I have not withdrawn the proposed test. I did get very interested oin the quoted paper because it added a very reasonable third possibility that can also be tested for. That possibility is that:

There are some objects that are physically associated with nearby galaxies (possibly globular clusters) that are acting as strong lenses (~1000 times brightness magnifiers) of distant active galaxies. Under this third possibility, which should be added to the test, quite a few things are explained that have never been explained before:

1. Why quasars have a poor brightness relationship to redshift. Answer - because the amount of brightness magnification has a wide range of possible values.

2. Why quasars are seen to be physically associated with nearby galaxies as found by Arp. Answer - because they are being lensed by objects that are associated with the galaxy.

3. Why quasars can be seen at extremely high redshifts. Answer - because their brightness is being increased approximately 1000 times by lensing.

There is at least one claim by Arp that cannot obviously be explained by the proposal and that is that quasars are seen in matched redshift pairs either side of a galaxy. However that is the only outstanding issue of debate that I can see that is not resolved by the proposal.

Of course that does not make it correct, just an ingenious idea. To be correct it must withstand a variety of additional tests. The probabilities of quasars being seen as that much brighter must be balanced with the number of objects at that distance. There will be a correct distribution of the redshift ratio of the galaxy and quasar according to the optical properties relating to the lensing which can be tested against the sample. It would also be helpful if the actual nature of the lensing objects could be understood well enough to make predictions.
Certainly the distribution of objects in the universe is not random but there is large scale structure. Interestingly, I have been arguing for this fact for decades while people who believed in the big bang told me that the universe was uniform at large scales.

However never mind that. The test fully copes with the non-randomness of both galaxy and quasar distributions. By excluding all cases where the galaxy and quasar redshifts are similar and only including those where the quasar redshift is much greater. Is there any reason to believe that the quasar distribution is an exact copy of the galaxy one but just at 100 times the scale? I think not. In that case, randomizing the pairings is a fully adequate measure to cope with all properties of non-randomness in the samples.
I think that a simple range of redshifts for galaxies is an adequate measure combined with classification as spiral galaxies. It is close by spiral galaxies that Arp claims quasars are ejected from. That is what should be the basis if the test.
Agreed. I am not sure what you mean by outliers, I assume those that are just beyond the magnitude limit or some such factor. I would deal with these by using limits that are well within the catalog sample limits.
If one is doing a test between two alternative cosmologies, then for an honest test the two must be on an equal footing. If you assume that one has only one in a million chance of being right, then a result that would arise only once in one hundred thousand times from the other will be accepted as the most likely choice over a result that agrees 100% with the other. In that case I say the investigator is not scientific but is acting from faith. I have no interest in such investigations or investigators. I am interested in the truth whether or not it agrees with what I think is most likely right now.
I wish to test both Arp and Big Bang as alternatives to explain an analysis yet to be done. That test remains as it was. In case both fail to some extend, it makes sense to now add a third possibility which is the proposal made by Bukhmastova.
When I first proposed the test I was not considering the possibility that quasars were objects that were being strongly lensed by objects associated with nearby galaxies. I do not think that many people have looked at such a proposal seriously. It would reconcile many (but not quite all) of Arp's observations with standard cosmology. Considering how vehemently people, even in this thread, have spoken against Arp, I do not believe that others have thought about this either. But I do think it is well worth thinking about. Isn't science interesting when we explore such possible tests and how we might think about it?

It has taken me a little while to digest these and I have been a little short of time recently. Please correct me if I am wrong, but it seems to me that the lensing being referred to is not in the same category as what Bukhmastova is stating, namely 1000-fold increase in brightness, and caused by very close by objects.

To that extent, although I can see that statistics will be affected, I think that my random re-pairing suggestion would deal with the issues of lensing effects on statistics if there are no real associations between galaxies at low redshift and quasars at high redshift.
I am not claiming Arp vindication. I am proposing to test two rival theories. However Arp has made a prediction about quasar distribution. Before one of the long thin sections of sky was sampled he predicted two peaks in the number of quasars at certain longitudes corresponding to two nearby galaxies near the strip. As I understand it he was quite correct about that.
Well, you may want that, and that is quite reasonable, but it wasn't what I was proposing to test.
I don't think that. However in the quantized redshift revisited thread I did discover that there are times when it is misused. When the redshift is included as a reliable measure of distance to calculate distances between galaxy pairs in 3D and then the result agrees with the big bang, the big bang has actually already been assumed to be correct. When testing between rival theories you cannot assume that one is correct in the analysis except in the case of reductio absurdum.

Let us accept this as correct when testing spatial density. This would not lead to a quasar's brightness having any correlation with a line of sight galaxy's redshift, would it? That is what I propose to test.

rtomes, can you please, in one post, state, simply and clearly, without editorial comment, just what the ATM proposal you intend to present (and defend) is?

