I Observational evidence against expanding universe in MNRAS

[elerner]

<< Mentor Note -- after a very long Mentor discussion, we acknowledge that this paper, while potentially controversial, has been published in a reputable peer-reviewed journal. We believe that a discussion of this paper can be useful and constructive. Thanks >>

This paper of mine was published online in Monthly Review of the Royal Astronomical Society.
The title is a good summary: "Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis".
For a non-technical description, see our press release here.

 

[rootone]

Interesting, but is this implying that Fred Hoyle's idea was right?
That the Universe is static and eternal (mostly), but we have not yet discovered how light (EM generally) behaves on the cosmic scale?

 

[elerner]

No.Hoyle hypothesized that the universe did not evolve. There is plenty of evidence that it does change over time. But evolution does not require expansion--the Earth we live on has been evolving at an accelerating pace but is not expanding. The universe too can be evolving in an accelerating way without either having an origin in time or undergoing expansion. The redshift-distance relationship does imply something we don't yet understand is draining energy from the EM radiation as it travels long distances.

 

[PeterDonis]

evolution does not require expansion--the Earth we live on has been evolving at an accelerating pace but is not expanding

The Earth is a gravitationally bound system so I'm not sure it can be usefully compared to the universe as a whole.

Can you describe what sort of model you envision for the universe as a whole evolving but not expanding? I'm particularly curious as to whether you expect such a model to be consistent with the Einstein Field Equation, or whether you think some new physics beyond that will be needed.

 

[elerner]

The evolutionary processes occurring on Earth have changed it a lot, but have nothing to do with changes in the structure of space. Similarly, in the universe on large scales, gravitational, electromagnetic and nuclear processes can change it over time, independently of any expansion. You don't need expansion to form galaxies, stars, or planets or to burn hydrogen to helium in fusion.

I don't think the second question can be answered right now. One possibility is that matter is distributed fractally at all scales with a dimension of 2 or less. In that case, GR effects would be small on all scales. (In other words, if the density keeps dropping the curvature of space is negligible at all scales. In that case GR does not predict any expansion or contraction.) A second possibility is that gravitation weakens at very large distances. If some process drains photons of energy over large distances, it may well weaken EM forces and perhaps gravitation as well. Again, that would result in no overall expansion or contraction.

Unlike some of my colleagues, I don't claim to have a Theory of Everything. Observations are the test of theories. If the predictions of the theory don't hold up, then either the theory needs to be changed, or the assumptions, like homogeneity, that go into the predictions need to be changed. To figure out what needs to be changed requires more work. The first step is to decide that predictions are wrong. What this paper is saying is that the predictions based on expansion don't work, at least not for this data set. What works are predictions based on the hypothesis of no expansion and a linear relation between z and distance.

 

[rootone]

It sounds a bit like a 'tired light' hypothesis
Not utterly implausible, but it requires an undefined parameter when there is no reason or evidence to assume it.

 

[elerner]

If tired light means that something happens to the light over long distances, yes. But no new parameter is needed, just the same old Hubble constant. With just the Hubble constant, the linear, no-expansion hypothesis fits the supernova data as well as LCDM does with three parameters (Hubble, dark matter, dark energy). No parameters at all are needed for the linear hypothesis to fit the galaxy size/surface brightness data. The value of the Hubble constant does not matter for that prediction of no change--there are no free parameters at all. And that data set can't be fit with LCDM hypotheses without violating other observational constraints, as I show in the paper.

 

[PeterDonis]

You don't need expansion to form galaxies, stars, or planets or to burn hydrogen to helium in fusion.

That's true, but I don't think this observation counts for much either way. It just means those particular phenomena, in themselves, aren't relevant to the question of whether the universe is expanding or not.

One possibility is that matter is distributed fractally at all scales with a dimension of 2 or less.

