Static universe - revisited

In two previous threads "static universe" and "static universe
- reply" I gave reference to papers that argue that "Observational
evidence favors a static universe". Unfortunately the discussion
in these threads got bogged down in s series of claims and
counter-claims that only touched on the major result of these papers.
In addition many may have found that the length of the 96 page paper
daunting. Here I will give a very brief outline of the crucial
results.
For all references, caveats and full details see arXiv 1009.0953:
http://arxiv.org/abs/1009.0953 (it includes a table of contents,
hyperlinks and several minor corrections) or see the JCos papers.

A major difference between cosmologies in an expanding universe
and that in a static universe is time dilation. Whereas a tired
light process could explain the energy loss of photons it cannot
produce the effect of time dilation on the rate of arrival of photons.
In an expanding universe cosmology the equations for the distance
modulus and for the angular size include a term, (1+z), to allow for
time dilation. Since the similar equations for a static-universe
cosmology do not include this term its presence (or absence) makes
a suitable test for determining whether the universe is expanding.
It is assumed that the static universe obeys the perfect cosmological
principle. The same everywhere and at all times.


Tolman surface brightness.
Sandage and Lubin analyzed the surface brightness of early-type
galaxies. A re-analysis using current Big Bang (BB) equations and
combining the two color bands (and for the Sersic radius 2.0) gives
an
exponent of 2.16+/-0.13. The expected exponent is 4. The difference
is attributed to luminosity evolution. A critical part of this
analysis
is the calibration of the absolute luminosity (and hence the SB) for
the absolute radii of the galaxies. Thus BB is used to compute the
radii of the distant galaxies. The surface brightness has a dependence
on the radius of SB = 9.29 + 2.83log(absolute radius).
Assuming that for a static universe the radii are all larger by a
factor (1+z) then the static universe exponent is
2.16 - 2.83/2.5 = 1.03(+/-0.14)
which is in excellent agreement with the expected value of 1.
Note Lubin and Sandage claim that their results are inconsistent
with a static universe. However they used their own tired-light model
which is different to the simple model used here.

Angular size.
Recently Lopez-Corredoira (2010) used 393 galaxies with redshift
range of 0:2 z 3:2 and found that in agreement with much earlier
work the data was consistent with a Euclidean geometry and was
totally unable to fit the data to an expanding universe.

Type 1a supernovae.
Here the analysis is more complex and is based on the assumption that
these supernovae have constant energy and not constant peak
luminosity.
There is no observational difference between peak luminosity and
total energy for nearby supernovae. The total energy is a product
of the peak luminosity and the width of the light curve.
The critical part of the analysis is that the distant supernovae have
been selected to have a very small variation in their peak luminosity
computed with BB. In a static universe this means that the selected
supernovae are biased to a lower luminosity (by a factor of 1+z).
Then if on average their total energy is constant then their widths
are
biased to larger values. On average a selection bias of (1+z) to
lower
luminosity corresponds to a selection bias of (1+z) in width.
Exactly what is observed. A fit of total energy verses redshift has a
function (19.070+\-042) + (0.047+\-0.089)2.5log(1 + z) which is
consistent with zero slope. Thus no evidence of dark energy!

Gamma ray bursts.
A remarkable characteristic of gamma ray bursts is that the raw
observations of the various time measures (burst duration, spike rise
time and spike rate) do not show any significant variation with
redshift
(out to z=6). The standard explanation is that there is an inverse
relationship between absolute luminosity and the time measures and
the
lack of variation in the time measures is due to selection effects.
In a static universe the lack of variation is expected and the
relationship with absolute luminosity is spurious and due to the
use of an incorrect distance modulus.

Galaxy luminosity function.
It is shown that E-S_a galaxies have a well defined luminosity
distribution with a peak that has essentially the same shape at all
redshifts but the position of the peak varies with redshift.
When analyzed for a static cosmology the magnitude of this peak has a
constant value independent of redshift with a Chi^2 of 6.1 for
3 degrees of freedom.

