lyman lines) and then 1.9 eV to 3.4 eV (Bahlmer lines) and so on. Are form factors much used at such low energies? Doesn't absorption with partial excitation show up somewhere? I saw a tabulation somewhere and the cross sections at those frequencies seemed to be huge. Shouldn't that show up in f2? Or is it so tightly focussed that it falls into the gaps in the NIST tables, which only tabulate seven energies below 13.6?

Any hints, explanation, or references gratefully accepted.

It doesn't really matter whether Lyndon is convinced or not; and indeed one of his posts in particular was a big help for me. His description of phase and group velocity clicked, and thereafter I was able to make much better sense of other material I had not really grasped. (Thanks, Lyndon!)

Digging into this material, even when totally irrelevant to Lyndon's claims, is worthwhile for its own sake. I remain entirely happy to let Lyndon go on advocating his notions as long as he finds mine unconvincing. I don't expect him ever to learn anything or to recognize any errors apart from typos.

For anyone still undecided... don't trust me, or Lyndon, or any other poster. Try following through and checking our arguments until you can identify on your own behalf which one is wrong. When you can do that you've really learned something. And if it's me that's wrong and you can tell me where, then I get to learn more also!

Cheers -- Sylas the armchair physicist

If Sylas ever moved to the UK he could find a job straight away – working for Camelot as a random number generator for the UK lottery!
Why is it that in Sylas’ posted table of ‘f_2’ values he misses out this one?


E/1.366800E-02 f1/-4.92163E-01 f2/9.5197E-01
That is, the one where f_2 has the value of ‘1’ and the photoabsorption cross section is 2rλ.
Was it just coincidence? A slip of the keyboard or is Sylas trying to deceive. No, he wouldn’t do that. Not on a Sunday. It must have been a slip of the memory.
He has also slipped back into doing his sums on a totally different effect – back to his old Compton effect. ‘Incoherent scatter’ is Compton effect but Sylas ‘forgot to mention this’.
As Sylas says, f-2 values depend upon the energy of the photon. BUT….. wait a moment, 2rλ is also energy dependent as lambda is = c/f and energy is E = hf.
We could write the whole photoabsorption cross section as being 2r(f(E))(ch/E) where E is the energy of the photon and f(E) is f-2 as a function of energy.
Now, why would we have TWO energy dependent terms in one formula with one disguised as a wavelength???
Ah! I know, because Lyndon is correct.
The ‘2rλ’ term represents the probability of the photon being absorbed in the first place. The bigger the particle or the longer the wavelength then the more likelihood of the photon being absorbed in the first place.
Then, what happens next depends upon the energy of the photon. If the energy corresponds to the resonant energy of the system of electrons then it is absorbed – f_2 is ‘1’ (the data point Sylas ‘forgot’ in his table!) If the energy of the incoming photon is well away from the resonant energy of the system of electrons then the photon is re-emitted. ‘f_2 is zero but the photo re-emission cross section is ‘1’
You see there are only two possibilities after the photon has been absorbed, it is either retained or re-emitted. f_2 is the case where it is retained and 1 – f_2 is the probability of it being re-emitted. Ergo when f_2 is zero, 1 – f_2 is unity and the total cross-section for absorption and re-emission is 2rλ.
Cheers,
Lyndon

ps. don't tell Sylas but the fact that we are loking at f_2 values etc means that they are published.

Sylas wrote
This is totally untrue and I am surprised that Sylas felt the need to write this.
In the derivation of H = 2nhr/m I include the cross sections in their algebraic form until the end. I then quantify the whole thing and show that the value of H predicted by this expression is in agreement with observed values. It would be incorrect to do as Sylas suggests and insert numbers into the middle of an algebraic derivation.
Good science says find the final expression and do your numerical vindication at the end - as I do.
Just a minor but important one.
Cheers,
Lyndon

Why Ashmore?