And, in a separate post, state:

a) exactly what you propose to test; if said test is of "Arp and Big Bang as alternatives", provide sufficient references to papers on these two as to comprehensively, quantitatively, describe them

b) exactly what the test will actually involve; this should be fully quantitative*

c) exactly how you will address the 'seek and ye shall find' shortcoming of 'fishing expeditions'.

* IOW, no more "very different redshifts", or "redshifts are similar", or "strong relationship", or "no significant difference", or "a simple range of redshifts", or "a fully adequate measure", or "well within the catalog sample limits", or ...

Not wishing to revive a now closed thread, the NGC 7603 work was not at all an example of what I suggested.

If the only photons detected by the spectrograph are from the parent and the object 'in' the bridge (whether continuum, emission or absorption lines), then all you learn is that the two objects have different redshifts.

The real test is how does the redshift of lines in the bridge vary along the bridge. If there's a systematic variation of a few tens or hundreds of km/s, then the bridge would seem to be local to the parent, and the high-z object apparently embedded in it would be a chance alignment*.

But - and this is the key part - if the ATM idea does not contain anything on how the redshift of material in such bridges is expected to vary, along the bridge, then this kind of observation is useless - no matter what is found, you have made no progress.

In any case, as rtomes has made clear, this kind of thing is not what his ATM idea (proposal, test) is about, so let's not hijack it ...

* This is just one example, of course.

Redshift is but one of many things to investigate to determine if a bridge is real or not. Actually, if redshift values along the bridge varied from that of the galaxy to that of the object, it would tend to disprove Arp's theory of redshift, and probably require a new theory different than Arp's or mainstream.

Actually, a result of Arp's theory would be that the bridge be either the same redshift as the host galaxy, or the same redshift as the connected object.
An apparent bridge between the objects is not a ATM idea, it is a physical observation that should be analyzed thoroughly. Advancement of knowledge is made by studying a physical observation including testing/analyzing the possibilities to explain it. If a scientist doesn't have a theory to explain the observation, this doesn't mean the observation is useless.
My initial post was meant merely to respond to what I thought was a misleading statement about the scope of Arp's work. It was meant as a one time comment, not a discussion starter.

I already did this in my first post of the thread:
There is no difference between my proposal and the test. The proposal, as stated is to perform a test.
Some of the parameters will need to be different depending on the catalog(s) used to get the data on galaxies and quasars. So I will express things in terms of those parameters:
z_G_min = minimum redshift of galaxies to include in the initial sample.
z_G_max = maximum redshift of galaxies to include in the initial sample.
Galaxy classification to include all types of spirals, exclude all other types.
dist_G_Q = distance limit set for true association of galaxy and quasar in alternative cosmology. This will be around 100 kpc (maximum 150 kpc).
The z limits will need to be set based on probabilities that depend on the particular catalog(s) used because it is desirable that when the alternative cosmological model is considered then the probability of line of sight coincidences must be kept low compared to the actual number of pairs found. Using too low value for z_G_min will cause too many random non-associated pairs.
The proportion of the sky within dist_G_Q of a galaxy at redshift z is:
(dist_G_Q/c/z*H)^2/4/pi
Z can be substituted by z_G_min to check that the number of galaxy-quasar pairs randomly expected is smallish compared to the actual number of pairs.
Because we are testing a correlation versus the galaxy redshift we need a ratio of at least one order of magnitude in the galaxy redshift, but not too much more or we will be sampling galaxies that are too far away for associated quasars to be seen in the alternative model. So z_G_max ~= z_G_min * 10.

For the quasars I think that a simple observed magnitude maximum limit is sufficient as a selection criterion once it is established that the definition of quasar is compatible with that used in Arp (and any other) papers that showed galaxy-quasar associations.
The maximum redshift used for galaxies by the above approach should be significantly less (say at least 25%) than the minimum quasar redshift, so it should satisfy the condition that in the big bang model there is no possibility of real association between the pair.

The magnitude limit for the quasars will depend on the catalog used. But it should be no more than the stated redshift to which the catalog is believed to be reasonably complete. This is to satisfy you, not me. I don't think that such aspects of the catalog will bias the result in any way as they are relatively independent variables. However the reduction of the quasar sample by a brightness limit can also reduce the probability of random line of sight pairs. This may be needed if the catalog(s) are very comprehensive ones. On reflection I think that a redshift limit should not be used as we are plotting the quasar redshift as the dependent variable in our results so that would cause a nasty cutoff that would mess with the statistics of correlation.

After catalog selection but before analysis the number of objects that will be selected needs to be estimated and using the probability of random pairs based on proportion of sky for galaxies and number of quasars in the sample, the free parameters adjusted to reduce the random pairs to less than 1 per galaxy while keeping the quasar sample of a similar order of size to the galaxy one.