I don't understand what this means. The universe has some average density of matter. That isn't a "fractal", it's just an average density. Unless you are claiming that the average density is zero, which basically means all the matter we can see is a finite "island" of matter surrounded by an infinite expanse of empty space. Is that what this hypothesis is referring to?

if the density keeps dropping the curvature of space is negligible at all scales

The relevant curvature is the curvature of spacetime, not space. Yes, a completely empty universe with zero density (and zero cosmological constant) is just Minkowski spacetime, which is not "expanding" and has zero spacetime curvature everywhere. Is this the model you are suggesting?

A second possibility is that gravitation weakens at very large distances.

Ok, this falls into the second category I mentioned: new physics that is not consistent with the Einstein Field Equation. See below.

that would result in no overall expansion or contraction.

But the only way we have of making any predictions at all regarding overall expansion or contraction, or lack thereof, is by means of the Einstein Field Equation. And if you're hypothesizing that that no longer works for the universe as a whole, you have no way of making any predictions at all, unless you propose some specific alternate model for how gravity weakens at large distances, how photons lose energy, etc. I'm not saying that can't be done; but it seems to me that unless and until it is done, you won't make much headway in trying to challenge current cosmology, which does have a model, and whose model is based on the EFE, which is well confirmed over a wide domain.

 

[PeterDonis]

What this paper is saying is that the predictions based on expansion don't work, at least not for this data set.

Can you give a brief summary of what mistakes you think the mainstream cosmology community (which says that the predictions based on expansion do work) is making in interpreting this data?

 

[PeterDonis]

Unlike some of my colleagues, I don't claim to have a Theory of Everything.

But you do obviously have some concrete model, since you are making predictions, and you can only make predictions if you have a concrete model. "I don't have a Theory of Everything" isn't a prediction. That's why I'm asking questions about your model: to try to understand what concrete model you are using to generate the predictions that you say match the data.

 

[Dale]

The redshift-distance relationship does imply something we don't yet understand is draining energy from the EM radiation as it travels long distances.

Please limit the discussion to the actual content of the paper. Such speculations were not accepted by MNRAS nor are they appropriate here.

For other posters, please try not to force the conversation into speculation. This is a controversial topic, so extra care must be made to keep it within the bounds of the professional scientific literature. As much as possible, support points with references in this thread, even before being specifically requested.

 

[rootone]

If tired light means that something happens to the light over long distances, yes

If red shift is not due to expansion then it must be due to something else.
As far as we know light does not change it's wavelength depending on only distance of the light source.
There is no reason I know of to think that it might be so.

 

[Dale]

@elerner I am not actually convinced that this statement in your paper is correct “To fit the data by excluding the nearest galaxies invalidates the comparisons. Rather, a fit has to be required to go through the low-z point”.

The key assumptions of the cosmological model are that at some large enough scale the universe is homogenous and isotropic. The cosmological models are not expected to work below that scale, and we know that those assumptions are invalid at small scales.

Perhaps the discrepancy in the low z values merely shows where the appropriate scale cut-off lies. In any case, it is certainly not required to fit nearby galaxies, and the comparisons are not invalidated by doing so. It merely informs the domain of applicability (in a rather expected and acceptable way)

http://www.tapir.caltech.edu/~chirata/ph217/lec01.pdf

 

[elerner]

A fractal of dimension n=2 means that matter is distributed in such a way that the total mass measured increases as D^2 (distance squared) when measured from any point. Average density then decreases with radius measured. Observations in peer-reviewed publications show that galaxies are distributed in this fractal way at least to scales of 200 Mpc, but it remains unclear whether that distribution is extended to still larger scales. There is no "special location" in such a distribution, but it would not be homogeneous at any scale. Prediction of the contraction or expansion of the universe requires a homogeneous distribution. (Indeed Edgar Allen Poe pointed out that Newtonian gravitation makes a homogeneous universe unstable to gravitational collapse.) If the universe is not homogeneous, the prediction is not valid.