On a serious note, please don't take my joking with too seriously. (But your ref there wasn't applicable, and you admitted it.) There have been a couple other times in the last couple weeks when I haven't posted information (or at least not fully, c.f. the 2-photon emission) and someone else got there before I got back to thinking about it.

Get over your BB obsession. Nothing that we are discussing here applies solely to the BB. For instance, the standard model of particle physics comes into play with these collisions at and below the atomic level. While there are applications of this to the BB, there are plenty of applications to it that only confirm the BB with the fact that they work at all. Finally, I will not apologize for my "preconceptions" being the standard theories that have been shown to work many times in many ways. Blind ignorance of anything counter to your beliefs is far worse. Just because you think it is so doesn't mean it is.


Sylas, you're welcome. However, you seem to be deeper into this than my brief foray into particle physics took me. I haven't really been following this too deeply, either, just staying on top what's going on. I can't offer a whole lot in the way of help, but you're doing fine on your own.

As for the low-energy question, I think I have an answer, but the early-morning caveat applies. :wink: My answer right now isn't much, mostly because I'm not sure exactly what you found there. The 13.6 eV cut-off makes me think that the cross-sections are for hydrogen atoms, not the electrons. If that's the case, then of course the cross-section will be zero below the cut-off because the photons that are not absorbed can't be siince they aren't at excitation wavelengths. That's the best answer I have right now.

Oh, and Lyndon, Sylas has shown many times (see plots in previous posts) that f2 approaches one at E=13.6 eV. But you're not interested in those photons; they're not optical. f2 is zero for all of your optical photons. Furthermore, the energy functions scale in completely different manners. That doesn't mean that Sylas is out to get you. It also doesn't make you any more correct than you have been. f2 varies with energy, and so it is one at only one energy. Only there does the cross-section equal 2r*lambda. But, as I said earlier, these are not the photons you are looking at. How did you miss the fact that every energy below 13.6 eV has an f2 of zero?

I pointed explicitly in the post that there is a special frequency (13.6 eV) with a cross section almost equal to 2rλ, so noises about "deception" are just contemptible.

The point of a table is to show trends over the spectrum. I posted energies at 10 eV and up by factors of 10. I used the numbers closest to these values, and this is particularly useful for log log plots. You can see a trend very quickly, and since log values are proportional to number of digits, you even get a crude log log plot just by eyeballing the number of digits in the table. Try it.

I have it all on a spreadsheet and generate such data quite quickly now. Here is a plot.


We can see in this plot that one special frequency where Lyndon's formula almost works. The problem is the rest of the spectrum. Lyndon's formula is totally incorrect at every other wavelength, which is why he has been unable to defend the claim about 2rλ being published as the cross-section.

I give all the data and links and show my working, and repeatedly urge readers to check it all out for themselves. The coherent+incoherent cross section is basically due to Rayleigh+Compton effects, which comes closest to what Lyndon calls absorption and re-emission. These are the real interactions where an atom cannot hold onto a photon.

Rayleigh scattering is the dominant contribution for higher energies, and this was the case Lyndon brought up previously with the RTAB data, because here indeed the relevant form factor f1 is very close to 1 over large parts of the spectrum. (X-ray and up.) This suggests that deep down, Lyndon understands that he needs f2 to be one to justify the formula 2rλ.

The plot of CS(ci) shows two things. First, it emphasizes that there are other interactions than photo-absorption, and Lyndon's argument that other effects must be understood in terms of the photo-absorption interaction is just an empty assertion. Second, it shows that cross sections in general are not simply given by 2rλ times a form factor. It depends on the interaction.

Check out equation seven in Chantler 2000. It gives almost that very formula, but expressed to give f2. The equation is
f2(E) = E*sigma_pe(E) / 2*h*c*r_e
It is explicit with the brackets that both f2 and the cross section sigma_pe are functions of E; and E also shows up in the equation itself. We do this, because the form factors and the wave length are used in many different contexts, and they are both useful numbers, both of which depend on photon energy.

