Got a link for the angular-size redshift relation?

[marcus]

http://en.wikipedia.org/wiki/Angular_size_redshift_relation

the Wiki entry for this declares itself a stub
What they have is just a few sentences serving as a place-holder until somebody contributes a real article.

the thing about angular-size redshift relation is that out beyond a certain distance (z about 1.6) things LOOK BIGGER THE FARTHER AWAY THEY ARE.

We talked about this some here at PF and arrived at a somewhat intuitive explanation of the effect. But I don't remember what thread. I can't find anything in PF about it. And anyway I would prefer to have some outside source----preferably edited, like an online science encyclopedia----or a Wiki article if they had something besides this stub.

But anything would help. Anybody have a link for this?

 

[marcus]

BTW if anyone wants to play around with angular size, there is Ned Wright calculator

http://www.astro.ucla.edu/~wright/CosmoCalc.html

if you put in z=1.6 you get that the current real distance to the object is 14.866 billion LY

but the object's angular size distance is 5.756 billion LY

but if you put in z=1.5 or 1.7 you will get that the angular size distance is LESS in both cases.

objects at redshift 1.5 or 1.7 look closer to us than objects at redshift 1.6

 

[marcus]

Maybe this is just too much of a finicky detail for some folks, but
I want to get this one simple fact into sharp focus, for myself at least (and anybody with a common vocubulary that is curious about these things)

I'm picturing a PARSEC RULER
and I try placing the ruler out at various distances or at various redshifts
and I see WHAT ANGLE IT MAKES in the sky
(I can easily do this using Ned Wright cosmo calculator)

The important angle unit, for me, is an ARC SECOND which is 1/60 of an arc minute, which is 1/60 of a degree of angle. So I am going to tell you, in fractions of an arcsecond, how big this ruler looks at various distances.

redshift       angularsize (arcsecond)     current distance (billion LY)
1.5               1/8540                         14.36
1.6               1/8556                         14.97
1.7               1/8555                         15.54
1.8               1/8540                         16.09

I can't tell where the minimum angularsize comes exactly, but I can see that it is around redshift 1.6 or rougly around 15 billion LY.
If I push my parsec ruler out that far, then thereafter if I push it any farther IT STARTS TO LOOK BIGGER AND BIGGER.
space=funhouse optics

 

[marcus]

related paper:
http://arxiv.org/astro-ph/0603637
The Mass of the Cosmos
Charles Hellaby
6 pages, 9 graphs in 3 figures. Replacement has very minor changes: puts greek letters on graphs, and adds small corrections made in publication

"We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. Unlike all other points on the past null cone, this maximum has an associated mass, which can be calculated with very few assumptions about the cosmological model, providing a measurable characteristic of our cosmos. In combination with luminosities and source counts, it gives the bulk mass to light ratio. The maximum is particularly sensitive to the values of the bulk cosmological parameters. In addition, it provides a key reference point in attempts to connect cosmic geometry with observations. We recommend the determination of the distance and redshift of this maximum be explicitly included in the scientific goals of the next generation of reshift surveys. The maximum in the redshift space density provides a secondary large scale characteristic of the cosmos."

 

[SpaceTiger]

Here's how I think about it:

In a flat universe, there are only two effects that you really need to consider when thinking about angular size. First, if we were able to view all objects in the universe at the same time in cosmic history, the more distant ones would appear larger. Objects at higher redshift are more distant (both in physical and comoving coordinates), so this effect always acts to decrease the angular size of a standard ruler.

However, we are not actually viewing the objects at the same moment in cosmic history. More distant objects also appear older (because of the finite travel time of light), so this means we're seeing them at a time when the universe hadn't expanded as much and things were closer together. This effect acts to increase the angular size of a standard ruler.

Nearby, the first effect wins out -- the rate at which objects are separating is negligible compared to the time it takes their light to reach us. At the highest redshifts (say, to the CMB), the universe has expanded many times over since the light was emitted and it turns out that, when their visible light was emitted, these objects were actually closer to us than a z~1 object. They are not, however, closer to us than the z~1 object at the present time. Their comoving distance is still larger and increases monotonically with redshift.

 

[marcus]

thanks for the discussion!