Thank you.

Please provide references which contain explicit, detailed, and (preferably) quantitative descriptions of "the rival theories" ("Big Bang" and "Alternative").

Please show, in detail, using pertinent material from those references, how each of the stated "expected outcomes" was derived.

Thank you.

"[...] to include in the initial sample." (emphasis added)
* how many samples will the test involve?
* to what extent will the selection of samples after the initial one be determined by the results of one or more analyses on the initial sample?

"Galaxy classification to include all types of spirals, exclude all other types."
* how will galaxies be classified?
* why are spirals the only galaxies to be included?

"dist_G_Q = distance limit set for true association of galaxy and quasar in alternative cosmology. This will be around 100 kpc (maximum 150 kpc)."
* how will distances be estimated?
* why "around 100 kpc (maximum 150 kpc)"?

"The z limits will need to be set based on probabilities that depend on the particular catalog(s) used [...]"
* how, explicitly and in detail, will "the z limits [...] be set"?
* specifically, to what extent will "the probability of line of sight coincidences" be calculated ab initio?

"it is established that the definition of quasar is compatible with that used in Arp (and any other) papers that showed galaxy-quasar associations"
* how will this be established?

Some minor clarifications:
* what are "c" and "H" in the formula "(dist_G_Q/c/z*H)^2/4/pi"?
* is "Z" a typo for "z" in "Z can be substituted by z_G_min to check [...]"? If not, what is it?

Sorry, I had intended to deal with this in the same post and forgot.

Th initial sample meant the galaxies and quasars eligible by way of magnitude and redshift to be in the sample. The final sample was to include only those that were sufficiently close to each other to qualify as pairs. That means being within (100 kpc or) 150 kpc at the distance of the galaxy.
I propose to use a catalog that has classifications and to accept those. Any classification with "Spiral" in its name would be accepted. The reason is simply that Arp has claimed that quasars are ejected from spiral galaxies along the axis. Therefore that must be the basis of a test for whether he is right or not.
The distance will be based on an accepted estimate of the Hubble constant (say 71 km/s/Mpc) and the redshift of the galaxy. You know the formula. :-)

That distance is a reasonable upper limit for quasars if they are ejected from galaxies. The typical distance is found to be 50 kpc on the projected line of sight. So I was inclined to use 100 kpc, but seeing that other researchers have used 150 kpc, that is also acceptable.
The line of sight coincidences can be set by combining the area of the sky that the chosen distance covers (square degrees or square minutes or whatever) as a fraction of the total sky in the sample with the number of objects that are initially selected. If for example there are 50,000 galaxies and 10,000 quasars initially selected and the region of 150 kpc around each galaxy covers 0.001% of the sky (this will depend on the average redshift so can be modified if need be) in the catalog then we expect about 0.1 quasars per galaxy to be within that region. Such a result is acceptable, being less than 1. That should lead to something of the order of a few thousand pairs, an acceptable result.

Of course I have ignored that even in the big bang there is supposed to be some slight lensing effects. But while this does affect the number of coincidences it does not affect the brightness of the quasar in relation to the galaxy redshift by an amount that could materially alter the scatter diagram in the way that would need to happen if Arp is right.
Maybe some astronomers can help me here.
c is the speed of light
H is the Hubble constant
yes, Z was meant to be z

How, if at all, will the range of distances and redshifts in galaxy clusters (esp rich clusters) be addressed, in estimating the distance of a galaxy, in the samples?

How - explicitly, with formulae and algorithms - will the difference between distance and projected distance be addressed?

Why is "[t]hat distance is a reasonable upper limit for quasars if they are ejected from galaxies"?

In which papers was "[t]he typical distance [...] found to be 50 kpc on the projected line of sight"?

Which "other researchers have used 150 kpc"?

(to be continued)

I am bumping this post, with its questions, because they are essential aspects that need to be addressed before the test(s) can be fully specified (so it seems to me).

This has already been recognised in a later rtomes post:For avoidance of doubt, I am asking for explicit, quantitative statements of the pertinent parts of "the rival theories" ("Big Bang" and "Alternative") - not word salads - and references to source material sufficient for any reader to be able to independently verify the statements.

I am also asking that the derivations of the explicit, quantitative "expected outcomes" be provided.

You may cout me in. I found another redshift that I call "Einstein's universe redshift" since it follows from Einstein's theory of gravitation and shows up in Einstein's stationary universe. This redshift is exponential with distance so it nicely fits the cosmological redshift and it has the same (observationally) acceleration of (apparent in this case) expansion. That's why I think it may replace not only the "cosmological redshift" in your equation for total redshift but it may apply to quasars as well since it shows up in any relatively dense cloud of dust (which I imagine might surround any quasar).