In this paper, and an earlier one with my colleagues, I tested the hypothesis that z in linearly proportional to D at all D against observations. That is a perfectly good test of the hypothesis that this is the actual relation between these two quantities. I don't have, and don't have to have, a model that explains why this relationship holds. That is a further step. It is just like when the formula for the Balmer series was discovered long before quantum theory, which explains that formula, was perfected.

Right now, no experimental test is sensitive enough to show if light does change just by traveling a large distance. But such a test could be done if the proper equipment were put on the planned LISA experiment.

 

[PeterDonis]

A fractal of dimension n=2 means that matter is distributed in such a way that the total mass measured increases as D^2 (distance squared) when measured from any point.

Ok, got it.

There is no "special location" in such a distribution

I'm not sure I understand this. Average density would be highest at the spatial origin and would decrease in all directions out from it, so that point is clearly a "special location".

Prediction of the contraction or expansion of the universe requires a homogeneous distribution.

Why do you think this? The fact that the standard cosmological model predicts expansion based on homogeneity does not mean there can't also be models which are not homogeneous but which predict expansion.

 

[PeterDonis]

I tested the hypothesis that z is linearly proportional to D at all D against observations.

Ok, but we don't directly measure D, so you have to make some other assumptions in order to extract D from the data. What are those assumptions?

 

[elerner]

Dale, the whole point of the Tolman test is to compare the apparent size or surface brightness of nearby objects with distant ones. If you throw out the nearby ones (which number in the thousands and go out to a z of 0.14) you are saying that we happen to live in the center of the one part of the observable universe that has galaxies twice as big as everywhere else. You want to make that hypothesis? I think Copernicus would have a good chuckle over that.

 

[elerner]

Peter, and others, look up fractals online. They are very common structures in nature. There is no special point of origin. If you go out from ANY point, you get the same results. In my paper, the necessity for assuming a relationship of z and D in the non-expanding case is in order to have a formula for deriving absolute luminosity from measured redshift and apparent luminosity. We do that so we can compare galaxy samples that have the same absolute luminosity. So we don't have to measure distance to test the predictions. The prediction is just that galaxies of the same luminosity have the same radius independently of z.

Signing off for tonight. Good night to all!

 

[kimbyd]

<< Mentor Note -- after a very long Mentor discussion, we acknowledge that this paper, while potentially controversial, has been published in a reputable peer-reviewed journal. We believe that a discussion of this paper can be useful and constructive. Thanks >>

This paper of mine was published online in Monthly Review of the Royal Astronomical Society.
The title is a good summary: "Observations contradict galaxy size and surface brightness predictions that are based on the expanding universe hypothesis".
For a non-technical description, see our press release here.

Eh. Galaxy dynamics are tremendously complicated.

The expansion of the universe is not, and is consistent with a wide array of observational evidence.

If there is a discrepancy between predictions based upon galaxy dynamics and the uniform expansion, by far the most likely resolution of that discrepancy is that the model of galaxy dynamics is wrong. There is potentially some value in this paper in highlighting a discrepancy that needs to be understood to gain a better understanding of our universe. But it's far, far more likely to result in increased understanding of galaxy dynamics rather than increased understanding of expansion.

If you want to try to draw some conclusions about the expansion rather than galaxy dynamics, it is an absolute necessity to start drawing in other data sets, from the CMB to primordial light element abundances to baryon acoustic oscillations to supernova measurements.

 

[Dale]

If you throw out the nearby ones (which number in the thousands and go out to a z of 0.14) you are saying that we happen to live in the center of the one part of the observable universe that has galaxies twice as big as everywhere else.

Do galaxies have a size distribution? Or are they all exactly the same size? If they have a size distribution then there will in fact be many pockets throughout the universe with large or small galaxies. And in any of those pockets that nearby datapoint will be off.

In any case, a model is based on assumptions, and when the assumptions are violated you expect poor fits. If a model designed for large scales fits well at large scales and not well at small scales then you use it for large scales and not for small scales, as it was intended!

I think you are incorrect in asserting that the previous comparisons are invalid. Certainly the professional community seems to consider it to be valid. How is it justified in the previous literature?