Quasar luminosity distribution.
At a fixed redshift the SDSS quasars essentially have a power law
distribution (exponential in magnitude). Since the distance modulus
is
additive and for a small range of redshifts is essentially constant
it can be derived from the distribution of magnitudes within that
redshift range. The sum of the probability of detection for each
quasar
in the range multiplied by the exponential of the luminosity function
is set equal to the expected number of quasars. The only complication
is the co-moving volume and density of the quasars. Assuming the
reasonable assumption that the the static universe has the same
volume as a function of z as BB and that the quasar density is
constant
the analysis shows a well defined preference for a static universe.
A BB model can only fit the data if it has a density evolution.

Quasar variability in time.
Hawkins has analyzed the time variability of 800 quasars over time
scales from 50 days to 28 years. He finds that there is no
dependence of the time variability on redshift.

The Butcher-Oemler effect.
They observed that the fraction of blue galaxies in galactic clusters
appears to increase with redshift. Andreon, Lobo & Iovino (2004)
examined three clusters around z=0.7 and did not find clear-cut
evidence for the effect. To quote one of their conclusions:
"Twenty years after the original intuition by Butcher & Oemler,
we are still in the process of ascertaining the reality of the
Butcher-Oemler effect".

David F. Crawford

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On Apr 18, 7:05 pm, davd wrote:

[...]

A major difference between cosmologies in an expanding universe
and that in a static universe is time dilation. Whereas a tired
light process could explain the energy loss of photons it cannot
produce the effect of time dilation on the rate of arrival of photons.

The process would also scatter photons, and take the deposited energy
and dump it somewhere. That somewhere would start glowing rather
strongly.

Neither eventuality has been observed.

In an expanding universe cosmology the equations for the distance
modulus and for the angular size include a term, (1+z), to allow for
time dilation. Since the similar equations for a static-universe
cosmology do not include this term its presence (or absence) makes
a suitable test for determining whether the universe is expanding.
It is assumed that the static universe obeys the perfect cosmological
principle. The same everywhere and at all times.

Tolman surface brightness.
Sandage and Lubin analyzed the surface brightness of early-type
galaxies. A re-analysis using current Big Bang (BB) equations and
combining the two color bands (and for the Sersic radius 2.0) gives
an
exponent of 2.16+/-0.13. The expected exponent is 4. The difference
is attributed to luminosity evolution.

The exponent is meaningless without additional assumptions. Either
there is evolution between the various galaxies (which are at
substantially different points in space-time) or there is not.

Either way tired light does not cut it, as the exponent would be equal
to 1 not 2.

[....]

Angular size.
Recently Lopez-Corredoira (2010) used 393 galaxies with redshift
range of 0:2 z 3:2 and found that in agreement with much earlier
work the data was consistent with a Euclidean geometry and was
totally unable to fit the data to an expanding universe.

Thanks for having us find http://arxiv.org/pdf/1002.0525v1 by
ourselves.

It is a red flag when the result is directly contradicted by SN1a
observations. Redshift vs distance/velocity is not linear past a
certain point, acceleration of expansion. Disagree on the result
but the data cannot be denied.

I am moderately amused that you toss the evolutionary arguments in
Lubin & Sandage out the window but buy - at face value - every
assumption used in a paper that agrees with you.


Type 1a supernovae.
Here the analysis is more complex and is based on the assumption that
these supernovae have constant energy and not constant peak
luminosity.

Eh?

The point of using the SN1a as a standard candle is that they have
constant luminosity. Barring redshift moving things around, how do you
imagine you could retain constant luminosity (thus constant peak
luminosity, and constant energy output) WITHOUT having a constant peak
luminosity?


There is no observational difference between peak luminosity and
total energy for nearby supernovae. The total energy is a product
of the peak luminosity and the width of the light curve.
The critical part of the analysis is that the distant supernovae have
been selected to have a very small variation in their peak luminosity
computed with BB.

What? The standard-ness of SN1a's isn't model dependent.

