Ray, here's a possible catalog for your usage:

Quasar-galaxy associations (Bukhmastova, 2001)

Abstract:
A new catalog of 8382 close quasar-galaxy pairs is presented. The catalog was composed using published catalogued quasars and active galactic nuclei containing 11358 objects, as well as the LEDA catalog of galaxies, which contains on the order of 100000 objects.

I haven't looked closely at this catalog, but it seems to me that it would be suitable for a first glance of the situation. Or, at least you might get some sort of candidate object list from that catalog.

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Thank you Ari. It is wonderful that such a compilation exists. Clearly it has not been selected with my proposal in mind, so is ideal for the purpose of this test.

I almost forgot, here is the paper that describes the catalog.

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This is really interesting. It is going to take me a little while to digest that paper. But even if they are right about the cause, it shows that Arp was at least right about the probabilities and the need to investigate further.

One thing about the catalog that surprised me was the number of pairs that have both one quasar paired with many galaxies and one galaxy paired with many quasars. That requires some different statistical measures.

They had a cut-off of galaxy redshift at z=.004 I think. Not sure why they did that, but given that Arp says there are many associations with very close galaxies, it may be cutting out some of the most interesting part of the data for testing Arp.

It might make sense to clean those out of the catalog, or at least treat them as separate data sets.

(Actually, it's 0.0004.) I don't know if it was their reason, but there's one practical reason for doing that: galaxies with that low redshift tend to be very close to us, and hence the projected area with 150 kpc radius will be very large. That results in finding too much quasars (since there is always certain amount of quasars within certain area and larger area means more quasars within that area) around them and within the 150 kpc radius. So I think it makes sense to define a cut-off, and I would have probably set it even higher than that.

Edited to add: By the way, most objects that Arp has discussed have higher redshift than the 0.0004, so I think there shouldn't be much worries that most interesting data would be excluded.

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I looked at the paper more closely, and I think you must treat their data with suspicion. Here's why:

Table 2 in their paper gives an example of a case where there's multiple quasars near one galaxy. That's actually a good example of why I would set the z cut-off even higher, to eliminate these galaxies with dozens of quasars "near" them. I got interested of that case, and searched for the galaxy's data in NED. It turns out to be IC 1613, but look at the redshift, it's -0.0008 (negative value)! Seeing that, I thought that well, they used HyperLeda, so perhaps there's some redshift discrepancy between the two databases. But no, here's that galaxy's data in HyperLeda and it has similar z than in NED. So, it seems that at least in one case, they have ignored the minus sign in redshift value and included a case that shouldn't belong in their catalog. At minimum, this means that anyone wanting to use this catalog has to check the redshift data for the galaxies (at least the ones having z < 0.02 or something like that) and eliminate those that have negative redshifts.

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As it is potentially very relevant to this thread, I'm linking to a post I just made in my "quasar?" topic, in regards to a talk about the million quasars from SDSS.

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Yes, good point about the projected size for closer ones. Some of Arp's close ones are a modest distance away, but it is the symmetry on axis that makes them convincing also.
What is the biggest -ve redshift known? Wouldn't it be a bit less that .02? The paper points out that the values for galaxy redshift cluster at the two ends of the quasar light path (i.e. near the quasar and near us). They attribute this to lensing effects being more effective at those two places. However there are a lot more at the end near us than the other end. The ones at the other end can be dismissed from my sample because there is a real association proven for the galaxy and quasar and those quasars must be accepted as having accurate redshifts.

It is not desirable to lose too many at the other end as they are a similar configuration to Arp's examples. I think at the least I need to check all the galaxies that have many quasars near to them. There are a few (with the lowest redshifts of .0004 - thanks for the correction) that have dozens of matched quasars.

I did have a quick look at some aspects of the data. When I selected just the .0004 galaxies and did a graph of apparent magnitude versus z for the quasars it gave a reasonably tight scatter diagram with a rapid decrease in brightness at low z and a more gradual one at higher z. Then I did another selection form around z=.04 which had a similar shape but with dimmer magnitudes, but not nearly as much as the Arp model would predict.

So the obvious expectations of either model are not met. The sample does not behave as expected for either big bang or Arp model. However it might be explicable by the paper's lensing idea because I would think that the optical effects with the galaxy at a different distance might be to change the quasar brightness by a different amount (on average).

