The space time will be based on GR. Of course the unseen waves have energy and so are causing space-time distortions in GR terms - I say unseen, but generally the nodes are occupied by visible objects. But whenever I suggest that large scale standing waves may be the cause of dark energy or matter then I generally get dismissed. It seems that people either:
1. Do not understand that there are stable (or near enough) solutions to electromagnetic or gravitational waves that have very uneven energy distribution. OR
2. Do not see how such wave structures could form or exist in the universe.

The eigenstates of systems like vibrations in a musical instrument are well understood. There are many other similar physical systems where the various modes are seen such as the solar 5 minute modes and the like. Why do people ignore this possibility in the large scale structure of the universe?

Yes, these waves would be of significant energy and mass. I did a calculation in 1994 in answer to a question from a physicist or astronomer, and assumed that the constant k was 2 in my harmonics formula, i.e. energy flowed at a rate that is the inverse square of harmonic number to harmonics. Normally I do not define k as the theory works with any k. Anyway I get sensible answers for the distribution of energy with scale that fitted the knowledge of the time. I do not put this forward now because I am less confident about it. It is the sort of thing that should be looked at once the theory is moderately accepted.

However for this to be so, there has to be communication for a long period of time between all parts of the universe. In 1994 the big bang theory people said that this was not so and I was wrong. Now with large scale structure visible they claim that it is early waves in the universe. They are changing their story gradually in to one more like mine.

The feedback is greatest at large scales. The wave with z=1 as a wavelength in harmonics theory loses energy gradually to all its harmonics, but the bulk to h=2. After traveling a distance to z=1 the relationship of all light to all matter is now shifted by a ratio 2 the other way. In the harmonics theory the next big peak after h=2 is h=12 (and 24). If a feedback with that loop is considered then the answer is the (1+z) factor of 1.230 which is what Arp claims exists in the quasar redshifts. This would be more applicable when the non-linearity is greater as might be expected for new matter developing very rapidly.

To keep things really straight with you, I want to avoid getting myself into areas where I am less confident which is a mistake that I made in the past. We are approaching those areas here. I am pretty confident that harmonics theory can make a useful contribution to the questions of large scale structure and dark energy and matter, but it will require other knowledge and maths that I do not have to achieve that.

Here is my original harmonics theory quanta table of redshift periodicities posted to usenet in 1994. Note the entry for the 16th harmonic has delta log(1+z)=.0433216 or 12987.5 km/s which is pretty close to 128 Mpc (/ho thingy) isn't it? There is one factor that will cause a slight disparity, and that is that astronomers generally look for variations in zc (or z) whereas Arp argues for variations in log(1+z) with which I agree is the better measure.
Just a note to explain that 128 Mpc * 100 km/s/Mpc = 12800 km/s = .0427c
Sp the observed periodicity is .0427 compared to my prediction of .0433 and if we assume 128+/-1 then we get .0427+/-.0003

I have not yet found the reference to the CMBR change, but have sorted out a fw other things.

In APJ 221:756-775 1978 May 1, Tifft gets this value for the universal frame: theta=234, pi=-18.8, z=-4.4, with a 72.135 km/s periodicity. I note that this is the 18.8 km/s "galaxy expansion" value that you mentioned. This is simply the component of the motion in the direction away from the galaxy centre, and is just part of the co-ordinates, not something extra.

In the papers in the 1980s the coordinates are usually close to theta=231, pi=-35, z=1. I did see a paper long ago where he showed that the solutions were quite good along a line with some bumps in it (probably at a smaller quanta interval). I suspect that he moved to a different bump when he got more data.

I cannot find any reference to the CMBR frame. Maybe that new frame does correspond, but I don't know what it is in galactic co-ordinates. Does anyone know when the CMBR was first determined accurately? That would help narrow the search. I do not think it is important when he made the change but it would be nice to know if his frame does correspond with CMBR now.

I think that this tidies up most of those matters now concerning what is the basis of Tifft's claims. See more in the following paragraph reference. His claim for a universal frame is based on the co-ordinates stated above and a set of quanta, being 72, 36, 24 and 12 km/s. Mostly he uses 72.45 km/s as a quanta and fractions thereof but the earlier work 72.135 km/s.