It is true whether or not the big bang is real or not, as it is
observational fact (within a few %).

In a static universe this means that the selected
supernovae are biased to a lower luminosity (by a factor of 1+z).

You are wishing and hoping. Supernovae searches use telescopes, not
models, in finding events.

Then if on average their total energy is constant then their widths
are
biased to larger values.

Except there is no bias other than apparent magnitude. You are making
the case against yourself.

On average a selection bias of (1+z) to lower
luminosity corresponds to a selection bias of (1+z) in width.
Exactly what is observed. A fit of total energy verses redshift has a
function (19.070+\-042) + (0.047+\-0.089)2.5log(1 + z) which is
consistent with zero slope. Thus no evidence of dark energy!

BAM! Unsubstantiated claim out of left field.

Take the existing SN1a observations, eg the Union(1,2) data set. Eg,
http://supernova.lbl.gov/Union/figur...n2_mu_vs_z.txt , then
plot magnitude vs redshift, eg http://supernova.lbl.gov/Union/figur...bble_slide.pdf
, then make the obvious conclusion.

Or, better yet, review the work of those who have already done that
particular work.

http://supernova.lbl.gov/Union/

Some good information there.


Gamma ray bursts.

....have literally zero bearing on cosmology at this point in time.

A remarkable characteristic of gamma ray bursts is that the raw
observations of the various time measures (burst duration, spike rise
time and spike rate) do not show any significant variation with
redshift
(out to z=6). The standard explanation is that there is an inverse
relationship between absolute luminosity and the time measures and
the
lack of variation in the time measures is due to selection effects.
In a static universe the lack of variation is expected and the
relationship with absolute luminosity is spurious and due to the
use of an incorrect distance modulus.

Which means the entire cosmic distance ladder is blown to crap, which
you should be able to establish as the methods and their relationships
are well published.


Galaxy luminosity function.
It is shown that E-S_a galaxies have a well defined luminosity
distribution with a peak that has essentially the same shape at all
redshifts but the position of the peak varies with redshift.
When analyzed for a static cosmology the magnitude of this peak has a
constant value independent of redshift with a Chi^2 of 6.1 for
3 degrees of freedom.

A Chi^2 of 6.1 isn't all that good.


Quasar luminosity distribution.
At a fixed redshift the SDSS quasars essentially have a power law
distribution (exponential in magnitude). Since the distance modulus
is
additive and for a small range of redshifts is essentially constant
it can be derived from the distribution of magnitudes within that
redshift range. The sum of the probability of detection for each
quasar
in the range multiplied by the exponential of the luminosity function
is set equal to the expected number of quasars. The only complication
is the co-moving volume and density of the quasars. Assuming the
reasonable assumption that the the static universe has the same
volume as a function of z as BB and that the quasar density is
constant
the analysis shows a well defined preference for a static universe.
A BB model can only fit the data if it has a density evolution.

Since no quasars are observed locally or 'anywhere near locally',
evolution is highly likely.

You need to think your claims through a bit better, David.


Quasar variability in time.
Hawkins has analyzed the time variability of 800 quasars over time
scales from 50 days to 28 years. He finds that there is no
dependence of the time variability on redshift.

And?


The Butcher-Oemler effect.
They observed that the fraction of blue galaxies in galactic clusters
appears to increase with redshift. Andreon, Lobo & Iovino (2004)
examined three clusters around z=0.7 and did not find clear-cut
evidence for the effect. To quote one of their conclusions:
"Twenty years after the original intuition by Butcher & Oemler,
we are still in the process of ascertaining the reality of the
Butcher-Oemler effect".

David F. Crawford

I'm not seeing the relevance of this to anything.

I do note you've ceased discussion of the CMBR which is *THE*
principle piece of evidence in favor of the big bang theory. Why is
that?

In article
, davd
writes:

For all references, caveats and full details see arXiv 1009.0953:
http://arxiv.org/abs/1009.0953 (it includes a table of contents,
hyperlinks and several minor corrections) or see the JCos papers.