But anyway, these are not thorough results, just messing about to see how to cut the data up for graphing.

If the paper is right about the lensing, then am I correct in saying that it means that the observed brightness of all quasars are quite wrong as a measure of their true brightness? There is needed another factor that depends on the lensing and which we cannot easily estimate?

If all that is so, then doesn't it also mean that distant objects are actually dimmer than we think but also that there are actually a lot more of them?

And what are these "obvious" expectations?

How did you derive the (expected) behaviour of the sample for the big bang model?

Specifically, what input parameters did you use?

It is ~a week since this thread was started.

The OP contains the following statement:This statement is quite unambiguous; there are no tentative modifiers (e.g. "may"), no caveats, no qualifiers, etc.

Yet, so far in this thread, you have presented nothing that comes even close to a clear, quantitative description of the test that the OP is so certain about.

In fact, many questions have been asked about the quite vague, unquantified draft presented several days ago; questions that remain unanswered.

When may we expect to see some meat on this test that you assert "alone disproves the cosmological nature of quasar redshifts and totally undermines all the interpretations of the big bang" (no would's, no if's, no maybe's)?

This relates to the catalog Quasar-galaxy associations (Bukhmastova, 2001) and here is the paper that describes the catalog as mentioned by Ari Jokimaki.

This is the distribution by zG/zQ which tells us about the light path, particularly in relation to the proposal that quasars are lensed by some objects near the galaxy such as globular clusters.

... sorry can't format this as I intended ...

zG/zQ
No.of pairs in interval

.0001
5068
.001
1218
.002
974
.005
486
.01
305
.02
169
.05
62
.1
13
.2
10
.5
1
.8
5
.9
2
.95
8
.98
2
.99
5
.995
8
.998
5
.999
44
.9999


The number in any interval is closely related to both delta log(r) and delta log(1-r) (where r=zG/zQ) as well as another factor of r, which seems very reasonable for the optical proposal of the paper, but I have not attempted to work out the actual formula.

In quoting me you omitted this sentence.
It effectively says that the obvious big bang expectation PLUS the the idea that quasars are lensed by globular clusters or some other objects associated with galaxies does seem to fit the data.

It explains why quasars are found preferentially near galaxy axes as Arp has noted and why they have brightness that is so extremely high compared to galaxies. It would mean that they did have correct redshifts just wrong brightnesses. It would validate aspects of both big bang assumptions and Arp observations, but not Arp theory.

I described a test in Galaxy-Quasar associations as a test for alternative cosmologies
Additional information in Galaxy-Quasar associations as a test for alternative cosmologies

Just to explain further, the proposal stated that galaxy-quasar associations (with them at different redshifts) are considered by the big bang to be simply line of sight associations. In that case there should be no dependence of the quasar brightness on anything to do with the galaxy. However there is such an association (although not fully studied yet, just a quick glimpse).

So as the test was originally formulated the first quick look shows that both models are wrong as currently stated. However the lensing proposal allows a reconciliation between big bang ideas and Arp observations. It validates aspects of both and rejects aspects of both.

Big Bang Correct: Quasar redshifts.
Big Bang Wrong: Quasar brightness. (They are all lensed objects)
Arp Observations correct: Association of quasar locations with nearby galaxies. (They are lensed by globular clusters or some other things associated with the galaxy)
Arp Theory wrong: The quasars redshifts would be correct.

The implications of that paper are quite profound.

Gonna snip this right here ...

A word rather often used in this ATM section is 'strawman'; I think just about all readers are familiar with it, and what it means.

It would seem that much of what rtomes has presented as "considered by the big bang to be ...", so far in this thread, bears a striking resemblance to a strawman (or a series of strawmen/(strawpersons?)).

But, let's see what else is in the post ...(emphasis added).

And where, rtomes, may readers of this thread find a reasonably complete, accurate statement of what the 'big bang model' is?

For avoidance of doubt, please be sure to provide links to relevant papers, published in peer-reviewed journals, to demonstrate that 'the big bang model' you have used is, indeed, consistent with the present-day mainstream consensus. To research this, you may wish to take up the suggestion, made earlier by parejkoj (or someone else?) concerning the literature on quasar lensing ... If, after you've done that research, perhaps you'd consider re-stating what 'the big bang model' is?