The APJ 345 paper by Martin Croasdale that I referenced recently is interesting because he pointed out that most people had just ignored Tifft and he did a thorough statistical analysis using mone carlo comparisons and also using previously found frames for further analysis to reduce the chance to "fit" data. His conclusion is that the results are quite significant.

As stated previously I have never checked his calculations. Croasdale refers to checking of the simpler claims by the referees, but the referees say about the more complex claims that they cannot find a mistake but do not necessarily agree with the conclusions. Good on them for accepting the papers anyway.

I will look to doing an analysis of a sample myself after the 30 days of Harmonics theory review is up. I only have enough time to keep up with the questions at present and my wife just returned from being away and will want me to talk to her sometimes. :-)

First, let me say that the list of papers I gave is not complete. It's probably quite thorough for older papers, but lot of newer papers are not listed mostly because there is a flood of newer papers that relate to the subject, but are more about large scale structure than about redshift periodicities directly.

Well, I think it's a good thing that none of the three papers you cited include selection effects.

Whole quote of the Bell paper...

...refers to this Bell (2004) paper (which seems to be missing from my list, probably because I compiled the list roughly at that time). I'm over my head here, so I really don't know if Bell's arguments there have legs or not.

Oh, it's the name of the phenomenon that is important? When observed redshift periodocities are called fluctuations of "large scale structure" (or something like that), the phenomenon is already placed in the context of a certain theory. When the phenomenon is called "redshift quantization", it is more neutral term containing less interpretation, it just addresses the observational nature of the phenomenon. But perhaps this is just a manifestation of the good old approach that observations are wrong if there's no explanation for them.

My point almost exactly. But where do you draw the line between redshift periodicity supporting some ATM theory and redshift periodicity indicating fluctuations in large scale structure? Why Tifft and Arp (for example) are "bad" and Broadhurst et al. are "good"? To me it seems that they are all looking at same observational phenomenon, but are just explaining it differently. If some of them has wrong explanation, they still might have correct observations.

Seems to be. It's too bad I can't access the Broadhurst et al. paper, but this Morikawa (1990) paper says that their periodicity was about z = 0.042. I wonder why they have to use so awkward units, when they could just give the periodicity in z. After all z = 0.042 periodicity is z = 0.042 periodicity regardless of what the currently favored Hubble constant is.

Well, I haven't checked the situation in full, but I just note that the Morikawa paper I mentioned above talks about variable ln(1+z) for QSOs. I just guess here, but it seems to me that periodicities for galaxies are usually reported in simple multiples of z (like Tifft), and periodicities for QSOs are usually reported as more complicated logarithmic steps (like Arp).

Could it be this Tifft (1997) paper?

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Thank you Ari Jokimaki, that is an impressive list. I think that it does highlight the fact that something really is going on. Of course this whole process is similar to what quantum physics went through about a century ago when everyone "knew" that the e/m field equations of Maxwell were right but then this weird quantum stuff started popping up. Of course the ultimate solution is not going to be apparent immediately in such a situation because part of the problem is deeply entrenched and widely practiced wrong thinking. No-one can easily break out of that. But it is helpful if people learn to say "I don't know why that happens" rather than "those guys are raving loonies".

IMO, Arp, Narlikar, Hoyle, Tifft etc have seen part of the way ahead but not all of it. Only by exploring all the established oddities that do not fit will
the way ahead become clear.

Perhaps you'd better stick to published papers then? Given the, shall we say, selection and massaging that happens between paper and popular article, it is surely sound to conclude that there is some, shall we say, noise introduced into the signal.

As I said, I'll eventually get into the details of this in the tread we talked about, since this is all directly dependent on what a quasar looks like spectroscopically (maybe I'll start that this afternoon, if it starts raining here...). Suffice it to say, selection effects have nothing to do with the cause of the redshift, just with how the redshift affects the colors of the targets. It doesn't matter whether the redshift is caused by cosmological expansion or something else. Because a quasar at a certain redshift will have a certain color, some are preferentially selected over others (see below).