Of course f2 values are published. I pointed out that they are not published for single electrons. They are only ever published for atoms. Atoms contain electrons, and Hydrogen contains one electron, but this is not "single electrons". The tables always identify them as being for Hydrogen. My post was perfectly clear on this distinction.

But what about 2rλ as a photo-absorption cross section. Is that published? Of course not, and the data I have given shows why.

Cheers -- Sylas

Good science says you actually compare your numbers with real results. That is what you don't do for cross sections. You calculate a number that bears no relation to any actually published cross section, using a formula that never appears in any published source, and you never actually compare that with real quantified cross section data.

When we look at the data, it become easy to see why you never do this. Your models don't match the data. You have yet to show any published work that gives the same cross sections as you give, or the same formula as you use.

Cheers -- Sylas

Lyndon, how does your redshift work. I'm having troubles with the calculation to prove that d-lambda is h/mc. However, I have a bigger issue with it.

You contradict yourself in your paper. You state that z=d-lambda/lambda is constant, but you also claim that each collision changes the wavelength by h/mc no matter the wavelength. This can't be; you can't have both d-lambda and z be constant if lambda can change. How do you reconcile this?

That's not actually a contradiction. In Lyndon’s model, the cross section is strictly proportional to wavelength, because he uses cross section = 2rλ. If each collision gives a characteristic dλ, then longer wavelengths get proportionally more dλ from more collisions, as required.

Cheers -- Sylas

Sylas,You are generating random numbers here. You are building castles on sand. You are drawing graphs tables all of which have nothing to do with anything. You have cross sections for Compton effect and even photo electric effect combined in your sums.
Why this fixation with Hydrogen energy levels anyway?
This has nothing to do with my posts or my theory.
We will start again shall we?
For a photon to be absorbed TWO separate things must happen - and when that happens we must multiply the probabilities.
Firstly the photon has to be absorbed and the cross section for this is 2rλ. That is the probability of it being absorbed in the first place depends on 'how big the particle is' (2r, the diameter) and the wavelength of the photon. The higher the energy of the incoming photon, the smaller its wavelength, the less likely it is to collide and so the probability of it being absorbed in the first place (2rλ) is less.
Secondly it has to be retained and the probability of this is f_2.
Hence the total probability of our photon being absorbed and retained is (2rλ)x(f_2)
there are only two possible outcomes. Lets assume a little maths on your part and call these out comes p and q.
Since there are only two possible outcomes either it is absorbed (p) or re-emitted (q) then p + q = 1.
In our formula for the photoabsorption cross section 2r(f_2)λ, f_2 is 'p'. We see that f_2 has values between 0 and 1 and that these values depend upon the energy of the incoming photon compared to the resonant energy of the system of electrons (13.6eV in the case of a Hydrogen atom but not in plasma)
If the energy of the incoming photon is well away from the energy at which our system of electrons resonate the photon is absorbed but not retained, probability p is zero and the photon is re-emitted. That means that probability 'q' is unity.
photoabsorption cross section = 0; photo re-emission cross section = 2rλ
If the energy of the incoming photon is near the energy at which the system of electrons resonate then the probability of it being absorbed 'p' increases whilst the probability of it being re-eimitted 'q' decreases.
photoabsorption cross section = 2rpλ; photo re-emission cross section = 2rqλ
At the resonant energy p =1 and q = 0 as you say.
But one has to compare the energies to the resonant energy of the system of electrons.
In IG plasma resonance occurs at a frequency of about 6Hz. This is what you should be comparing things to not hydrogen energy levels.
If the incoming photon has a frequency of 6 Hz it will be absorbed and the whole plasma set into oscillation. 'P' is 1 and q = 0 because it is not re-emitted.
photoabsorption cross section = 2rλ; photo re-emission cross section = 0
Since our photons have frequencies well away from this p = 0 and they are not absorbed, they are always re-emitted (q = 1).
photoabsorption cross section = 0; photo re-emission cross section = 2rλ
and this is what we want.
This is why I am happy that at frequencies well away from resonance f_2 is zero, it means that 'q' is 1 and the photo re-emission cross section = 2rλ
The cross section for a photon to be absorbed and re-emitted for frequencies well away from the resonant frequency at which the electrons in the plasma oscillate (6hz) is 2rλ.
Cheers,
Lyndon