Perhaps a brief mention on how a static universe is gravitationally
stable would be in order.

Tolman surface brightness.

I think anyone with experience in this area knows that the observational
difficulties, unknown evolution etc makes it difficult, otherwise there
would be several independent confirmations of the effect. Keep in mind
that (at least in the standard cosmology) the signal-to-noise ratio in a
given band goes down like the TENTH power of (1+z).

Angular size.
Recently Lopez-Corredoira (2010) used 393 galaxies with redshift
range of 0:2 z 3:2 and found that in agreement with much earlier
work the data was consistent with a Euclidean geometry and was
totally unable to fit the data to an expanding universe.

No-one can seriously claim that the angular-size test can tell us
anything about cosmology, mainly due to actually measuring the angular
size, again due to evolution and observational effects. It is no
coincidence that current cosmological models are based on the CMB and
other, more "modern" results, as opposed to the classic tests.

Type 1a supernovae.
Here the analysis is more complex and is based on the assumption that
these supernovae have constant energy and not constant peak
luminosity.
There is no observational difference between peak luminosity and
total energy for nearby supernovae. The total energy is a product
of the peak luminosity and the width of the light curve.
The critical part of the analysis is that the distant supernovae have
been selected to have a very small variation in their peak luminosity
computed with BB. In a static universe this means that the selected
supernovae are biased to a lower luminosity (by a factor of 1+z).
Then if on average their total energy is constant then their widths
are
biased to larger values. On average a selection bias of (1+z) to
lower
luminosity corresponds to a selection bias of (1+z) in width.
Exactly what is observed. A fit of total energy verses redshift has a
function (19.070+\-042) + (0.047+\-0.089)2.5log(1 + z) which is
consistent with zero slope. Thus no evidence of dark energy!

This is a relatively straightforward argument. If correct, it would be
important. Why not try to get just this argument published in a
reputable journal?

Quasar variability in time.
Hawkins has analyzed the time variability of 800 quasars over time
scales from 50 days to 28 years. He finds that there is no
dependence of the time variability on redshift.

At least in his earlier papers, Hawkins actually used the fact that
there was less variability at low redshift to support his idea that a
significant fraction of the variability of many quasars is due to
microlensing (which has since been disproved, but not because of
anything to do with the redshift dependence).

On Thu, 21 Apr 2011 10:31:03 EDT, Phillip Helbig wrote:
Perhaps a brief mention on how a static universe is gravitationally
stable would be in order.

Possibly Crawford's "surface tension" achieves this, if it means (as
other models do) that matter is gravitationally depressed into the
surface of an additional large dimension. This manifests as a
gravitational scalar which overcomes small local gravity effects, so
distant objects don't attract eachother.

Possibly this effect also works in elliptical galaxies and globular
clusters to prevent collapse. Does anyone really understand how they
remain stable?

On Thu, 21 Apr 2011 10:30:16 EDT, Eric Gisse wrote:
On Apr 18, 7:05 pm, davd wrote:
Tolman surface brightness.
Sandage and Lubin analyzed the surface brightness of early-type
galaxies. A re-analysis using current Big Bang (BB) equations and
combining the two color bands (and for the Sersic radius 2.0) gives
an exponent of 2.16+/-0.13. The expected exponent is 4.
The difference is attributed to luminosity evolution.

The exponent is meaningless without additional assumptions. Either
there is evolution between the various galaxies (which are at
substantially different points in space-time) or there is not.

Either way tired light does not cut it, as the exponent would be equal
to 1 not 2.

This is a profoundly unfair reply as Crawford continued (and you
snipped): "A critical part of this analysis is the calibration of
the absolute luminosity (and hence the SB) for the absolute radii of
the galaxies. Thus BB is used to compute the radii of the distant
galaxies. The surface brightness has a dependence on the radius of SB
= 9.29 + 2.83log(absolute radius). Assuming that for a static
universe the radii are all larger by a factor (1+z) then the static
universe exponent is 2.16 - 2.83/2.5 = 1.03(+/-0.14) which is in
excellent agreement with the expected value of 1."