They've got less legs than a mudskipper. I skimmed that letter before posting yesterday, and his arguments are just plain wrong. I'd hazard a guess from that paper that he doesn't understand what the selection function for Sloan is, since he does not mention any specifics of the selection function, and they are absolutely vital to his thesis. Here's the basic problem:

You recall from our discussion that some stars look very much like quasars photometrically--their colors are the same--and so when Richards et al. were designing the SDSS quasar targeting algorithm, they knew that not every quasar candidate targeted for spectroscopy would turn out to be one. And there are only a finite number of fibers to go around.

As an example, say I have 2000 spectroscopic fibers to allocate to quasar candidates and I choose to give 1000 fibers to one range of predicted redshift, and 1000 fibers to another range. But it turns out that ~600 targets in the first range will be stars, while only ~50 in the second range will be. Thus we now have ~400 quasars with spectra in redshift range one, and ~950 in redshift range two. "Look, the redshifts are quantized!" One way to correct this would be to increase the number of spectra allocated to candidates in the first range, but then I'd lose targets in the second range: only 2000 fibers are available!

And quasar researchers aren't the only people in SDSS; there are folks who study stars too! And they might be very interested in the oddly colored stars in region two, so if we reduce the number of spectra in region two, they're unhappy (and I am too: those are some very interesting stars!). Also, the more complicated we make this "selection function," the harder it will be to understand exactly what the resulting catalog represents. So, there was some optimization of the selection function after the Early Data Release (the test set, if you will), but nowhere near as much as Bell claims. And since there are only finitely many fibers to allocate, you have to make trade-offs somewhere.

I grant that this is a rather contrived example, but it is actually not too far off from one of the problems faced during SDSS spectroscopic target selection. There are many more, such as the redshift-space degeneracies induced by the nature of the photometric filters. And like I said, these issues do not depend on what causes the redshift of a quasar, just that what the redshift value is.

Does this make sense, and do you understand why it is so damning to Bell's thesis?

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(my bold).

rtomes, if you don't know what the "ho thingy" is, why not avail yourself of the resources of BAUT's Q&A section to find out? It's too late for you to do this before you wrote this post (so you may be challenged on your statements), but ...

If you do know, then please show that "delta log(1+z)=.0433216 [...] is pretty close to 128 Mpc (/ho thingy)". In your answer, please be sure to include a specific explanation of the meaning of "the 16th harmonic" in an F(L)RW (or similar) universe (or, if your ATM idea explicitly rejects the applicability of GR to the universe, an explicit statement of the geometry of rtomes' ATM idea's universe). Please also include a description of an objective method for determining "pretty close to".

As you have explicitly labelled the "redshift periodicities" you expect to exist, from your ATM idea, "quanta", please describe the physical processes by which an observation of one of these quantum states may deviate from its exact value, and give at least an OOM (order of magnitude) estimate of a) the expected distribution of observations about the exact value (the 'line profile'), and b) references to where calculations of such expected distributions arise from the physical processes you have identified as most important in such distributions have been published.

Where did you publish* even an outline of a solution to the Einstein field equations of General Relativity that incorporates your idea?

Where did you publish* estimates of P(k) - the fourier transform of the two-point correlation function - derived from your ATM idea?

What is the relationship between the 'harmonics' in your idea and P(k)?

In a universe where the rtomes idea rules, what contributions to the large scale (cold matter) structure are there, other than that generated by the 'harmonics'?

*In 1994, before 1994, or since 1994.

Your point taken. The problem is that the language of many papers is so full of jargon that I cannot understand them. Clearly this often applies to the people writing for the magazines too. I do think that research scientists would be well advised to sit down now and then with a person who is writing popular articles so that they do a better job of it. It would benefit the scientists in the long run through better public understanding as the public ultimately fund most research.

Specifically this has been a problem for me in understanding the papers that deal with looking at the clumping at various scales. They use terms and have graphs that show some things that look like weak periodicity but I have no idea how they calculate these. Perhaps I need to go to the question thread.

I do understand the Ho thingy concept, I just couldn't remember whether to multiply or divide ;-)

Incidentally, the New Scientist article omitted the Ho altogether and so I didn't know what H had been assumed. When I found the article itself it was clear that 128 Mpc is based on H=100 km/s, so that it means 12,800 km/s in velocity terms. What they actually found was a periodicity of 0.0427 in z and the other stuff is all highly theory laden.