And I asked >20 questions on that test, as described, here. I also stated "I have many, many other questions about the proposed test, but they will have to wait for at least some answers to the questions here."

Perhaps I missed it, but I did not see any response to any of those questions; if I did miss any such response, would you be kind enough to point me to the post(s) which contain them?

OTOH, if there have been essentially no responses to any of those questions, when may readers expect to them?

No. Wrong again. An increase in the number of quasars around galaxies is a prediction of standard cosmology. You've had this explained to you before. It isn't a large increase, and it isn't monotonic (in fact, it's quite complicated), and it only comes out when looking at a very large number of objects. There are a number of causes, which combine in a nonlinear fashion:

1. strong lensing (multiple images of the same quasar, and amplification of the quasar's light) due to galaxy clusters and massive galaxies almost directly along quasar sightlines.
2. weak lensing (shifting the on-sky position of the quasar and amplification of the quasar's light) due to galaxies clusters and massive galaxies in the vicinity of quasar sightlines. This can also increase the distance between the quasar and the lensing galaxy (notice I said not monotonic!).
3. microlensing (amplification of the quasar's light) due to "individual" objects in galaxies (stars, star clusters, etc.) passing directly along quasar sightlines.
4. the fact that quasars are in galaxies, and generally turn on during merger events, meaning there should be more AGN near the galaxies they are interacting with, as well as in clusters and cluster-precursors.

(Nereid: am I forgetting anything? The lensing effects are intertwined, but I think those are the four big contributors. I suppose, to be complete, I should also include absorption and reddening, which would cause a decrease in the cross-correlation...)

Here's one example from 1999 of the quasar/galaxy cross-correlation function (selected relatively randomly). Here's a more recent one, that you even brought up in a Q&A thread back in August, and you stopped posting to it after Nereid asked you if you wanted to work through some of the math. I suspect her offer is still open, if you were to ask very nicely.

But, again: your summary of the standard cosmological predictions are, again, incorrect.

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The following is a partial analysis of results. The following steps were taken:

1. Remove n=80 cases where zG/zQ > .5 (all but one >.8 and mostly near .99) as these quasars are clearly at distances similar to a galaxy (similar redshift).

2. Remove n=7623 cases where zG<=.005 as the galaxies are so close that the area searched for quasars is too great.

3. Remove n=8 cases where obs-mag-Q was unknown as magnitude is part of the test.

4. Divide into zG ranges for simple analysis with groups starting at .005, .01, .02, .05, .1 and highest was .2154

These 5 groups were averaged to see if any trends were apparent:
(in CSV format)

n,zQ,obsmagQ,zG,kpc,zG/zQ

450,1.52,18.77,.0067,97.0,.0074
225,1.74,19.41,.0162,99.3,.0151
268,1.67,18.97,.0267,92.7,.0236
58,1.73,18.79,.0649,89.3,.0618
25,1.63,19.19,.1308,95.4,.1159

There is no obvious trend in the quasar z or magnitude. For the zG group that had lower z that was excluded there was probably some variation from this.

The average distance from galaxy of the quasar line of sight is always between 89 and 99 kpc (not surprising as selected at <150 kpc).

These results listed here are consistent with big bang expectations.

Other aspects not consistent with the normal big bang expectations are the concentration of cases where the galaxy is a little less than the quasar distance (80 to 99% of the way there) and possibly the variation of the lower redshift galaxy cases (z=.0004 vicinity).

All the data does support the proposal that all quasars are active galaxies at their true redshift that are being lensed by objects close to galaxies. Such a proposal also explains many other (all?) aspects of Arp's observations. Strange objects at anomalous redshifts connected to galaxies and in bridges. They are all actually distant objects being lensed by a real object that is connected with the galaxy. It also explains why quasar brightness has a poor relationship to distance - it is the amount of magnification of the lens varying.

The question is, what are the lensing objects? I will make another post about that.

If quasars are lensed objects, then what is doing the lensing?

First off it is useful to derive a formula that will be useful in considering the amount of lensing of an object depending on its mass, radius and distance.