 

[marcus]

related paper:
http://arxiv.org/astro-ph/0603637
The Mass of the Cosmos
Charles Hellaby
6 pages, 9 graphs in 3 figures. Replacement has very minor changes: puts greek letters on graphs, and adds small corrections made in publication

"We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. ... We recommend the determination of the distance and redshift of this maximum be explicitly included in the scientific goals of the next generation of reshift surveys. The maximum in the redshift space density provides a secondary large scale characteristic of the cosmos."

IIRC Lineweaver and Davis ("Expanding Confusion") indicated they had ruled out Milne cosmology at the twentythree sigma level.

I don't know of any working cosmologist who takes Milne cosmology seriously and I don't know if a sensible person can, given the load of evidence.
It was invented by Milne in the 1930s because he didnt like the General Relativity picture---basically uses flat Minkowski space and a kind of physical explosion. that occurs at some definite point.

But anyway if anyone believes the Milne picture, tell me. I'd be curious to know.
=======================

The reason I thought of that is I can't guess how a Milne-minded person would cope with the ANGULAR-SIZE DISTANCE MAXIMUM at about z = 1.6

this is an observed thing. If you have a whole bunch of approximately equal size galaxies that are at all different distances and thus all different redshifts.

Then the galaxies at z = 1.6 LOOK SMALLEST in the sense of having smallest area in sky, or angular size.

Like the full moon and the sun are both about half a degree angular size.
As things get farther and farther away they get smaller and smaller angular size UNTIL they reach 1.6, and after that they get bigger as you go farther away.

If there are any sincere Milne-people still around, how do they explain this?

If they have an ingenious explanation it would be delightful to have it presented

 

[chronon]

IIRC Lineweaver and Davis ("Expanding Confusion") indicated they had ruled out Milne cosmology at the twentythree sigma level.

Before your text expands any more you should take a look at Cosmology under Milne's shadow by Michal Chodorowski http://arxiv.org/abs/astro-ph/0503690

 

[marcus]

Before your text expands any more you should take a look at Cosmology under Milne's shadow by Michal Chodorowski http://arxiv.org/abs/astro-ph/0503690

Thanks chronon!

Chodorowski says:
"Specifically, using these data alone, the Milne model is ruled out only at a 2 sigma level. Although not a viable cosmological model, in the context of current research on supernovae Ia it remains a useful reference model when comparing predictions of various cosmological models."

So I will reduce the typesize a bit.
The twentythree sigma sounded crazy to me, so I'm very glad to have Michal's two sigma for modesty and balance. :-)

I surmise that by using other data one could rule out Milne at considerably more than 2 sigma---I'll suggest one possible avenue in the next post (if anyone were to want to pursue it.) What Chodorowski says is using these data alone and with additional ingenuity I suppose one ought to be able to do considerably better than 2 sigma

 

[marcus]

Chronon, the Chodorowski paper you pointed out to us suggests another (possibly even more decisive) way to rule out Milne.

(In case anyone is interested in ruling Milne cosmology out---I see no indication that any professional takes it seriously or as anything but a reference case.)

But just in case someone wants---look at equations 14 and 6.

(6) is the Angular-size distance as a function of redshift D_A(z)
calculated for an EMPTY FRW universe.

It would not fit observations---like those suggested by Hellaby in the paper I cited. But it is the correct function in the hypothetical empty universe case.

(14) is the same D_A(z) derived for the Milne picture.

they are identical. So doing what Hellaby suggests namely determining by observation what z maximizes D_A should provide another way to exclude Milne.

 

[Wallace]

What Chodorowski says is using these data alone and with additional ingenuity I suppose one ought to be able to do considerably better than 2 sigma

This is the key point, no one uses anyone cosmological data set to constraint parameters since they are all known to have degeneracies that are only broken by using other parameter sets. The tripod on which the LCDM model is built is CMB, Structure (galaxy redshift surveys mostly at present) and Supernovae 1A.

Chodorowski has a very checkered publication history so be wary of taking his claims at face value. Every paper of his I have read in detail has contained glaring errors that undermine his conclusions.

 

[MeJennifer]

Chodorowski has a very checkered publication history so be wary of taking his claims at face value. Every paper of his I have read in detail has contained glaring errors that undermine his conclusions.