Let me have a little rave here. When a periodicity is found in z it should be first and foremost stated as such. To convert it too a velocity is to assume that the big bang is correct. To convert it to Mpc based on an assumed value of H (which is known to be wrong) is really rather quaint because you then need a little adjustment factor to allow for that fact. And after all, a parsec is a dam silly unit that goes back to the days when astronomers couldn't afford computers and worked out stellar distances by inverting stellar parallaxes and avoided multiplying by a constant to get light years. Really, they ought to use the metric system! We have had computers now for some time! As for the Hubble constant, it is stated in units of km/s/Mpc. What a really confusing set of units. Yes, I know the reason why, but it is still absurd. The dimensions are actually 1/time and so the units ought to be seconds^-1. Life would be a lot easier. OK, I am done now.

I have not done this in the way that you seem to be suggesting. The way I see it connected is that GR is a non-linear theory. This is confirmed by physicists when it is recognized that matter affects space-time. The condition of non-linearity is all that is required to cause harmonic formation from standing waves. GR will support standing waves because it is a wave theory. This has been my understanding since the early 1990s. I went through a series of attempts to describe the waves as e/m or gravitational and m,et with resistance from physicists. I simply state now that they are velocity c waves and leave it open the exact form. The process of harmonic formation does not care about the type of wave or even the exact nature of the non-linearity.
I do not understand the details of the two-point correlation function and so have never expressed my calculations in those terms. I would like to know more about it though.
I don't know.
I think that the "universal wave equations" may be seen as the ultimate cause of everything. Harmonics theory may be seen as describing the scales and periods that determine all wave formations. Therefore I would expect any results for any form of matter or energy to show harmonic structure once there is enough data.
The time scale of my results runs roughly like this.
In 1977 find 4 economic cycles that I used in computer modelling
In 1978 realize that they were harmonically related and gather other data which had similar patterns.
Intervening years spent mostly on other stuff (system software development).
In 1984 return to studying cycles and broaden my studies to economic, climate, geology, astronomy, and whatever else had cycles in it.
By 1989 worked out the calculation that I use now but not solved it to high numbers.
In 1990 retired from working in computers to continue this work full time.
1990 presented first talk on it at Foundation for the Study of Cycles in Califiornia, but simply describing it as non-linear systems results rather than a universal phenomena, though I did close with a statement that it might be.
1993-4 got on the internet and presented my work of the preceding few years. Apart from the 1990 paper at FSC the rest was all private unpublished research. The stuff that I put on the web in 1994 is all still available, but I have learned a few things since then. Much can still be found via google in usenet discussion groups from that period.

Additional note to my reply #161

I have previously answered the question on pretty close to. All real measurements are tainted by the fact that we live in a wobbly universe. There is no constancy anywhere. The longer the period of time or the larger the distances measured, the more accurate will be the measures. However the statistical tests such as Chi-squared will show that data is statistical close to predictions even if there is a difference in the significant digits.

This has always been true in science. It was true when the periodic table was worked out that He/H mass was not 4.0000; it was true of lines in the spectrum where additional wobbly components needed to be added to the exact Bohr model. It will be continue to be true for all theories for the reasons that I have given.

I prefer the term "periodicity" to "quantization" or even "structure" for what I look at. They are not quanta because they are violated as a 36 km/s quanta has to violate a 72 km/s one. They are tendencies only.
Yes. We have to distinguish between the observation and simple analysis part and the theoretical part. They need to be kept separate.

The problem is that people did simply state observed periodicities but no-one took them seriously because they seemed to violate things that they "knew". I suggest that this lead to Arp and Tifft and others to trying to create a theoretical framework as no-one else did. Because Arp worked with Hoyle and Narlikar, he was reasonably successful at that. I think that Tifft naturally used the period doubling properties of chaos theory as a basis, but it is not right. Chaose does not make a pattern with both ratios of 2 and 3 present at the same time as Tiffts analysis has, but harmonics theory does.
I get 0.0427 from 128 Mpc as follows... 128 Mpc * 100 km/s/Mpc = 12800 km/s, and 12800 km/s/c = 0.0427 z value.

Yes! Well done. I was looking too early for it. Nereid, here is the answer to the question about when Tifft changed to the CMBR frame.

I wrote: Astronomers cannot see how a 72 km/s periodicity can exist all over the sky unless we are at a special place which they cannot accept.