The redshift is predicted by Einstein's theory adjusted to "dynamical friction" of photons (considered "negligible" by the mainstream) through energy conservation. The only adjustment to Einstein's theory turns out to be the introduction of a new tensor, that I call tentatively the "general time dilation tensor", which equals minus the 3D space curvature tensor (3D Ricci tensor). The necessity of the adjustment follows from the principle of conservation of energy in Einstein's theory. Since the mainstream theory rejects the conservation of energy for the whole universe this theory is unpopular whith the Big Bang people and has to stay ATM. Scientific journal editors mainain it won't be interesting to physicists despite being formally sound (according to referees). If just energy were conserved globally...

Physical sense of this theory is that in the curved space the time runs slower by the factor of exp(-x/R_E) where x is distance from us to the point in space and R_E is radius of curvature of space (in case of Einstein's universe it is so called "Einstein's radius of universe"). It predicts the local Hubble constant of apparent expansion as H_o=c/R_E, where c is speed of light, and predicts acceleration of expansion as dH/dt=-H_o^2/2 (as actually observed within observational error). The details are in http://geocities.com/jim_jastrzebski/sci/3270.htm

To be the only source of cosmological redshift the density of the universe would have to be 6x10^-27Kg/m^3 while present estimate is only 2.3x10^-27kg/m^3 with accuracy 7.5% (as I was told, but I didn't check the reliability of this source yet).

BTW, "Einstein's theory with conservation of energy" predicts the same shape of the spacetime as Narlikar/Arp theory (namely the "flat" spacetime, wich also has to be "flat" due to Noehter theorem). It just explains its physics differently, through the geometry of the spacetime, and not trough the variable mass of particles, as does the Narlikar/Arp theory. Also it may be verified that the result of Einstein's theory, that time runs slower in deep space for any observer in the uiverse (on the Copernican principle) might seem strange but surprisingly enough (at least for me) it turned out not to cause any logical contradiction. Just one more strange result of Einstein's relativity.

__________________
Forming opinions as we speak

As stated earlier, the distance for galaxies will be based on the assumed Hubble constant and the observed redshift. Clusters make no difference to that.
Only projected distance (at the galaxy redshift distance) is to be used. All statements about galaxy-quasar separation are taken as projected distance. No attempt is to be made for the true angle of projection which will not necessarily be across the line of sight. Ultimately of course that means that real line of sight coincidences are also included. The degree to which this is happening can be estimated based on the samples and the formula for this has already been given and anyway is a simple matter of probabilities. On grounds of symmetry, in the alternative cosmology case, the average projected distance is reduced by a constant proportion from the average actual distance.
Because of observations of galaxy-quasar associations made by the alternative cosmology groups.
As already given in my opening discussion - In 1990, the Astrophysical Journal supplement series published "Associations between Quasi-stellar Objects and Galaxies" by G Burbidge, A Hewitt, J V Narlikar and P Das Gupta. My statement in that first post "These values correspond to a distance of around 40 megaparsecs and a separation of about 40,000 parsecs. The actual average separation would be more like 50,000 parsecs because sometimes we see the pair at an angle."
As already given - Quasar-galaxy associations (Bukhmastova, 2001)

There is no source material as this is a newly proposed test.

In the big bang theory high redshift quasars are at cosmological distances and have no real association with nearby galaxies that share a common line of sight. Therefore in any line of sight pairs matching it will make no difference if the quasars are shuffled in the pair matching. You don't need any formula or references for this, you just need the ability to think and a slight understanding of statistics.

In the alternative cosmology case (as proposed by Arp, and supported by Narlikar, Burbidges etc) the quasars are physically associated with the galaxies and therefore are actually at very close to the same distances. That means that if the galaxy redshift is plotted against quasar brightness we are doing a true correct plot of quasar distance versus brightness which has never been done before as far as I know. However strong the true quasar distance versus brightness relationship is, it will obviously be much less strong when a wrong distance is used - the quasar redshift which is not the true distance in this model. Therefore if this alternative cosmology is correct then the plot must show a higher correlation than is shown when the quasar brightness is plotted versus the quasar redshift. Also, in the alternative case, randomizing the quasar galaxy pairing must destroy that relationship as the galaxy randomly paired with the quasar will no longer be the true distance. So there is a huge difference between the big bang and alternative cosmologies on what must happen between the line of sight pairs and the randomly rematched pairs in the difference between the two plots.