That's not what he says, Sylas. Using his energy balance equation on page 3, Lyndon ends up with the boxed equation "d-lambda=h/mc." He later goes on to say, "If the initial wavelength is λ, then [the shifted wavelength] will be (λ + h/mec) after one collision,...." This is after (correctly) stating that d-lambda/lambda is a constant for a given source. Lyndon has claimed that d-lambda is a constant for all wavelengths. (There is no wavelength dependence in h/mc.) This can't be true. Lyndon, I'm still waiting for your response to this. It should be addressed. If your z is incorrect, then so is your derivation of H.

I've been thinking about this for a few weeks, and finally decided to post it. Since Lyndon is claiming there are effectively hydrogen atoms in IG plasma, and since he's focusing on f2 being 1 at the hydrogen ionization energy, what is the ionization energy for his effective atoms?

Lyndon's favorite electron density is n_e=0.6 m^-3. Charge neutrality gives us n=1.2 m^-3. This gives us and average separation between any two particles of 0.941m (= n^(/-1/3). For the sake of arguement, then, let's say that the electron radius is 0.45 m so that it's definitely more bound to one proton than to the others.

Now, the radius of an electron orbit is given by r=a_0*n^2, where a_0 is the Bohr radius and n is the energy level. The ionization energy of an electron in a given energy level is E=13.6/n^2 eV. This becomes E=13.6(a_0/r) eV. a_0 is 5.29e-11m. That gives our "peak' energy at 1.6e-9eV. This corresponds to a wavelength of 775 meters. That's Lyndon's "resonance wavelength," well above visible, infrared, and microwaves. (This also shows that the electrons are unbound in the plasma, since n~100,000.)

Check out page 5 of his preprint paper.
IMO, the analysis of the individual collisions is completely wrong; but that the rest does follow correctly and consistently from the collision analysis.

The collision analysis involves a dλ per collision that is approximately the same over all wavelengths (section 3) and a cross section that is proportional to wavelength (section 4). The derivations go on to show (page 6) that the consequent Hubble law is an exponential, which approximates z = Hd/c for small z factors, as required.

The dλ per unit distance is just dλ per collision multiplied by collisions per unit distance.

Some folks might object that the exponential law is very different from the linear Hubble law. Actually, it's quite close. Bear in mind also that the strictly linear Hubble law as used in conventional cosmology uses d as distance to the galaxy right now; not the distance to the galaxy at the time a photon was emitted. This distance is not a directly observable quantity. Other distance measures used in astronomy include an angular distance (based on the angle subtended in the sky of an object of known or estimated size) and a luminosity distance (based on the amount of light from an object of known or estimated absolute magnitude), and using these observable quantities the Hubble relation diverges from linear.

Cheers -- Sylas

You're right. The cross-section (and therefore the mfp) is lambda-dependent, so the number of interactions depends on wavelengths. I see what I did now.

However, the distance used in the Hubble law *is* the distance to the object when the photon was emitted. We measure it using the photons that we observe, and so we get the distance at that time. The redshift and distance measurements are both contemporaneous when applied to the Hubble law.

The distance d used in the Hubble law v = Hd is the distance to the object at the time when the photon is received. Check out Part 2 of Ned Wright's cosmology tutorial for a nice discussion of this point. He writes this distance as D_NOW.

The velocity v is the rate of change of separation distance (now), and in conventional cosmology this is proportional to the rate of expansion of space (now). Using the notion of scale factors "a", the "proper distance" co-ordinate at proper time "t" is a(t)*D_NOW, so the Hubble constant H is defined to be (da/dt)/a. You'll find this equation frequently in the literature. The theory of general relativity equates this term to sqrt(E), where E is a mass energy density at a point in time.