What I suggest is nothing like a conspiracy. I am defending their difficulty in accepting the observations because it clashes with their beliefs. If Tifft's observations are taken at face value, then the Earth seems to be at the centre of a whole series of regular shells of matter. This violates the cosmological principle. It is astronomers that have to see a conspiracy in this not me.

It is not possible to see this as anything other than absurd unless you disbelieve in a big bang and see the redshift as steps in time and not velocity or distance as Arp has done.

I ask you a question in return. How many astronomers understand that Arp offers this explanation and that it avoids the dilemma?

Why not ask a question, in BAUT's Q&A section, on the history of the CMBR frame, its relationship to the galactocentric motion of the solar system barycentre, and the accuracy (including estimates of random and systematic uncertainty) of the vector?

Note that none of these questions need reference Tifft, Arp, or anything to do with 'quantized redshifts'.What are the estimates of uncertainty that Tifft gives for these values?

Does he himself call them "quanta"?

What classes of extra-galactic object (galaxies, subsets of galaxies, etc) does Tifft claim have these specific redshift periods?(my bold)

What results does Croasdale conclude "are quite significant"?

What kind(s) of galaxies does Croasdale's paper cover?

What is the frame within which Croasdale analysed the galaxy redshift data (heliocentric, galactocentric, CMBR, something else?)? How did he decide which parameters to use (except if 'heliocentric')?

Croasdale excluded some 25 galaxies that otherwise met his selection criteria (see Table 2). Within the framework of the rtomes ATM idea, how appropriate is it to exclude these?

Of direct interest here: the Croasdale paper which you put on the table earlier was sent to ApJ in mid-1988, some 6 years before 1994.

You may find a reference or three to 'large-scale structure', of a kind which 2dF and SDSS found in spades ... it's not called that, in the paper, but the reference is there nonetheless.

In post #164 Ari Jokimaki has referred to this paper http://adsabs.harvard.edu/cgi-bin/np...20b0ec3be24584
and I confirmed that in post #164 with the quote from the paper abstract:
He mostly doesn't. I do not that he starts with 72.135 and fractions thereof, then moves to 72.45 and later to still higher values. I think his measurements are accurate to ~0.02 km/s for these values, but clearly they vary by more than that. In such cases one must use the average and the observed spread as a measure of accuracy I think.

It would seem that this effect might be related to having deeper sky samples as time goes by. I think that this might be due to something like cosmic curvature (or acceleration or such like parameter) and that the lower limit might be the harmonics theory value but at larger scales it is not following the log(1+z) formula. This is an area for further study and todays big surveys will surely answer the question if the periodicity is present in them. Even with a sample spread over the range z=0 to z=1 it should be possible to get the 72 km/s quanta to an accuracy of the order of .01 to .03 and the smaller quanta (if the red shift measurements are accurate enough and they are found) to even better percentage accuracy like 12 km/s +/- less than .001.
Yes. Initially of course when there was only the 72 km/s this was sensible. But with the finding of other periods he made his various other notations.
He sticks to just galaxies as far as I know.
the 72 km/s, 36 km/s and maybe one or two others. The first two are at about the level of significance like p~.004 but in the conclusion he refers to a lesser level of significance. I think this is because he allows for the chance of getting the result by varying the parameters.

It is worth mentioning that the 36.225 km/s shifts to 36.375 km/s when the z basis is changed between straight z and log(1+z), so this gives some idea of some slight variations due to this. It will depend on how deep the sample goes how big the difference is.
He simply says "galaxies".
I see no mention of anything but heliocentric redshifts, so don't think he looked at that aspect at all.
They seem to all be based on multiple galaxies close together and the difficulty of having a blend of redshifts. If they are removed for this reason and no other then it would not assist in any way in finding periods. Actually there is a chance that it would reduce periodicity if multiple galaxies together is evidence for a stronger harmonic through extra energy at that location (assuming that they were not just line of sight pairs in which case it would have no effect at all).