What? The standard-ness of SN1a's isn't model dependent.

No, but the data is published in model-dependent ways. 10 years ago I
collected supernova data to do some independent analysis, but the raw
data is rarely available; instead it comes in prepared form where time
dilation has already been factored in, etc. So I made no headway.

Except there is no bias other than apparent magnitude. You are making
the case against yourself.

There is a big problem in SN 1a data which is that the peak
luminosities drop off at large redshift. Malmquist bias means we
should be seeing higher peak luminosities at high z. This is a
fundamental problem but doesn't seem to be troubling researchers, and
it should be. Why isn't it?

On Apr 23, 12:17am, Eric Flesch wrote:
On Thu, 21 Apr 2011 10:30:16 EDT, Eric Gisse wrote:
On Apr 18, 7:05 pm, davd wrote:
Tolman surface brightness.
Sandage and Lubin analyzed the surface brightness of early-type
galaxies. A re-analysis using current Big Bang (BB) equations and
combining the two color bands (and for the Sersic radius 2.0) gives
an exponent of 2.16+/-0.13. The expected exponent is 4.
The difference is attributed to luminosity evolution.

The exponent is meaningless without additional assumptions. Either
there is evolution between the various galaxies (which are at
substantially different points in space-time) or there is not.

Either way tired light does not cut it, as the exponent would be equal
to 1 not 2.

This is a profoundly unfair reply as Crawford continued (and you
snipped): "A critical part of this analysis is the calibration of
the absolute luminosity (and hence the SB) for the absolute radii of
the galaxies. Thus BB is used to compute the radii of the distant
galaxies. The surface brightness has a dependence on the radius of SB
= 9.29 + 2.83log(absolute radius). Assuming that for a static
universe the radii are all larger by a factor (1+z) then the static
universe exponent is 2.16 - 2.83/2.5 = 1.03(+/-0.14) which is in
excellent agreement with the expected value of 1."

It is not at all unfair. He's picking and choosing the data he wants,
and arbitrarily adjusting things to get the answer he wants.


What? The standard-ness of SN1a's isn't model dependent.

No, but the data is published in model-dependent ways. 10 years ago I
collected supernova data to do some independent analysis, but the raw
data is rarely available; instead it comes in prepared form where time
dilation has already been factored in, etc. So I made no headway.

http://supernova.lbl.gov/Union/

Scroll down to the light curve data section. Isn't that what you want?


Except there is no bias other than apparent magnitude. You are making
the case against yourself.

There is a big problem in SN 1a data which is that the peak
luminosities drop off at large redshift. Malmquist bias means we
should be seeing higher peak luminosities at high z. This is a
fundamental problem but doesn't seem to be troubling researchers, and
it should be. Why isn't it?

What do you mean 'higher peak luminosities'? The luminosity of a SN1a
is constant to within a few percent, which is why they are so
important.

Seeing less of them at higher redshifts than at lower redshifts with
the same kind of instrument isn't a big surprise, given that the
apparent magnitude falls off fairly quickly.

You can see the falloff directly with the Union1 and 2 datasets [1] -
note the existence of several magnitude 45 objects. Those are *HARD TO
SEE*.

[1] - http://supernova.lbl.gov/Union/figur...n2_mu_vs_z.txt

On Sat, 23 Apr 11 18:58:34 GMT, Eric Gisse wrote:
On Apr 23, 12:17am, Eric Flesch wrote:
There is a big problem in SN 1a data which is that the peak
luminosities drop off at large redshift. Malmquist bias means we
should be seeing higher peak luminosities at high z. This is a
fundamental problem but doesn't seem to be troubling researchers, and
it should be. Why isn't it?

What do you mean 'higher peak luminosities'? The luminosity of a SN1a
is constant to within a few percent, which is why they are so
important.