I've given a more detailed discussion of this point in the thread Cosmic Coincidences.

Cheers -- Sylas

#-o I knew that. Really, I did. That was one heck of a brain fart, there. ops: Those types of posts aren't supposed to happen at that hour.

Working through this gave me another way to compare Lyndon's model with the conventional model.

The relation v = Hd does not involve any directly observable quantities. We don't observe a velocity. We observe a redshift. We don't observe a distance. We observe luminosity, or angular size.

The Hubble relation was originally calibrated using Cepheid variable stars, which have a regular variation in brightness. The period of the frequency of the variation is proportional to absolute luminosity, and so from the apparent brightness of a Cepheid variable and a measure of its frequency, the distance can be given, and compared with the redshift. Since then, a number of other distance yardsticks have been defined.

There are two basic distance quantities that are observable. If you have a good idea of the absolute size of an object, then you can infer how far away it is by the angle it subtends in the sky. If you have a good idea of the absolute brightness of an object, then you can infer how far away it is by its observed brightness.

There are also two distance measures that are not observable. One is the so-called "proper distance" used in the Hubble relation, which is basically how far away an object is at the current instant if it could be measured with a long measuring tape. Another is the "light travel time", which is the amount of time light took to get here, multiplied by the speed of light.

In a static non-expanding space, all these notions of distance are ways of describing the same quantity. This is the case in all normal experience over small scales, and it remains valid in Lyndon Ashmore's model. But in an expanding space model, the four distances are different as you approach scales measured in billions of light years. The full theoretical explanation is given in Ned Wright's cosmology tutorial.

At that same link you can see, near the bottom of the page, a plot of the observable redshift z against these four distance measures. The plots vary depending on how the expansion of the universe develops over time, and so three different models are presented. The right hand model is the consensus model that is the present leading contender in the mainstream cosmology. Alternatives are always being explored, but improved observations are giving stronger and stronger constraints on what is consistent with the data.

Two of the plots, for Luminosity distance and Angular size distance, are observable in principle, as long as we can compare observations of objects at different distances that have similar sizes or luminosities.

Lyndon's model also relates quantities that are observable in principle, using the relation z = exp(HD/c)-1. This should allow a quantified comparison.

I've superimposed the relation given by Lyndon's model with the relations used in mainstream cosmology as plotted by Ned. Here it is:


As the plot shows, Lyndon's model and the Big Bang model should start to diverge for observations with redshift of z greater than 0.1 and for which angular size can be estimated. They should also diverge for observations with redshift z greater than 2, and for which absolute luminosity can be estimated.

I don't know off hand what observations are available, but here is a chance for someone to chase up some quantified data. (Hint, hint.)

Cheers -- Sylas

Thanks Sylas and Tobin Dax (mr bain - I am with you now.)
I had to dash out last night so I didn't have time to answer Tobin's posts but i think Sylas has answered quite a few.
So let me post something about the exponential nature of the Tired Light Hubble diagram. If there are still any outstanding points Tobin, let me know.
I believe that nearly all Tired Light models come up with an exponential Hubble diagram. In my theory the reason is that after every interaction the wavelength of the photon is increased so it stands more chance of bumping into the next one so it travels shorter and shorter distances between collisions as it travells along. Whenever the rate at which something changes is dependent upon how much of that substance one has at the time, you always get an exponential curve.
I will have a look at Sylas' plot in a minute but just to show him that even I do back up my claims with data and do it quantitavely let me refer you to a friend of mine (yes I do have the odd one).
What Karim has done is to look at the supernovae data. We need distant supernovae as this is where any difference between Tired Light and alternative theories such as the Bb will show up. Exponential functions exp(x) are linear for small x (up to about z = 0.2) and then start to curve upwards as the exponential function really kicks in.
In the BB they tweak the data to allow for 'relativistic' effects caused by the 'expansion' of the universe. They then find that the data does not agree with the theory so they dream up 'acceleration' to make up for the 'problem' with the data.
Now in Tired Light we don't have expansion so we do not need to tweak the data. This is what Karim has done and he shows that the data fits the predicted exponential Hubble diagram perfectly. This is with H = 72km/s per Mpc (or n = 0.6 electrons per cubic metre in my case)
Equation (3) readily changes to my formula of z = exp(Hd/c) - 1 when one substitutes t = d/c.
So you see the quantitative work has already been done. Tired light's exponential Hubble diagram matches the data, the BB does not so they have to invent acceleration.
Cheers,
lyndon