Even before seeing Bell papers I thought that the SDSS explanation was agreeable, although I didn't know specifics so well. Some years ago I studied redshift distribution of SDSS quasars (I used the ~16700 quasars release), and noted the valleys at z = 2.7 and 3.5. I then wondered why are there such valleys in the distribution, so I dug up SDSS papers. I found Schneider et al. (2003) explanation for it, and was satisfied. The way Bell describes the process also makes some sense, but I was also disappointed by the lack of details, so at this point I think I disagree with Bell, at least on these two redshift distribution valleys.

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Here's Tifft (1973) paper discussing quasars as well (and apparently Tifft (2003) does also).

This Tifft (1977) paper discusses the effect in stars.

Cocke & Tifft (1989) paper discusses the effect in Lyman-alpha forest.

By the way, is this Tifft (1976) paper the one that you meant that showed evidence for redshift stepping in the disk of individual galaxies?

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Tifft is pretty prolific.

The place where I came across this before was a mention by Arp. However he might have been referring to Tifft.

The multiple redshift states in single galaxies is not as convincing as the individual galaxy differences I think. You cannot see it very clearly in the rotation curves, but it does show in the histograms after removing the curves.

Please show, quantitatively, that "large scale standing waves" will have the observed properties of the (cold, non-baryonic) dark matter derived from observations of spiral galaxies, galaxy groups, and (rich) clusters.

Please show, quantitatively, that "large scale standing waves" will have the observed properties of the dark energy derived from observations of high-z Ia supernovae.

Please show, quantitatively, that "large scale standing waves" will have the observed properties of (cold, non-baryonic) dark matter and dark energy derived from observations of the CMB.With specific reference to the many papers on the large-scale structure of the universe, please provide support for your claim.
Please provide a reference, where you published these calculations.

If you did not publish your work, please provide sufficient details of that work that any reader of this thread may verify your claim ("sensible answers for the distribution of energy with scale that fitted the knowledge of the time") independently.

Please provide similar details, in terms of fitting the observational results published to date.If that is so, then why do you put such things on the table here?

After all, any ATM claim you - or any other BAUT member - make may be questioned or challenged, in any way that is within the bounds of the claims you make. And any and all direct, pertinent questions on those ATM claims, as presented, must be answered in a timely manner.

This is a good question, and one of (potentially) wide general interest.

So I have started a thread in the Q&A section on it: (redshift) periodicies or quantisation - what's in a name?

How does it so highlight?

Specifically, what - quantitatively - is common among these papers (that is not now part of mainstream astronomy)?What special insight do you have into the results of future developments in theory and observational results that are not contained in the combined body of published papers?

What character of the universe are you claiming here (assuming that you are making such a claim, rather than simply reporting what you see as a commonality in the history of physics)?

If you are making a claim concerning the history of physics, what historical evidence can you present that 'past performance is a reliable guide to the future' (to paraphrase)?(my bold)

What "deeply entrenched and widely practiced wrong thinking"?

Specifically, in what way is the current practice of astronomy and astrophysics "wrong thinking" wrt those fiedls being sciences?Who are you quoting (re "raving loonies")? In which paper were these words published?Do you have a list of "all the established oddities that do not fit"?

What, in your HO, are the criteria for determining, or selecting, "established oddities that do not fit"?

How should they "all" be explored?

Unless I misread the various papers you and Ari Jokimaki have put on the table in this thread, Tifft did not make any "observations", nor ever claim to have done so.

In which published paper, by Tifft, are such observations presented?

If there are no such "observations", by Tifft, then what are you referring to?As I read them, the various Tifft papers present an analysis of observations of a very small sample of galaxies, one done within the framework of an explicitly stated 'redshift state' model.

Please explain - with equations, etc - how you conclude that Tifft's reported results (based on his 'redshift state' model) means that "the Earth seems to be at the centre of a whole series of regular shells of matter"?Once you have addressed my questions concerning Tifft's "observations", and the logic (+equations) chain between his reported conclusions and "regular shells of matter", please expand upon your claim here.Please list, as completely as you can, all alternative explanations* of the conclusions published in Tifft's papers that you investigated.

Please ensure that, where applicable, you reference the relevant theoretical papers for all such alternatives, which include presentation of the relevant physics and cosmology.I am unaware of any Arp explanation that is consistent with survey results such as SDSS and the various deep and medium-deep surveys ... in any waveband.

If you have references to papers in which such consistencies are published, please provide them.