Let B be the amount in radians by which light is bent by a mass M when the light passes at a distance R from the object. Then B=4GM/c^2/R as Einstein showed (have I got that right ... not sure about the 4). For light passing the sun at its surface this amounts to .0000086 radians or 1.75" of arc.

In the case of an object of radius R at a distance D acting as a gravitational lens of a much more distant object then R/D is the amount of bending that is required to achieve focus at the observer on Earth. So we may set R/D = B approximately but if the object is nearer to the thing being lensed this will be a wrong calculation.

R/D = 4GM/c^2/R or M = (c^2/4/G)*R^2/D

This gives a constant k=3.4*10^27 g/cm, and as Msun=2*10^33 g and 1 pc = 3.1*10^18 cm, we can make M in units of the Sun's mass and R and D in pc, with a constant 5.3*10^12 Msun/pc

M = 5.3*10^12 Msun/pc * R^2/D

For a typical globular cluster we might take M=10^6 suns and radius 20 pc. This will form a lens at distance D=2 gigaparsecs. It won't really do the job as observed for these quasar observations where the distance is smaller by a factor of nearly 1000. It either needs a lot more mass or a fair bit smaller smaller radius. Or some entirely different beast.

What about a white dwarf in a globular cluster? Well we don't really want its radius in pc, but take it as 10,000 km and mass 1.4 suns, and we get that a white dwarf can be a decent lens at a distance of less than 1 AU. So maybe something like that would work, but it needs an awfully accurate alignment. However there are probably quite a few white dwarfs in globular clusters of all the galaxies out there.

You have referred to the number sen rather than the brightness (which is what I was referring to), but perhaps these are connected.

It does seem to me that the slices (taken according to galaxy redshift) do show a better correlation between quasar brightness and quasar redshift than the normal scatter diagrams. Of course that was what I was originally looking for as a result but expecting it to be more strongly correlated with the galaxy redshift distance.

That particular paper that goes with the catalog I think really resolves all the observational issues at dispute between big bang and Arp. Of course the theoretical preferences will remain as to whether redshift is expansion or variable mass. I think that the Tifft discoveries deal better with that issue. But I am now reasonable open to the idea that quasar redshifts are not dominated by an internal component and not ejected by galaxies. They are observable though because of something close to galaxies and possibly ejected by them. One remaining thing of Arp's is not explained by this, and that is the pairs of quasars with similar redshift on opposite sides of a galaxy and on the galaxy axis. So not quite every issue is resolved.

Nereid, my apologies for not having answered this post. Things were happening very fast and I got distracted a bit with the catalog and paper on it.

This is based on my experience in statistics. In market research surveys they generally used 1000 people, but I found that for many purposes you would come to the same conclusions with only 30 people. In this case we only want to distinguish between a random scatter (r=0) and a significant correlation such as in a galaxy redshift versus brightness diagram. That can easily be distinguished with less than a thousand. With a thousand it can also show whether there are effects due to galaxy distance for example.
Well originally I expected a sample with 100 different pairs although expecting some galaxies to appear multiple times with maybe 2 or 3 quasars. The actual survey found is very different from that as both galaxies and quasars are sometimes paired with dozens of the other type. As pointed out this is due to low z and the 150 kpc limit. The implications of that are somewhat unsatisfactory as I don't think anyone believes that one quasar is associated with 10 galaxies although Arp would consider that many quasars could be associated with one galaxy.
It means in the brighness versus redshift diagram making a 45 degree (or something like that) line rather than a vertical or horizontal one. Just looking at the scatter diagram, this might be better.
How did you ask that question before I answered the previous one? You knew the answer. :-)

Probably, but it depends on the scale and the units so it isn't really an angle at all.
Avoiding nasties that result from selection effects. However the cutoff itself is a selection effect, but at least a known one.
It is his and Narlikar's alternative cosmology that si being tested agaisnt the big bang.
Which is what Arp claims. He also claims that the quasars are connected with nearby galaxies which is what is being tested. It is only through that test that the non-cosmological basis of quasar redshifts could possibly be proven.
From the original, a modification was made that introduced the idea of shuffling the pairings as a control. That is the only real change. Also introduced were options to examine separately some subgroups, but this was an addition not a modification.
Not all. As stated at the start I accept that Stockton proved some quasar redshifts are accurate.
Not sure which z cutoff, there are potentially 4. Presumably you mean galaxies?