I agree that this exponential curve is significant, particularly with luminosity based measures. The exp(HD/c)-1 function starts to diverge significantly beyond z=2.

But the really dramatic difference is with the angular distance measure. In this case, the Big Bang model predicts a reversal! We normally think that the further away something is, the smaller it appears. With expanding spaces, however, as you go back to smaller scale factors an object takes up proportionally more space. The differences with the tired light model become significant beyond z=0.1, and the current consensus model suggests that beyond around z=1.2, the further away something is the LARGER it appears in the sky! This is very counter intuitive when you first meet up with the notion, but it is a definite prediction.

This means, for example, that as long as galaxies with z factors from around z=1.2 to z=2 have roughly comparable sizes, the Big Bang model predicts that those with higher z values will appear larger in the sky; whereas the tired light model predicts they will appear on average smaller because they are further away. I don't know of any surveys checking this result, but it seems doable when I think about it. You'd have to be careful with Malmquist bias, and there is a major difficulty with finding some standard size to allow comparison across different z factors; but the difference is so dramatic that I would think it should be detectable.

Not really. I'm not an observational astronomer, but I am a mathematician. I can solve the equations, and have tried to work out my own predictions from the model. The thread on cosmic co-incidences is an example. The model has a number of parameters, which are highly constrained by many observations. The redshift to distance relations fall out quite naturally from the maths. You do fit the model to the data, as happens in any theory; but it won't let you fit anything. For example, if the angular size reversal effect is clearly refuted, the model is in trouble.

For comparison, n is a tuneable parameter of your model. You can fit to any expansion rate by using the appropriate n value; but whatever n you choose you still predict the exponential effect. Thus finding a particular value for H is not a good test of your model. The possible values for n can be chosen to fit all kinds of H values. But you do have a solid prediction with the exponential divergence of z verse D, and another prediction with the close correspondence of D calculated by luminosity by angular size, where data allows luminosity and angular distance estimates to be made.

I looked at Karim's page some months ago, and I cannot figure out what he is doing. I don't see where he has actually quantified the exponential effects in the data. If you can present some tabulated figures of observable data, to illustrate and quantify the exponential, that would be great.

Cheers -- Sylas

[[Edit for minor clean up]]

Weird. I thought he quoted from sources on photo-absorption.

Well, you started it, by citing in your paper the photo-absorption in Hydrogen.

So, you admit that using photo-absorption in Hydrogen is not relevant to your "theory".
Then, why do you use it in your paper?

__________________
papageno


"Why waste time learning, when ignorance is instantaneous?" - Hobbes (Calvin and Hobbes)

"It's all about context!" - Vince Noir (The Mighty Boosh)

"I've never heard of such a brutal and shocking injustice that I cared so little about!" - Zapp Brannigan (Futurama)

"...because the logic of the lines traced from reality is as poor of aesthetic value as it is strict in consistency. " - Paolo Bozzi (Naive Physics - free translation)

This behaviour of the angular size distance is the reason why I do not think Lyndon can use gravitational lensing estimates of H0 to support his "paradox" - the calculations need to be redone with the angular size distance applicable in his cosmology.

I think there is a recent one; I seem to remember seeing it mentioned on this board. I can't find the reference.