A third case is the proposal of Yushchenko, Baryshev, Bukhmastova and others that quasars are active galaxies being strongly lensed by globular clusters, dwarf galaxies or other objects that are associated with nearby galaxies. If this proposal is correct, then the quasar redshifts are cosmological but their brightness is not a simple function of distance but is amplified by huge factors of the order of 100 to 10,000 times. Therefore there should be no improvement in the scatter diagram correlation when the galaxy redshift is used versus the quasar brightness (the same as the big bang). This proposal can be differentiated from the big bang proposal due to the fact that the line of sight is meaningful because the lens is at the distance of the associated galaxy. If correct there must therefore be meaningful effects of the galaxy redshift or the ratio of the galaxy redshift to the quasar redshift on the amount of brightening of the quasar. This can be found by dividing the pairs into groups based on either the galaxy redshift or the redshift ratio (as was done by Bukhmastova) and then plotting quasar brightness versus quasar redshift separately for the groups. Again this should be done for the variation of projected distance from the galaxy into groups such as < 50 kpc, 50 - 100 kpc, 100 - 200 kpc, 200 - 400 kpc. If the lensing proposal is correct then these various divisions should show some variation in the brightening due to the lens because the size of the lens as seen by us will be varying and its real size might be expected to have some relationship with projected distance.
I have only indicated that the expected outcomes are either uncorrelated, or no different between the pairs sample and the randomized pairs sample, or that they are expected to be different. The difference between the big bang and alternative cosmology is so great that it will be obvious. If the alternative cosmology is correct then additional factors can then be used to arrive at a model of quasar brightness. I would use multiple regression here to establish the important factors and arrive at a formula for quasar brightness in terms of all the above mentioned factors as well as any other known morphology factors for objects where available. This same applies to the 3rd possibility where an empirical formula for lens brightening would be derived from associated galaxy factors such as redshift, redshift ratio (to quasar), projected distance and any galaxy morphology factors.


It is also worth mentioning that apart from this test, there are additional tests that could be done in this third case. If a low redshift globular cluster is lensing a high redshift active galaxy then either that globular cluster must be visible next to the quasar or its light must be mingled with it. In that case there must be a second (fainter) spectrum with different redshift that can be detected within the spectrum. This is a very clear test that would demonstrate beyond any doubt that the lensing was a fact.

When I started this thread I was assuming (and I suspect that many others were too) that there was just one dimension to be tested. However I now see that there are two dimensions so I will clearly describe these as separate factors:

Factor A: Quasar redshifts are either reliable cosmological distance indicators or they have a strong internal redshift component.

Factor B: Quasar are observed to be either associated with nearby galaxies or not.

The combination of these two factors lead to four possibilities not two.

Big Bang: Quasars are at cosmological distance and have no association with nearby galaxies.

Alternative Cosmology: Quasars are not at cosmological distance but are physically near associated galaxies, probably being ejected from them.

Globular Cluster Lensing: Quasars are illusory objects being active galaxies that are strongly amplified by objects associated with the nearby galaxies. Therefore the quasar redshift is real but not the brightness. The association is real, but between the lensing object (who's redshift is not measured) and the galaxy.

4th: Quasars have bung redshifts but it has nothing to do with nearby galaxies.

The following graphs have been produced using a spreadsheet program and some random numbers. They fall into two sets, those generated assuming that the big bang is correct and those generated assuming the alternative cosmology is correct. In each case three graphs are produced, being a galaxy-galaxy scatter diagram, a quasar-quasar scatter diagram and a pair scatter where the galaxy redshift is graphed versus the quasar apparent magnitude.

The key point is that if the big bang is correct that last scatter diagram must be more random than the original quasar-quasar scatter diagram. If the alternative cosmology is correct the pairs scatter diagram must be more highly correlated than the quasar-quasar scatter diagram.

For the big bang case, there is no meaning to the pairing of a galaxy with a quasar so they are just random pairings. Randomizing the pairings would make no difference. For the alternative cosmology case, I assumed that the internal variation in brightness of a quasar was a lot less than that used in the big bang, because the redshift is essentially meaningless and so that is the cause of the scatter. I don't propose to go into a lot of details of the simulations. If you want to satisfy yourself about this, I suggest that doing the exercise yourself is worthwhile. I will note that there is probably a bit of difference between the quasar-quasar scatter between the big bang and alternative cases. That simply means that I didn't spend time trying to fine tune the result to be exactly the same as it is all just a seat of the pants simulation.

They key point, I repeat, is the huge difference in the galaxy-quasar pair scatter diagram compared to the quasar-quasar scatter.

Assuming that the big bang is true. That means that quasars do have huge variations in absolute magnitude and the redshifts are cosmological.


galaxy redshift and galaxy apparent magnitude


quasar redshift and quasar apparent magnitude


galaxy redshift and quasar apparent magnitude i.e. pairs

Assuming that the alternative cosmology is correct. This means that quasars are at the distance of the associated galaxy. Quasars brightness variations must then be less than in the big bang model to produce a similar quasar-quasar scatter. That leads to a much tighter scatter diagram in the pairs case.


galaxy redshift and galaxy apparent magnitude


quasar redshift and quasar apparent magnitude


galaxy redshift and quasar apparent magnitude i.e. pairs

So the comparison between these shows what we are testing for. I have not produced the random pairs comparison charts here. For the big bang it remains unchanged because the associations were random in the first place. For the alternative case it produces a totally uncorrelated graph (similar to the big bang one).