The *integrated* luminosity is modelled as constant, but the peak
luminosity inversely varies with the width of the light curve, which
is why it's essential to map out the full light curve for each SN1a.

Seeing less of them at higher redshifts than at lower redshifts with
the same kind of instrument isn't a big surprise, given that the
apparent magnitude falls off fairly quickly.

My point, obviously, is that at high z we should preferentially be
seeing those SN1a which have higher peak luminosity (and thus,
narrower light curves), because of Malmquist bias. But the opposite
happens - at high z, we see SN1a with lower peak luminosity and
broader light curves (after FRW-modifying the raw data). This outcome
is statistically unlikely, and the longer it continues as new SN1a are
added, the more it indicates a fundamental problem with the FRW model.

I'm happy to be told that my picture is out of date, and that recent
data shows results consistent with Malmquist expectations, should that
be so. Otherwise we have a BIG problem which is currently being dealt
with by pretending it isn't there. What Disney calls a "scandal".

Eric Flesch

On Apr 24, 8:00*am, Eric Flesch wrote:

[...]
Seeing less of them at higher redshifts than at lower redshifts with
the same kind of instrument isn't a big surprise, given that the
apparent magnitude falls off fairly quickly.

My point, obviously, is that at high z we should preferentially be
seeing those SN1a which have higher peak luminosity (and thus,
narrower light curves), because of Malmquist bias.*But the opposite
happens - at high z, we see SN1a with lower peak luminosity and
broader light curves (after FRW-modifying the raw data).

No, the opposite does not happen. The overwhelming majority of the
SN1a dataset is biased towards low z supernovae. The term 'Malmquist
bias' is a fancy way of saying there is a selection bias against
things you can't see with an instrument of finite sensitivity.

The population of high z data is small in comparison [z ~ 1.4,
apparent magnitude 45!] - isn't that textbook Malmquist bias?

You'll note that the increasingly-broad light curves at high z matches
the predictions of the big bang theory.

This outcome
is statistically unlikely, and the longer it continues as new SN1a are
added, the more it indicates a fundamental problem with the FRW model.

I'm happy to be told that my picture is out of date, and that recent
data shows results consistent with Malmquist expectations, should that
be so. Otherwise we have a BIG problem which is currently being dealt
with by pretending it isn't there. What Disney calls a "scandal".

Eric Flesch

Eric Flesch wrote:
at at high z we should preferentially be
seeing those SN1a which have higher peak luminosity (and thus,
narrower light curves), because of Malmquist bias.

That would only be true if this were a magnitude-limited sample,
i.e., if the criterion for observing a SN1a were (only) that it's
above a certain apparent luminosity. You can (and observers do)
avoid Malmquist bias by choosing other selection criteria. In
this case the SN1a are all chosen to be close enough to be well
above the limiting magnitude of the survey, so Malmquist bias
doesn't occur.

--
-- "Jonathan Thornburg [remove -animal to reply]"
Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA
"Washing one's hands of the conflict between the powerful and the
powerless means to side with the powerful, not to be neutral."
-- quote by Freire / poster by Oxfam

On Mon, 25 Apr 11 11:20:14 GMT, Jonathan Thornburg wrote:
Eric Flesch wrote:
at at high z we should preferentially be
seeing those SN1a which have higher peak luminosity (and thus,
narrower light curves), because of Malmquist bias.

That would only be true if this were a magnitude-limited sample,
i.e., if the criterion for observing a SN1a were (only) that it's
above a certain apparent luminosity. You can (and observers do)
avoid Malmquist bias by choosing other selection criteria. In
this case the SN1a are all chosen to be close enough to be well
above the limiting magnitude of the survey, so Malmquist bias
doesn't occur.

That does not follow because either way you are magnitude-constraining
the sample. The only way to avoid Malmquist bias would be by
discarding the fainter narrow-width lightcurves, but these would be
precisely the high-z SN1a that everyone wants. I would be pleased to
read a paper on how they have catered for this problem -- haven't
seen such a paper thus far.