For those interested, more Chodorowski, this time about:

"We have argued that expanding space is as real as ether, in a sense that they are both unobservable."

http://arxiv.org/PS_cache/astro-ph/pdf/0610/0610590.pdf"

Perhaps in the future everybody will have to admit that intellectual integrity demands that the term "crackpot" should be as much associated with "expansion of space" as is "ether".
Time will tell.

P.S. Hmmm, A universe that expands like a pot that, eventually, due to dark energy, cracks... now there a metaphor

 

[marcus]

Hi Jennifer,
I'm not sure I see what your point is.
===here are Chodo's conclusions===
6 SUMMARY AND CONCLUDING REMARKS
This paper has been devoted to a critical discussion of the concept
of the Expansion of Space (EoS) in cosmology.We have argued
that expanding space is as real as ether, in a sense that they
are both unobservable. More specifically, propagation of light is
a relativistic phenomenon: for light, the analogy of a swimmer
in a river does not work; the velocity of light is c in every inertial
frame. This explains the null results of all the ether-drift
experiments, and enables one to predict the null results of any
expanding – or drifting – space experiments.
We have shown that both the superluminality of distant
galaxies and the travel-time effect for photons are merely coordinate
effects: they vanish in a suitably chosen coordinate system.
Therefore, they are not real phenomena, which different
observers will agree on. In the Milne model, the travel-time effect
– present in the RW coordinates – is explicable entirely by
the relativistic phenomenon of time dilation. Since in the real
universe distant galaxies recede with relativistic velocities, time
dilation must play a role also in the case of more realistic FL
models.
The concept of the EoS has been invented to stress that
the GR description of the expansion of the universe can conflict
with our intuitions based on SR. However, for non-specialists
this concept can be very misleading: in their minds, it can easily
become endowed with force or some sort of physical or causal
power. This point has been extensively discussed in Section 1.
Therefore, the author of the present paper prefers to advocate an
alternative, semi-popular description, or model, of the universe
and its expansion. Namely, the universe is like theMilne model,
but with effects of mutual gravity. Gravity modifies relative motions
of the particles of the cosmic substratum and makes GR in
cosmology indispensable. The conflict of the GR description of
distant events in the universe with our SR expectations is only
apparent: the velocity of light in vacuum is c only in inertial
frames, while in the real universe such frames are only of limited
extent.
Is the concept of the EoS dangerous also for specialists?
Not necessarily. Some specialists use it, but in a somewhat different
sense: for them, the EoS is just the GR solution for the
expansion of the universe when expressed in RW coordinates
(Davis, private communication). Also, all relativists agree that
matter and space are inexorably intertwined in GR. Therefore,
indeed the debate on the meaning and the use of the phrase ‘Expansion
of Space’ “is somewhat a matter of philosophy and semantics,
rather than hard science” (Davis, private communication).
However, we believe that philosophy and semantics do
matter in cosmology. Therefore, we suggest to avoid using the
phrase ‘Expansion of Space’, as potentially leading to confusion
and wrong intuitions.
===endquote===

BTW he several times talks about private communication with Tamara Davis who is Charles Lineweaver's grad student and subsequent co-author
and he cites Lineweaver and Davis stuff
Davis, T. M. 2004, PhD thesis, preprint
arXiv:astro-ph/0402278
Davis, T. M., Lineweaver, C. H. 2004, PASA, 21, 97
Davis, T.M., Lineweaver, C. H.,Webb J. K. 2003, AmJPh, 71,
358
============
I wouldn't call him "crackpot" just based on these conclusions.
I think that there are serious problems with the idea of space, and with the idea of Expansion of Space as many people use the term (perhaps without enough understanding).
============

I expect that as Hellaby says the next generation of observations will be able to establish the angular size minimum, which is already thought to be around z=1.6. And this will finally drive the stake through Milne's heart.
The angular size minimum is not something Chod talks about trying to explain--he tries to fit other stuff to the Milne picture.

For now, Chodorow seems to think he can get around the other obvious objections by some vague talk about "Milne plus gravitational effects". That strikes me as handwaving and probably shallow, but not worth arguing with.

I don't know anyone besides Chod who still clings to Milne. (and he has a "chequered record" nice rhymed phrase )

Keep your eye out for articles about things looking bigger out past z = 1.6 and when we get that amount of detail observation that can set your mind at rest.