Two issues which require z cutoffs. At the low end for galaxies, very small z means that 100 kpc (as I was going to use, or 150 kpc as the catalog used) is a quite big angle. That would almost certainly introduce a huge number of quasars that are not associated with the galaxy in the Arp model. The actual cutoff depends on the sample. It needs to make the probability of random line of sight associations small enough that in the Arp model the majority are real associations.

There is also a high z cutoff for galaxies. Arp generally reports the quasars to have far higher redshifts than the galaxies. That means a high z galaxy would only be associated with quasars that are at z=100 or something, so we don't want them in the sample as there will be no real quasar associations if Arp is right.
Again, not sure if this is galaxies or quasars.

I think that for galaxies the high z is enough, but I would possibly exclude galaxies with a low absolute magnitude or certainly non-spiral galaxies as Arp states that quasars are ejected from spiral galaxy axis.
Actually the very first paragraph reads: "Although a majority of astronomers / cosmologists seem to favour a Big Bang model, there is a significant minority that does not accept that redshift is mainly related to cosmological distance and due to expansion of the Universe. This minority includes Arp, Narlikar, the Burbidges and others. And me. ;-)"
I will use whatever samples satisfy the statistical requirements. For galaxies the redshift would be used as a reliable distance indicator. (Another reason to not use very low redshifts).
If quasars are ejected from galaxies then they must be within a reasonable distance of them (including in line of sight). The typical distance of companions to galaxies is about 50 kpc. The survey that I quoted in OP supports this conclusion. So about 100kpc should include most true associations but not introduce too many chance associations.
There need be no lower limit on quasar brightness and no lower z limit. At the high end it would be nice to avoid as many statistical quirks as possible. That was what the 45 degree cut was about. The objective should be to make the quasar selection as similar to the types selected by Arp in his studies. I think that can exclude the very furthest ones.
As indicated previously any known multiple lensed quasars should have only one case used. I don't think that the other issues are relevant unless the things are happening as a result of being next to that galaxy. The random pairing as a control will deal with all such issues at reddening. I think that a control such as that removes the bulk of unquantifiable factors and comes down the the one issue - the association with that galaxy - is it relevant?
Already answered above. Unless you refer to definition of a quasar, in which case I don't know.
The quasars should be selected on the basis that they are the type that Arp selected in his studies. This does not cause any problem to the Big Bang in the analysis. It says that the distant quasars are not really associated with nearby galaxies and so they are random line of sight associations. By randomizing the pairings we can test that regardless of any quirks in the selection process.
Sorry I missed the joke.

Ray

At this time I am very happy with how this thread has gone. Having a catalog almost made for the job pointed out by Ari Jokimaki was a big bonus. The paper that goes with it has to some extent obviated the need for this test. Unless I can find some reason why that paper is wrong, I am forced to come to the conclusion that some parts of the test actually go each way. The surprising result (which I had not even included as a possibility) seems to be that quasars are observed to be associated with galaxies in the way Arp says because of lensing by objects associated with that galaxy. I am not yet convinced about the type of objects that could do that, but it is consistent with a lot of facts. However at the same time, It seems that the quasar redshifts are actually correct, or at least there is no reason to believe they are wrong. This idea that there is a lensing object associated with the galaxy but the quasar is a distant object is a wonderfully unexpected solution to reconciling what seemed irreconcilable differences. I often think that nature does not have paradoxes, only people do.

Did you even read my post above? You seem to have missed the entire point of it. Did you read any of the papers I linked to?

Has Arp (or any other intrinsic/quantized redshift proponent) ever made a quantitative prediction (or even a retrodiction) about the shape of the galaxy/quasar cross-correlation function? I don't care about pictures that show quasars in various positions. You seem to be claiming that the Arpian view is vindicated here: do you mind either spelling out the predictions that are vindicated, or linking to a paper that does so? Most of Arp's claims are based on images that he claims show more quasars around galaxies than there "should be" (or in "strange" configurations), without any bother to show what that "should be" is. Can you provide such a prediction (or retrodiction)?