The simulation data has not been produced for the 3rd theory where quasars are considered to be distant active galaxies lensed by nearby objects associated with galaxies. This is less straight forward to simulate because the quasar brightness is going to depend on more factors that relate to the whole geometry and is stated to result from 100 to 10,000 fold brightening which affects the magnitude by 5 to 10. It is anticipated that at least some of that variation must be correlated with several aspects of the geometry in a meaningful way.

In the test, if there is a close correlation of quasar brightness with galaxy redshift as shown in the last simulation graph above, then the alternative cosmology must be accepted and both the big bang and lensing proposals rejected. If the pairs remain highly scattered then the alternative cosmology must be rejected.

To decide between big bang with quasars being real objects of the assumed brightness, and the lensing proposal where the true brightness is less by 5 to 10 magnitudes, there are several additional tests that may be done.

1. The number of pairs detected versus what is expected from random line of sight must be tested. The slight increase due to expected (by the big bang) lensing by galaxies and clusters must be allowed for.

2. The sample my be divided into sub-samples depending on separation in kpc, galaxy redshift, galaxy redshift divided by quasar redshift. If these samples have significant differences in quasar apparent magnitude in a coherent way that can be explained by the lens geometry then that proposal would be favoured over the big bang, otherwise not.

I would also note about the above diagrams that even a sample of 100 makes these relationships perfectly clear. However for the purpose of making subsamples to compare big bang to the lensing hypothesis a sample of 1000 or more is desirable.

I do suspect that this test will show some holes in Arp's theory and want to say a few words about the significance of that. It is important to look carefully at the difference between Arp's observations and his theory. It is also important to distinguish between the several different factors that the Big Bang and Alternative Cosmology disagree about, because they may well go different ways.

If the quasar-galaxy pair plot does not show a stronger correlation than the quasar-quasar plot, then that should lead to rejection of Arp's hypothesis that quasar's are ejected from spiral galaxies and at the same distance. However it would not disprove his observations that quasars are associated with galaxies, but it would at least show that the quasar redshift is cosmologically correct, or no longer under suspicion. It would mean that Arp's ideas about quasars coming rapidly into line with frequencies of other matter via the VMH would be wrong because quasars would not be new creations. However the VMH itself would not be disproved as it also rests on evidence such as redshift periodicity and explains that evidence where no other theory can.

But the lensing proposal if supported would cast suspicion instead onto the quasar brightness as being not a true measure of intensity but a result of magnification. It would offer an alternative explanation to what quasars are - illusory objects resulting from two real objects, the lens and an active galaxy nucleus far away.

If the galaxy-quasar scatter was a good correlation, the big bang would demonstrably wrong because quasar redshifts would be demonstrated to be non-cosmological. If there was no good correlation the big bang would not be threatened, although if the lensing proposal was supported it would mean that the interpretation of quasars would need serious revision and all deep space statistics would need to be seriously revised. If quasars were found to really be active galaxies magnified 1000 times in brightness, then not only would quasars be a different class of object 1000 times dimmer, but there would be 1000 times as many of them.

Would you mind providing the input data please ("some random numbers")?

Also, what is actually plotted in each of the three graphs?

For example, what is "z"? and what is "App. Magnitude"?

I'm having particular difficulty with the x-axis of first and third graphs; for example "log(1+z)" with a value of -2 means z is -0.99, and -1.1 means a z of ~-0.92 (as far as I know, no galaxies have observed redshifts in this range).

The second graph would seem to imply quasars with a redshift range of ~0.12 to 3 - is this what you intended?

I will come back with the actual distributions used later. Will just answer the other questions now.
z is a thing astronomers use that measures the proportionate change in wavelengths. Apparent magnitude is observed magnitude rather than absolute magnitude. The magnitudes may not be in quite the correct range as I just generated absolute magnitudes in some range and adjusted them for distance based on z. The intention is to try and get a scatter diagram for the galaxy-galaxy and quasar-quasar cases that are reasonably realistic (ignoring any bulk displacement in magnitudes because I started with the wrong range of absolute magnitudes).
Oops, sorry, my mistake. That axis should be labeled log(z) not log (1+z) ... force of habit as I am so used to dealing with log(1+z). So -2 means z=0.01 and so on. (the graphs are now corrected)
That sounds about right. This will become clearer in my next post where I will give the rough distributions that I used. I did not intend these to be especially accurate as far as real data goes, just to highlight that data based on one or other model being correct can give similar results for galaxy-galaxy and quasar-quasar scatter diagrams but will give very different results for the pairs case of galaxy (z)-quasar (app.magnitude).