 

[Dale]

The expansion of the universe is not, and is consistent with a wide array of observational evidence.

This is a critical point that must not be forgotten. An alternative cosmology must not just explain one type of observation, it must explain all of the different kinds of observations. In fact, even this one kind of observation is well explained by the current model at sufficiently large scales.

 

[elerner]

Dale,
Galaxies of the same luminosity have significant spread in size, but the expected variation in the mean or median of a sample decrease with N^0.5, where N is sample size. So with samples of the size used here, we can get pretty small statistical uncertainty. If you look at the size of the error bars, you get an idea. To hypothesize that regions as large as 800 Mpc across, the nearby samples or even 200 Mpc across have galaxies 10 sigma away bigger than elsewhere is a big leap. If you really want to hypothesize that, the easy test from the data is to compare galaxies in different parts of the sky. If they are the same, then you would also need to hypothesize we are right in the center of this very odd patch of galaxies. Is that the pocket you want to hypothesize? Ptolemy would doubtless approve. Or would you accept isotropy of galaxy size as falsification of your idea we are in some special pocket?

There were no justifications for leaving out the nearby galaxies. It was just not part of most of those studies. They compared HST observations at large z with each other. They omitted to compare them with nearby galaxies, which necessarily would be observed with other telescopes (at low z the HST survey volumes are too small).

 

[Dale]

but the expected variation in the mean or median of a sample decrease with N^0.5, where N is sample size. So with samples of the size used here, we can get pretty small statistical uncertainty.

That assumes that the measurements of nearby galaxies are uncorrelated or independent. But you are still missing the point.

I start with assumptions X, Y. With those assumptions I generate model Z. Model Z is shown to fit a wide variety of data under conditions where assumptions X and Y are expected to hold. You diligently show that model Z does not hold in all cases, the specific case being one extreme data point of one data set where assumption X may not hold. By your own analysis model Z does hold for the remainder of the data set where assumption X holds. It is only when the assumptions are violated that the model fails. I agree and point out the fact, recommending that model Z be used only when the assumptions X, Y hold. It works as designed!

It is like you are buying a car and complaining that it doesn’t float well. It wasn’t intended to float well, it was intended to drive well.

I believe that the usual length scale for cosmological scale is something like hundreds of Mpc. Isn’t z=0.027 smaller than that?

which necessarily would be observed with other telescopes

And which could therefore have measurements which were non-randomly different from the remainder of the dataset, thereby negating the statistical benefit of large sample sizes.

Don’t get me wrong. I do accept your paper as evidence against the standard cosmology, just not as very strong evidence due to the issues mentioned above. So (as a good Bayesian/scientist) it appropriately lowers my prior slightly from “pretty likely” to “fairly likely”, and I await further evidence.

 

[elerner]

"It is important to note that any over-all comparisons of cosmological models must be based on all available data-sets."
That is the last sentence of my paper--hope you all read to the end. But, given that, it is essential to state when each data-set contradicts the overall model. If you want to look at an informal list of other contradictions, based on peer-reviewed literature, see <unacceptable link deleted>

 

[elerner]

By the way, Dale, z=0.027 defines a region 200 Mpc across and the nearby data goes out to z=0.14, which defines a region 1100 Mpc across.

 

[Dale]

By the way, Dale, z=0.027 defines a region 200 Mpc across

Ok, so that is getting towards the lower end of what is generally considered “cosmological scale” to my knowledge. It appears then that the primary contribution of your work may be to show that the lower limit of the “cosmological scale” is a little larger than previously assumed. Or it may be that the HST data is systematically different in some way than the nearer data.

Your data does not seem to contradict previous studies showing the validity of current models at substantially larger scales.

 

[Dr. Courtney]

@elerner I am not actually convinced that this statement in your paper is correct “To fit the data by excluding the nearest galaxies invalidates the comparisons. Rather, a fit has to be required to go through the low-z point”.