*[ETA: you may be interested to read one of the papers you introduced to all BAUT readers earlier in this thread, wrt alternative explanations.]

Can you please quote from the Broadhurst et al. paper ("fair use" allows you to do so), to show that "128 Mpc is based on H=100 km/s"?

For the record, I don't think you can ... because Broadhurst et al. did no such thing.

Please state the consistency between "redshift periodicity" published in papers by Tifft and by Arp.

In your reply, please be sure to include, at minimum, the following:

* the frame(s) within which the reported "redshift periodici[es]" exist

* the classes of objects for which each report such "redshift periodici[es]" (be as specific as possible)

* the number of objects for which each report "redshift periodici[es]"

* the stated estimates of uncertainties of the reported "redshift periodici[es]", both random and systematic.

For Broadhurst et al., please state the size of the sample, the stated "redshift periodici[es]", and the stated estimates of uncertainty. Please also state the commonality between Broadhurst et al. and Arp and Tifft wrt specific objects.

I am not going to attempt a quantitative proof. I will however outline an argument for the possibility.

It is possible to do these calculations for energy for 3D standing waves of any sort, and I think this applies equally to gravitational or electromagnetic waves. Any spherical standing wave structure in 3D will have places where there are wave centres (the centre of the spheres). The centres will be regions of greater energy density with roughly an inverse square relation moving out from those points. Nearer the centre of each wave the inverse square relationship breaks down, especially over the inner wavelength where it reaches a finite peak. Depending on how many waves there are between the centres, the inverse square relation may not really show. For example if there were a 2.5 million light year standing wave with galaxies at the centres, the inverse square would not really show as we only have one wave between a pair of galaxies. But a 110,000 light year or 4.45 light year wave between galaxies would have a significant inverse square energy drop off between the galaxies. The energy distribution would be a spherical distribution. That is what is found for missing mass in galaxies as I understand it. The 110,000 light year wave would have a fairly even energy distribution within and near the galaxy, whereas the 4.45 light year wave would have a strong concentration of energy near the centre of the galaxy. I have been told by Rusian astronomers that 160 minute oscillations are observed in galactic cores (sorry no references available). But I do not that galactic Black Holes have masses that are consistent with BH radii that are 160 minutes and related values.
The above description will have to do for all of these questions. However the high energy of a supernova made me think of some additional aterial that I have not explained (not an answer to your question, but very relevant to the whole theory).

Because harmonics theory is all about non-linearity causing waves to produce harmonically related smaller waves, it is worth thinking about the necessary conditions for this. Non-linearity is greater when waves have more energy. Light waves traveling across the universe are not affected by non-linearity because the e/m fluctuations due to them as they expand into an ever greater spherical traveling wave are so small that they behave linearly to probably better than 1 part in 10^10 or even 10^20. However near the centre of a galaxy (as compared to between galaxies) the energy density of galactic scale waves would be at a peak and so the non-linearity is greater there. Therefore harmonics form faster there. Therefore stars form with greater density in galaxies compared to between gaalxies, and more still near the core.

Likewise, planets form near stars and moons near planets. And so on. Eventually, nucleons form within atoms. In the distant past (and I mean a lot more than 10^10 years ago) there would have been no nucleons but the atom waves would have had the most energy. Now they have lost it to the nucleon waves. The process continues and quark waves form within nucleons but are not fully formed so they cannot exist as free particles.

I hope that this explains why all the cosmic and other objects have the type of structures that we see with dense cores and stuff whirling around them and then bigger gaps between them with much less going on. It is all about non-linear formation of harmonics and where that happens fastest.
I have made no such publications or done such calculations. But see the above desriptions for a guide to how to start going about it.
I hope that I have given the necessary means for the calculations to be done. There might be minor differences for gravity or e/m waves, but I do not think there is much. The energy distribution of a spherical standing wave is reasonably universal I think.