Here is what I calculated in OpenOffice spreadsheet language with explanation. I can provide the file if desired, it is about 100KB type SXC.

For the Big Bang
============

For quasars
=========
(100 generated)

quasar abs.mag = -30 +5*rnd() +5*rnd()
(these rnd() are in the range .000 to 1.000 and so the values used will peak at -25 and have a triangular distribution with limits -20 and -30 abs.mag.

z = 3*(rnd()+rnd())^0.4
the random numbers will make a value averaging 1 with triangular distribution and limits 0 and 2. I take this to the 0.4 power to allow for more being further away, but do not use the 0.333 power because the fractal dimension of the universe is less than 3 (taken as 2.5). This is not very important, just affecting the density of points at higher z.

log(z) = log(z) to base 10 incorrectly stated as log(1+z)

app.magnitude = =abs.mag+5*LOG10(z*300000/70*100000)

For Galaxies
=========
(100 generated)

abs.mag = -25 + rnd()*2 +rnd()*2
makes a mean of -23 with triangluar distribution and limits -12 to -25

z = =(RAND())^0.4*0.1
again a fractal distribution by distance (with 2.5 fractal dimension)


log(z) = log(z) to base 10 and wrongly labeled as log(1+z)

app.magnitude = =abs.mag+5*LOG10(z*300000/70*100000)
(same as quasars calc)

Note that each time anything is done in the spreadsheet it recalculates the page so a new graph results with the same characteristics. Therefore the pairs do not reflect the other graphs data but are an equivalent set of new samples.

For Alternative Cosmology
===================

All calculations for galaxies are the same. For quasars the following calculations are different.

abs.mag = abs.mag.galaxy +RAND()*2+RAND()*2+5
(note much dimmer as it is at galaxy distance only - assumed to relate to galaxy brightness although that is not essential)

app.mag calculated from galaxy z not quasar z
(as quasar is taken to be at galaxy distance)

I have loaded the spreadsheet to my website. You can obtain it from: http://ray.tomes.biz/scatter-gqp.sxc which is an open office spreadsheet. It has 4 sheets, the first one being the big bang and second is alternate cosmology. These two have the quasar-quasar and galaxy-galaxy graphics. The other two are repeats of these with the columns reversed as that was the only way that I could get the quasar-galaxy graphics.

Hi Nereid

I have replaced the graphics in my earlier post, correcting the log(1+z) mistake so that they all now say log(z). Therefore these will show correctly in my post and your reply. I don't know if you are able to edit your post to indicate "now corrected" or something like that. Thanks

Ray

Thanks.

I'm still confused though; the x-axis on the Quasar graph goes from 0.05 to 0.6, which if it is log(z) then z would range from ~1.1 to ~4, which is quite different from the ~0.12 to 3 you said "sounds about right".

Could you clarify please?

Thanks for this.

I'm having difficulty with the link; apparently my PC doesn't know about .sxc files (probably something really simple that I'll figure out with seconds of posting this!); so I can't check what's plotted in the 'Quasar-Galaxy Pairs' graphs - would you mind explaining what these are? In particular, which quasar's apparent magnitude is paired with which galaxy's redshift?

Treating the methods you used to come up with "App. Magnitude" and z, for galaxies and quasars, as a black box, it would seem that one way to test whether you are modelling the real universe is to ask how closely the cumulative distribution function of quasar apparent magnitudes, and the cumulative distribution function of quasar redshifts, and the cumulative distribution function of galaxy apparent magnitudes, and the cumulative distribution function of galaxy redshifts match the same four functions estimated from observations.

Have you done such a test? If so, what "from observations" data did you use?

Peeking into the black box, through just one small window, it seems you have made a fixed assumption about the geometry of the universe:

"app.magnitude = =abs.mag+5*LOG10(z*300000/70*100000)".

If your test involves "the Big Bang", shouldn't you be using the geometry of LCDM models, with parameters from the Year 5 WMAP papers perhaps? Of course, this applies only to the mock quasars ...

Well the 1.1 to 4 sounds more right. The figures are log(z). The mean is 3 with a skewed distribution.

Yes, sxc is a spreadsheet for open office (a free product).
I can load the data again in CSV (comma separated values) which you can read as plain text or use with any spreadsheet or programming language, but I will have to convert to values (not the formula) and leave out the graphics to do that. Is that useful?