The key assumptions of the cosmological model are that at some large enough scale the universe is homogenous and isotropic. The cosmological models are not expected to work below that scale, and we know that those assumptions are invalid at small scales.

Perhaps the discrepancy in the low z values merely shows where the appropriate scale cut-off lies. In any case, it is certainly not required to fit nearby galaxies, and the comparisons are not invalidated by doing so. It merely informs the domain of applicability (in a rather expected and acceptable way)

http://www.tapir.caltech.edu/~chirata/ph217/lec01.pdf

Emphasis added. This view is convenient. But it renders the current cosmological model invalid on the basis that it is not falsifiable. In the face of any purported falsification, proponents can always claim, "Maybe you've just found where the cut off is." To be falsifiable, a scientific model must specify the domain of its validity.

This is a critical point that must not be forgotten. An alternative cosmology must not just explain one type of observation, it must explain all of the different kinds of observations. In fact, even this one kind of observation is well explained by the current model at sufficiently large scales.

But you are breaking your own rules by going outside the bounds of the current paper. The current paper does not purport to be a comprehensive alternative cosmology, but merely pointing out where the current consensus cosmology (expanding universe) is contradicted by observations. Yes, it also contains some hints and elements that may represent progress toward an alternate cosmology, but the current consensus cosmology did not emerge in a single paper.

 

[Dale]

Emphasis added. This view is convenient. But it renders the current cosmological model invalid on the basis that it is not falsifiable. In the face of any purported falsification, proponents can always claim, "Maybe you've just found where the cut off is." To be falsifiable, a scientific model must specify the domain of its validity

I don’t think this objection is a strong one. The domain of validity always depends on the specific purpose intended, and is not a hard and fast boundary that is generally explicitly specified. For example, what is the domain of validity of Newton’s laws? Precisely who “must specify” it, and what is the specification?

In any case, all your suggestion would lead to is a series of models Z1, Z2, Z3, ... identical except for their specified their domains of validity. Each model would be falsifiable per your criterion, and you would simply reject Zn and use Zn+1 as needed. You would wind up at the same point.

The objection is particularly not strong here since the scale of the discrepancy reported is on the order of the previously known limit. It is perhaps a small refinement to the domain, not a radical change.

 

[Dr. Courtney]

I don’t think this objection is a strong one. The domain of validity always depends on the specific purpose intended, and is not a hard and fast boundary that is generally explicitly specified. For example, what is the domain of validity of Newton’s laws? Precisely who “must specify” it, and what is the specification?

In any case, all your suggestion would lead to is a series of models Z1, Z2, Z3, ... identical except for their specified their domains of validity. Each model would be falsifiable per your criterion, and you would simply reject Zn and use Zn+1 as needed. You would wind up at the same point.
oun
The objection is particularly not strong here since the scale of the discrepancy reported is on the order of the previously known limit. It is perhaps a small refinement to the domain, not a radical change.

One can frame the discussion that way, but then one needs to acknowledge that moving what were previously thought to be firm boundaries of well established theories is not usually treated as an insignificant accomplishment. "On the order of ..." That's astrospeak for a factor of 10.

The domain of Newton's laws was thought to be truly universal at one time. Now we know that the validity depends on the accuracy needed for a specific prediction and is never absolute. The current cosmological model has nowhere near the supporting evidence as Newton's laws. It may be that the current paper merely represents moving the domain of it's validity. But it also may mean an alternate cosmology can emerge which better explains the available evidence AND accurately predicts new findings.

I like to keep an open mind.

 

[Dale]

one needs to acknowledge that moving what were previously thought to be firm boundaries of well established theories is not usually treated as an insignificant accomplishment

So acknowledged! Although this particular boundary is not that firm and I suspect that the OP considers that to be an insignificant accomplishment, particularly compared to what he wanted to accomplish.

But it also may mean an alternate cosmology can emerge which better explains the available evidence AND accurately predicts new findings.

That is not in the MNRAS paper.

I like to keep an open mind.