Again, I don't want words, I want an analytic or numerical prediction about the galaxy/quasar or galaxy/AGN cross-correlation function, which is what the papers I listed above are fundamentally about. The effect they are measuring is not something one can determine by just looking at a bunch of pictures by eye...

You still seem to think that the shape of the cross-correlation function is some big revelation for the mainstream. Here's a hint, as you appear to have missed it:


It isn't.

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"For a successful technology, reality must take precedence over public relations, for nature cannot be fooled." -- Feynman, at the conclusion of his Challenger report

I checked that yesterday from NED's Advanced All-Sky Search. Here's a list of objects having z < -0.01. There's few curious 2SLAQ objects with huge negative redshifts, but I assume those are some kind of mistakes somewhere. But you see a few there that have redshifts slightly smaller than -0.01. That made me to suggest the (rough) limit of 0.02. Of course, best action would be to check all the redshifts in that catalog.

There's also one other point about nearby galaxies that is relevant here; the nearby galaxies have relatively larger proportion of Doppler redshift from peculiar velocities, so the measured redshift of a nearby galaxy is more likely not to be their cosmological redshift than the measured redshift of more far away galaxies.

I don't know much about lensing, but I think the lensing should make background objects brighter, so I suspect that you are correct.

I'm not sure I get your exact meaning here, but I think you are correct. Some distant objects are being brightened by lensing so that we can see them regardless of their normally too large distance to be seen, and therefore there must be more in the places where there isn't lensing foreground objects. Was that what you meant?

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Yes, thanks for that.
Yes, I understood that already (being the statistics side of things).
According to Bukhmastova the amount needed is a few orders of magnitude.
Yes. If some objects are being brightened by about a factor of 1000 it seems to me that 999 times as many other similar objects are going to hidden as a result because the lenses.

(my emphasis)

In light of two subsequent rtomes posts¹, I gather that the proposal, and test(s), in the OP (the one in bold, italicised dark red text) is now off the table/finito/moot/(etc).

If so, then it's hard to say what I, or any other BAUT member, may have asked about, concerning signals in the test(s) that would be expected in contemporary LCDM models (a.k.a. 'the big bang theory', BBT), and so should have been explicitly modeled. Nonetheless, the only major one that I thought of before, that you did not mention, that may have been pertinent, relates to the fact that neither galaxies nor quasars (however defined) are expected to be distributed randomly on the sky ... galaxies aggregate into groups, clusters, super-clusters, filaments, sheets, etc (for example). Depending on exactly how the proposed test would have been set up, the expected (separate) aggregations of quasars and galaxies may have produced a non-null signal (correlation); and maybe the strength of that signal would be expected to have a critical dependence on the details of the proposed test(s). From what rtomes has written in this thread, and other ATM threads, I expected this aspect would have been one that merited many probing questions.

Beyond making sure that the expected signal (expected from BBT) from any proposed test(s) was explicitly and carefully understood (and, preferably, modeled) before the test was run², there are quite a few things that I was prepared to probe, including (not an exhaustive list):

* selection criteria (we barely scratched the surface on this one), for both quasars and galaxies (catalogues, cuts, etc, etc, etc)

* treatment of outliers (every modern catalogue comes with carefully expressed caveats about completeness, accuracy, etc, etc, etc; all these should be properly addressed in any test design, before the test is run)

* controls (e.g. mock catalogues, tests using objects known to be either associated or not associated).

And I'd've liked to question and challenge on frequentist vs Bayesian statistics, if the test had been specified in a way appropriate to such questions and challenges.

Of course, many of these may still be quite pertinent, if rtomes (or other BAUT member) states - explicitly - that he wishes to present (and defend) a proposal for testing any 'Arp theory' wrt quasars and galaxies ...

¹ In particular "All the data does support the proposal that all quasars are active galaxies at their true redshift that are being lensed by objects close to galaxies.", from the first
² I note, in passing, that rtomes seems to have not been careful enough about this; despite what was written in earlier posts, he seems to have neither specified the details of the test(s), nor the expected signals (under 'the big bang theory') before running the test(s). As a statistician, I'm sure he can tell us just how big a no-no this violation of protocol is.

My response is also one to posts #77 and #78.

rtomes, do you still have any ATM ideas on the table, in this thread? If so, would you please state what they are, clearly and explicitly?