When trying to compare the relative energy of waves at different scales there are unknown factors. In about 1994 I did do a calculation based on 1/f^2 energy in waves that did give a sensible missing mass variation with scale, but I do not see that this is necessarily correct.
The main feature of the harmonics theory is to predict the scale at which various waves form and in that part I think it compliments other theories. If I understood the correlation function for different large scales used in CMBR etc then I think I could check whether harmonics theory is useful there. I have not previously made such a claim (on CMBR waves) here yet, but I would expect some agreement.
Yes, I am happy with that. I think that harmonics theory is rather more far reaching than the typical ATM proposal, so that we might not get done in 30 days, be we will surly get a lot done. I suppose that if the forum organizers think it interesting and we are not going around in circles they might consider a time extension if it is needed. But I am not assuming that for now. I am trying to show as far as possible where harmonics theory has been applied and how well it works at both fitting previously anomolous results and predicting new things that are not predicted by any other theory. There are surely additional applications of it such as CMBR which I could do if I understood the jargon better. I might add some question about this to your new periodicity question thread.

(my bold)

Please show this consistency, quantitatively.

Please include references to sources of estimates of "galactic Black Hole [...] masses".
If I may summarise:

* nothing published

* nothing quantitative, in terms of either consistency between GR/Newtonian gravity (or any part of the Standard Model, of relevance to astrophysics), or any extra-galactic observations.If my summary above is accurate, what leads you to expect that your ideas should receive special treatment?

That there are so many reports of periodicity and certain common ones such as 72 km/s and many different authors indicates that there is something real going on. The fact that it is difficult to join it seamlessly with existing knowledge is the only reason that it might be called ATM. But these reports are from within the astronomical community, so calling them ATM is a bit severe. They are more properly an additional stream.
Well I haven't read the vast majority, so I couldn't say with any certainty.

I think that your original statement about Tifft can now be simplified to:
1. There are certain periodicities in galaxy redshifts that can be observed within clusters. Most prominent is the 72 km/s one. Others are related harmonically to this.
2. When such observations from all over the sky are combined, there can be found a frame in which the base offset of all the periods is common. That frame agrees with the CMBR frame.
3. There are some strange goings on within galaxies that appear to mean that multiple different redshifts can exist within a single galaxy.

Conclusions from these:
A. From Arp and Narlikar, the idea that redshift may be a function of time and not motion or distance. Of course this is strongly correlated for galaxies.
B. There is some component of redshift that is not cosmologically related. It might be called internal redshift. It takes steps like 72 km/s and harmonics.
C. The total sky problem of redshift being co-ordinated is resolved by A above, but the result implies that most galaxies do not have significant random velocities. Also that there is no expansion.
D. From Tomes, that the redshift periodicities can be explained by non-linear standing waves forming harmonics combined with Narlikar's variable particle mass theory.
a. That redshift is velocity of expansion.
b. That particle masses are universal constants for all time.
c. That there are no solutions within well known physics for explaining dark matter - there are, using standing waves.
No, I do not have a specific list. For those interested in anomalies tyhat have been reported in peer review journals, then I recommend the books of William Corliss. These include thousands of items organized in a structured way. They include redshift periodicity as well as mass extinctions and many other things. When you start to look at these together, catastrophism and redshift periodicity fit together like a hand and glove. Regular events in time have huge changes in particle masses! Imagine being a living being when all your protons suddenly did a big quantum energy jump!
It should be based on repetition and statistical tests. Disagreement with theory is not a basis fro rejecting results, although it certainly is a basis for looking closely to see if something has been missed and checking wioth new data by other researchers. I hope that our views are similar in that regard, because I think it is the scientific method.
Well of course we all know that funds are limited. I have the luxury of being a self-employed natural philosopher who has to answer to no-one for where I decide to look. I know that many are not in that position but they have other advantages such as access to journals and so on very close by. For that reason I have set up a trust fund that will allow people to get grants to do research that seriously explores the issues that I raise. I do not want applications from people that are not really serious about this. But I want to make sure that these avenues are not closed off just because people cannot get funding for ideas that are outside the mainstream. I really liked Hoyle's statement that went something like...

If you want to look for diamonds, find a likely spot and dig deep. Don't go where the herd is digging because that ground is already well worked over and the clever ones will be well ahead of you.

Each person makes their own choices. New important results are found by those that really believe what they are doing and stick to it until they penetrate some of the previous wrong ideas. Continental drift, quantum mechanics, relativity, all have to go beyond limitations in thinking where every expert already "knew" that idea was totally daft.

Of course as the QM people used to joke, "your idea is crazy, but is it crazy enough?" also realizing that craziness is no guarantee on its own.