In the big bang the pairing is effectively random as they are actually unassociated. In the alternative cosmology it is always a genuine associated object. Of course in a real sample there will be some proportion of random associations in the alternative case, so we would expect something like maybe 75% of the alternative graph with 25% of the big bang graph. The proportions will depend on the proportions of real associations.
I have not tried to make the distribution particularly accurate because that will not affect things a great deal. What I am trying to show is simply what an uncorrelated sample will look like (big bang) versus a correlated sample (alternative cosmology).
Yes, the parameters used are simple ones. If you want to give me a set of formula that you would be happy with and a graph of a distribution then I can make a distribution something like that with random numbers and redo the graphs. However I do not see it as particularly valuable as uncorrelated data will still be uncorrelated whatever the distribution. All it will mean is a little higher density at some places than others. I guess that I am relying on my experience of statistics here. I am happy to try and satisfy other people but will need help with what you consider a satisfactory basis of the data.

But aren't you asserting that you are modeling the real universe?So the expected result will be the same whether the first quasar is paired with the second/third/fourth/... galaxy, the second quasar paired with the third/fourth/... galaxy, and so on?

Why not actually test that (instead of assuming it)?
Now I'm confused ... I understood the 'alternative' to be pretty darn precise - (almost) all quasars 'near' an active spiral are physically associated ... yet the test, as you've described it, make random associations of quasars and galaxies.

Perhaps I missed it; where is the step in which you estimate projected distance, and assign a physical association?(emphasis added)

Surely, by now, you realise that such an assertion would be challenged?

Please show - quantitatively - that "that will not affect things a great deal".

Please show - quantitatively - that your "big bang" sample does, indeed, correspond to one consistent with an LCDM-based model.

(to be continued)

Yes. That is why I say that the shuffling will have no effect in the big bang case. The galaxy and quasar at a very different redshift have no actual physical relationship in big bang cosmology, just a common line of sight. It has been pointed out that some slight lensing due to large clusters etc is expected, but I am uncertain what the actual quantity of this is. Do you know?
No, in the proposed test the pairs will be as seen in the sky together. As a control a randomized pairing will also be studied.

If the big bang is right then these two cases will both look the same. If the alternative cosmology is correct then the pairs and the randomized pairs graphs should be very different. The true pairs will be correlated and the randomized ones should be uncorrelated. It is the degree of difference that tells whether the model for the big bang or alternative cosmology is right.

The generated data is done two ways. Once assuming that the big bang is true and once assuming that the alternative cosmology is true. The first 3 graphs and the second 3 graphs.
The simulated data is not the same as the test. It is showing what the test results will look like if:

A. the big bang is true and the pairs have no common relationship at all.

B. the alternative cosmology is correct and the quasars are really near the galaxies but with large internal redshifts.

You then have two sets of results that show how extremely different the third graph is (the first two graphs would be the same in both cases if I had done a more careful job of making the quasars exactly match in the alternative case).

When the real test is done, the third graph will either be correlated of not. If it is much more correlated than the quasar-quasar graph then the alternative cosmology is confirmed. If it is much less correlated than the quasar-quasar graph then the big bang is confirmed.

I'm still unclear - how will the test galaxies and quasars be placed 'on the sky'?

In any case, it seems that the 'big bang' mock catalogue doesn't reproduce such aspects as the well-known galaxy-galaxy correlation function (in real space, galaxies tend to cluster, over a range of scales, in quite particular ways). In some way, randomising the mock quasar-galaxy pairings should leave some kind of echo of the non-random distribution of galaxies in real space ...

Finally, whatever the test shows, it can't possibly 'confirm' anything! The best it could do is show consistency within some (quantitatively) bounded range (or inconsistency within some such range).

What am I missing?

They aren't actually placed on the sky. I did not generate any coordinates for that as they are not used in the graphs.
Well that would be a minor effect in the graphs produced. I was not trying to produce such subtleties, just trying to demonstrate the difference between the galaxy-quasar pairs plot between big bang and alternative.

Can you see that difference? Do you understand what it means? It is quite independent of all these other things.
It isn't supposed to confirm anything. It is showing only one thing for those that cannot visualize it from the original stated conditions:

If the big bang is true the proposed scatter diagram of log galaxy redshift versus quasar observed magnitude will be uncorrelated. If the alternative cosmology is true the same scatter diagram will show a strong correlation. That fact should be clear and all the other issues raised have no bearing on it.

Yes, if you wanted to do a really accurate simulation of the two cases you could add a lot of other factors. You could add some spurious line of sight cases to the alternative cosmology. You could add clumping to both cases. You could add stars and planetary systems in all the galaxies, and oceans and animals and atoms. The result would still be the same. The big bang predicts an essentially uncorrelated graph because the objects are mere line of sight associations. The alternative cosmology predicts a correlation in the graph, and that correlation should have a particular slope (although there will be some contamination by non-true pairs, so it will be a mixture of the two graphs shown).