Me too, but I try to do so in a roughly Bayesian framework. As Bayesian evidence this is a small update to my priors.

 

[PeterDonis]

A fractal of dimension n=2 means that matter is distributed in such a way that the total mass measured increases as D^2 (distance squared) when measured from any point.

I don't see how this is possible, at least not if space is Euclidean (which it appears to me that you are assuming, at least in the SEU model). Pick any point A, and consider two spheres centered on that point: one with radius $D$ and one with radius $3 D$. The total mass within these spheres, by what you say in the above quote, should be $D^2$ and $9 D^2$ [edit--fixed typo] respectively (with some constant of proportionality that doesn't matter here).

However, consider now ten other spheres, all with radius $D$, all disjoint with each other and with the sphere of radius $D$ centered on point A, and all contained within the sphere with radius $3 D$ centered on point A. Six of these spheres are centered on the vertices of a regular hexagon inscribed in a circle with radius $2 D$ centered on point A. Four others are centered on four vertices of another regular hexagon, inscribed in another circle with radius $2 D$ that is perpendicular to the first and intersects it at two of the vertices of the first regular hexagon (these two vertices are shared with the second regular hexagon; the four additional spheres are centered on the other four vertices of the second regular hexagon).

This makes a total of eleven spheres, all with radius $D$, all disjoint, and all contained in the volume occupied by the sphere with radius $3 D$ centered on point A. But by your quote above, since no point is special, each of these eleven spheres must contain a total mass equal to $D^2$. That makes a total mass of $11 D^2$ contained within the sphere of radius $3 D$ centered on point A, which contradicts your statement that the total mass contained within that sphere is $9 D^2$.

 

[elerner]

Well ,try this--published in a peer-reviewed source unless you are going to exclude the Russians: http://de.arxiv.org/abs/astro-ph/0505185

 

[rootone]

Well ,try this--published in a peer-reviewed source unless you are going to exclude the Russians: http://de.arxiv.org/abs/astro-ph/0505185

Please don't get political. Science has no policy.
Science is the same (or should be) in any country,

 

[elerner]

I was being sarcastic because a whole bunch of peer-reviewed references were just deleted from one of my posts by management. Scientific knowledge certainly has political implications and since cosmology is entirely government funded, the process of deciding who to fund is also political. However, I would advocate that such topics be discussed in a different thread just to keep things orderly.
Along the same lines, I would say that if I am to be <deleted> by management when I point out that there are many other problems with concordance cosmology, I think those who say there are no other problems should also be <deleted> from the thread. Why don't we limit it to the question of whether the data sets used in my paper do in fact contradict the predictions of the expanding universe hypothesis?

 

[Dale]

Please post forum feedback in the forum feedback section. Such feedback does not belong here.

And no links to peer reviewed references were deleted, a single link to a personal website was deleted. Having a few links to valid sources in amongst the speculation does not make your personal website a valid reference

 

[Dale]

Why don't we limit it to the question of whether the data sets used in my paper do in fact contradict the predictions of the expanding universe hypothesis?

They do not appear to do so to me. In fact they seem to show good agreement at large distances, as expected, and to deviate at smaller distances, also as expected. The deviation even seems to occur on the order of the scale expected from other sources.

I am not saying that the paper is not worth publishing, but it is also not a death knell for standard cosmology as you seem to wish. I think you need to put your work in perspective.

 

[rootone]

would advocate that such topics be discussed in a different thread just to keep things orderly.

Some interesting conversation happens in the PF lounge,https://www.physicsforums.com/forums/general-discussion.14/

Eeek what is my phone doing:
I said 'interesting', not intermarriage whatever that is,

 

[PeterDonis]

try this

I'll take a look, but this is a 95 page paper. Is there a particular part of it that you think addresses the objection I raised?