That way I, and other BAUT members, can prepare questions on, and challenges to, them.

For avoidance of doubt, it seems to me that you may be presenting one or more of the following:

* (modern) astronomical observations, of quasars and galaxies, are consistent with one or more Arp ATM ideas (e.g. preferential distribution of quasars along galaxy axes)

* (modern) astronomical observations, of quasars and galaxies, are consistent with one or more Tifft ATM ideas (e.g. quasar redshifts are due to variable mass).

You may be right about "most" of Arp's claims, because position, brightness, and redshift are about the only parameters relating to this subject, which can be resolved from the images presently available.
But what I think is the most relevant claim is that some of the available images that have been highly resolved show what could very likely be physical connections between two or more objects with very different redshifts. The "bridged objects" are probably the most dramatic of these. These images are not of the type to be treated statistically, which is what this conversation is about, but they are an important part of the whole subject. That is because if the physcal connection can be demonstrated to be a fact, or very likely, then statstical studies can point to other cases to be studed in detail. If a physical connection is shown to be correct, at some future date, this will cause much rethinking of present views. That is because, in current thought, the "should be" is that the physical connection "shouldn't be".

And, surely, extremely easy¹ to test ... simply put the (long) slit of a spectroscope along one of these bridges ...

Or not; I guess it depends upon how well quantitative models could be developed, to be used to formulate hypotheses that the observations would be designed to test. Not least of the difficulties of developing these would be how to specify the expected emission and absorption lines in any alternative model ...

Would you care to have a go at drafting the outlines of such a model, TomT?

Oh, and surely statistical considerations would be critical in the Discussion section of any paper that came from such observations, wouldn't they?

¹ Of course you'd observe more than one object, and considerable care would have to be taken to plan the observations well

I believe this has been done in the case of NGC 7603 and 7603B and the 2 objects also in the same bridge. Discussed at length here:
More from Arp et al.

For those not familiar with this, search the thread for NGC 7603 to review the discussion.

I'm talking about observations of possible bridges. I don't see where quantitative models come in. I can see where one could study a set of observations of a bridge with say spectrometers, and conclude if there was evidence of a bridge from the quantitative results. This has been done also. See same thread as above. Search for NGC 4319 and Markarian 205. Note spectroscopic tests using both land based instruments and the Goddard spectrometers aboard the HST.

No. As I said there are examples of the tests already done.

Depends. For example, if you had a large number of bridge observations, you could then look at the results statistically. The statistical results would be one thing, but the actual test results for the physical presence of a bridge is what would count the most. Perhaps it would be the statistical results that would justify (or not) conducting the deciding tests.
Also, Arp has done a calculation on the probability of a chance alignment of a high redshift object with the end of the arm of a spiral galaxy. Critics said his analysis was not correctly done. I would lke to see an Arp critic, or perhaps an expert at such calculations participating in this thread, perform what they think is a correct calculation of the probability of a high redshift object lying at exactly the end of a spiral galaxy arm. Then I would like to know the probability of also finding 2 such additional objects in the same arm.

Sorry, I have had a busy day and will have again tomorrow. Will try to catch up with the ones I haven't replied to soon.

I have stated quite clearly what the test is. It is between two possible situations as regards quasar-galaxy associations with very different redshifts as seen in the sky. One, the big bang, is that they are merely random associations. The second of Arp and others, is that they are really associated and the quasar redshift is not a measure of cosmological difference.

The test is clearly stated to examine the plot of galaxy redshift versus quasar brightness. It should be compared to a graph of the same sample with randomized pairings. If a strong relationship is seen between the galaxy redshift and the quasar brightness then it cannot be that the objects are merely line of sight objects. No-one has put forward any reasonable argument for why this would not be so. Talk of a straw man does not invalidate this argument. Why is it a straw man?

The idea of the control case with randomized pairings is simply to correct for any selection effects. If there is no significant difference between the graphs for the true pairs and the randomized pairs then clearly the alternative cosmology in which quasar redshifts are an unreliable measure is proved useless to explain the data.

This thread is not about proving one cosmology of the other. It is a proposal to perform a test that potentially has the power to show one or other or even both cosmologies to have weaknesses to explain observations. It does this by a new way of testing the apparent associations to see whether they are real just line of sight.