There are so many parametric assumptions necessary, and the geometric angle as so small, I don't see how gravitational lensing can be used do do anything other than proof gravity 'sucks' light, focusing, bending, dispersing and in general making it much more difficult to interpret anything.

Great thread!

__________________
jwj

It's a big universe out there...is it really unwinding, really burning out?

Like?

Small compared to what? A typical galaxy lens produces image splittings of an arcsecond or so, and a cluster produces arcminute-scale splittings. Those angular scales have been accessible for a very long time.

Then educate yourself. I have posted some useful links further up the thread.

Lyndon asks me a very odd question in this post, which I did not answer previously.
Here is where Lyndon uses energy levels in his theory.
He doesn't actually say "energy levels", but the reference number 16 is to Special Relativity by A.P French, and Lyndon reports the result incorrectly. The actual formula used by French is Q0^2/2Mc^2, and Q0 is not a photon energy, but an energy level for an atom. Quoting French from the section that derives the formula to which Lyndon refers:This is the definition of Q0, the term actually used in the equation (6-25) cited by Lyndon. It's an excitation energy for an atom. The derivation is easy, and it only works for the excitation energy of the atom. Lyndon does not derive the formula himself, but merely substitutes the photon energy in place of the excitation energy, and then uses that same formula over the whole spectrum!

What French explicitly calls a well-defined, fixed energy is replaced in Lyndon's paper with energy for any photon in the spectrum.

In fact, Lyndon has no theory. He never derives the formula Q^2/2mc^2 himself. He just takes it from French, and changes the meanings of the variables. It's not a theory, but a long succession of many elementary errors in simple physics at about upper high school level.

Cheers -- Sylas

The size of the lensing quasar or galaxy, the mass, the magnetic field strength, the distance between the quasar and the lensed galaxy. the size of the lensed galaxy, dust reddening, quasar halo lensing.... We don't even have a very good number for the radius of the sun.

Not to mention intrinsic redshifts, proper motions, metallicity corrections, binary fringes or wobble, distortions caused by clustering, black holes, intervening stars, hubble flow 'zero' point, permeability of galaxies, assumed rates of evolution, uncertainty in the supernova Ia distance scale...

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jwj

It's a big universe out there...is it really unwinding, really burning out?

I just looked up the radius of the Sun in Fundamentals of Celestial Mechanics by J.M.A. Danby, one of the current standard texts on celestial mechanics. He gives the radius as 696,265 km. Sounds like a pretty good number to me. Of course this number is based on the application of Euclidean geometry within the Solar System and the assumption that light propagates in straight lines at constant velocity. Without these assumptions the ancients would never have been able to figure out planetary motions at all, nor would Kepler have had even so much as a starting point. And general relativity only changes the trajectory of light by at most 1.75 seconds of arc for a light-ray grazing the Sun. The above assumptions hold true to a remarkable degree.

You've really got to get out of your fun-house more often!

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Microsoft is over if you want it.

The bar has been lowered for the promotion of ATM ideas; the bar for the acceptance of ATM ideas must remain high.

I turn my back for five minutes to go and watch Preston North End fail miserably in their attempts to gain promotion to the premier league and Sylas is at it again!
Lyndon quotes French to shorten the paper. Lyndon has done his sums and that result is true for any energy of incoming photon.
Consider an incoming photon energy Q, frequency f, wavelength λ, colliding with and being absorbed by an electron mass m.
Lets do it classically since this also applies here.
Momentum of incoming photon is h/λ.
By conservation of momentum h/λ = mv or v = h/mλ
Since c = fλ, v = hf/mc
KE gained by recoiling electron = mv^2/2 = (h^2f^2)/(2mc^2)
Since Q = hf,
Energy lost by photon to recoiling electron = Q^2/(2mc^2)
Why does this depend on the energy level? Since the energy of our incoming photon is well away from the resonant energy of the electron in the plasma, it is re-emitted once absorbed.
Cheers,
Lyndon.