 

[elerner]

Peter, it shows that observationally that the number of galaxies in a volume increases as the square the radius, not the cube. I gather you did not look up "fractals" on the web, so I will describe one. Imagine a checkerboard of 4 squares with the upper right and lower left one black. Now put two identical such patterns in a twice as large square so that they occupy the upper left and lower right corners. Then put that twice as large pattern in a twice as large pattern in the same way--and so on indefinitely. You can see that in this two-dimensional space the area that is black will increase linearly with radius, not as the square of the radius. It is a fractal of dimension 1. By analogy a similarly nested set of structures can--and does--form a 2D fractal in a 3D space. You can go out from any point and still get a mass that increases as the square, not the cube, of the radius. There is a vast literature on fractals, but I am sure you can find some brief descriptions on websites.

 

[elerner]

They do not appear to do so to me. In fact they seem to show good agreement at large distances, as expected, and to deviate at smaller distances, also as expected. The deviation even seems to occur on the order of the scale expected from other sources.

As expected by who, Dale? You? Find for me any published paper that "predicted" that galaxies near to us are two or three times bigger than the average in the present-day universe. You can't . No one has written this. This is purely your speculation, no citation, which I gather you get to write on this forum because you are a moderator.

As I posted earlier, if you want to test your hypothesis that there is a 2-3 fold variation in mean galaxy size over volumes of 200-800 Mpc, we can do that by looking at different parts of the sky. You want to bet that we will find a 2-3 fold variation? Will you accept this as a a test of your personal hypothesis? Because if you accept this, I can do the comparison very quickly as I have the data needed already from GALEX.

 

[PeterDonis]

it shows that observationally that the number of galaxies in a volume increases as the square the radius, not the cube

I understand that that is what the paper claims to show, yes. I have not read it through or tried to work through how it actually derives this conclusion, which does not appear to be generally accepted by cosmologists, from the data.

I gather you did not look up "fractals" on the web

I didn't have to. I already know what fractals are. The questions I am asking about your description of the model in question are not because I need to have the concept of fractals explained to me. They are because the claims you were making, in the specific form you were making them, appear to me to be self-contradictory. Throwing around the word "fractal" does not address that kind of question.

From what I have read so far in the paper you linked to, it does not seem that your claim that every point in a fractal matter distribution is the same as every other point is correct. The paper clearly distinguishes between fractal and homogeneous distributions; the statement that every point is the same as every other point only applies to homogeneous distributions. The paper also clearly describes why fractal distributions are not homogeneous: because in fractal distributions, the points where the actual matter exists (the paper calls them "structure points") are different from points that lie in the voids between the matter. The claims about how much matter exists in a sphere of radius $D$ about a given point, and how that quantity varies with $D$, only apply if the point in question is a structure point; they do not apply if the point in question lies in one of the voids. From the paper's description, all of the structure points within a fractal distribution appear to be identical, yes; but not all points are structure points.

Btw, the paper also says that the model it is describing is not fractal out to arbitrary distances from a given point; there is a distance scale $R_{\text{hom}}$ above which the distribution becomes homogeneous. The key question from the paper's point of view appears to be what the correct value of $R_{\text{hom}}$ should be; it says that it was assumed at first to be around 10 Mpc, but now a value of at least 100 Mpc seems to be the best fit to the data. That distance still corresponds to a fairly small redshift (about z = 0.013, based on the numbers you give in an earlier post), so the model the paper appears to be favoring would not be expected to have a fractal distribution at most redshifts (since IIRC we can see quasars out to about z = 6).

 

[Dale]

As expected by who, Dale? You? Find for me any published paper that "predicted" that galaxies near to us are two or three times bigger

You are still missing the point. The model does not make any predictions for small scales. It is expected to fail at small scales. The model deliberately, specifically, and explicitly limits its predictions only to very large scales. It doesn’t matter how much or in which direction it fails locally. You cannot falsify a model which only makes predictions for large scales by showing that it fails only for small scale data.

See http://arxiv.org/abs/0808.0012 chapter 6 for a good discussion of how this works

As I posted earlier, if you want to test your hypothesis that there is a 2-3 fold variation in mean galaxy size

That is not my hypothesis, I am not making any hypothesis. I am merely pointing out your fallacy of trying to use small scale data to falsify a model that explicitly makes predictions only at large scales.

 

[elerner]

Dale, the Tolman test has no limits on its applicability. Again, you are inventing some model out of thin air that is nowhere in the literature. Find me any paper that says there are limits on the applicability of the expanding universe formula of surface brightness. It applies anywhere the Hubble relation applies. You want to find papers that say there is no Hubble relation on scales of 200Mpc ( which are the scales in fact where it was first discovered)?

 

[Dale]

Dale, the Tolman test has no limits on its applicability.

The cosmological model does. Are you trying to falsify the cosmological model or the Tolman test?

https://en.m.wikipedia.org/wiki/Cosmological_principle
http://www.as.utexas.edu/astronomy/education/spring05/komatsu/lecture11.pdf
http://www.springer.com/cda/content/document/cda_downloaddocument/9783642540820-c2.pdf?SGWID=0-0-45-1481916-p176497146

 

[elerner]

Peter,
The reason I think you need to familiarize yourself a bit with the mathematics of fractals is that in an earlier post you were attempting to prove that fractals of dimension D=2 could not exist in a 3D space. So, I was trying to show you that indeed such a mathematical concept of fractals (which have dimensionality different than the space they are embeded in) is indeed well-developed and well-proven. I referenced that observational paper to show observational evidence that in the nearby universe, the distribution of mater is indeed a fractal of dimension D=2. I did not claim that it has been demonstrated that the distribution is fractal out as far as we can observe. But we do see larger and larger structures as far as we can observe, so the possibility is open that the fractal distribution extends very far out. If the density of matter gets low enough, GR becomes a negligible correction on scales of the observable universe.

 

[elerner]

Show me any reference that says the Tolman relation, based on the expansion of the universe, does not apply to all scales where the expansion of the universe applies. Are you saying there are published papers saying that expansion does not exist within 800 Mpc? The only small scales excluded by the expansion hypothesis are those that are gravitationally bound and therefore not assumed to be expanding. Again you are inventing out of thin air a restriction that in no way appear in the published literature. Show me one citation to support your speculation.

 

[Dale]

Show me any reference that says the Tolman relation, based on the expansion of the universe, does not apply to all scales where the expansion of the universe applies.

Why should I? I have shown references that support my actual point, not the straw man point you wish I were making.

Are you or are you not trying to show evidence against the standard LCDM cosmology? If you are, then your data do not provide that evidence, for the reasons I stated: The cosmological model only claims to work at large scales and your data shows that, according to the Tolman test, in fact it does work at large scales.

 

[elerner]

The cosmological model only claims to work at large scales .

Your personal cosmological model, I guess, but show me one citation that says the expansion hypothesis, which is what I am testing, does not apply on scales of 800 Mpc.

 

[Chronos]

Can you elaborate on the apparent suggestion that the surface brightness and angular diameter of galaxies is in conflict with special relativity and/or their inferred distances are in error.

 

[PeterDonis]

in an earlier post you were attempting to prove that fractals of dimension D=2 could not exist in a 3D space

No, I was showing that your particular claim about a so-called "fractal distribution" was self-contradictory. If you drop the (incorrect) claim that every point (instead of just every structure point) in a fractal distribution is identical, there is no problem having a fractal distribution of dimension D=2 in 3D space.

the possibility is open that the fractal distribution extends very far out

"Very far out" relative to the scales we can observe, yes. But that's still infinitesimal compared to the total spatial size of the universe, if the universe is spatially infinite.

If the density of matter gets low enough, GR becomes a negligible correction on scales of the observable universe.

Which just means the observable universe is spatially flat, to within our observational error--which the current mainstream cosmological model says it is anyway. But this does not entail that GR is a "negligible correction" on the scale of the entire universe. If the entire universe is spatially infinite, which the current mainstream cosmological says it is, then GR is not at all "negligible" on the scale of the entire universe.