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Still lower noise radio astronomy (was: low-noise amplifiers for radio astronomy )



 
 
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  #111  
Old November 22nd 06, 11:40 AM posted to sci.astro.research
Phillip Helbig---remove CLOTHES to reply
external usenet poster
 
Posts: 198
Default Galactic Evolution (was: Still lower noise radio astronomy )

In article , Oh No
writes:

The cosmological parameters are pretty well tied down by supernova
observations, and that should tie q=q(t) down too.


Within the context of GR cosmology, knowing q_0 and Omega_0 (or
lambda_0, or any two independent cosmological parameters except H_0)
completely determines q(t).

The only thing is, q
is used in a series expansion, which we don't much use any more, and it


True. At small redshifts, q is the most important term, so historically
this was important. However, it is just Omega/2 - lambda, so is well
defined in a much larger context. Practically no modern cosmological
test "measures" q in the sense that the gradient of probability in
cosmological parameter space is shallowest along lines of constant q, so
this is another reason it is not used as often as it once was. However,
it does tell one whether or not the universe is accelerating.

makes not a lot of sense to use q(t) for any purpose I can think of.
What is usually discussed is q0=q(t0), i.e. now.


Right, though one might say something like "at a redshift of x,
corresponding to a time y years ago, the universe was still
decelerating".
  #112  
Old November 22nd 06, 05:26 PM posted to sci.astro.research
Oh No
external usenet poster
 
Posts: 433
Default Galactic Evolution (was: Still lower noise radio astronomy )

Thus spake Phillip Helbig---remove CLOTHES to reply
LOTHESvax.de
In article , Oh No
writes:

The cosmological parameters are pretty well tied down by supernova
observations, and that should tie q=q(t) down too.


Within the context of GR cosmology, knowing q_0 and Omega_0 (or
lambda_0, or any two independent cosmological parameters except H_0)
completely determines q(t).


Right. I could have expressed myself more strongly. Sloppy of me. I only
intended the looseness of expression to allow for error bounds.

The only thing is, q
is used in a series expansion, which we don't much use any more, and it


True. At small redshifts, q is the most important term, so historically
this was important. However, it is just Omega/2 - lambda, so is well
defined in a much larger context. Practically no modern cosmological
test "measures" q in the sense that the gradient of probability in
cosmological parameter space is shallowest along lines of constant q, so
this is another reason it is not used as often as it once was. However,
it does tell one whether or not the universe is accelerating.

makes not a lot of sense to use q(t) for any purpose I can think of.
What is usually discussed is q0=q(t0), i.e. now.


Right, though one might say something like "at a redshift of x,
corresponding to a time y years ago, the universe was still
decelerating".


Yes. But that bears on something else which this thread has caused me to
ponder. q is termed the acceleration parameter, or more properly the
deceleration parameter. I think if someone said that I would think the
were talking about acceleration not the acceleration parameter. I would
take that to be adotdot. Mind you, I suppose its academic in this case.
Neither a nor adot changes sign, so q and adotdot have the same sign.



Regards

--
Charles Francis
substitute charles for NotI to email
  #113  
Old November 22nd 06, 05:27 PM posted to sci.astro.research
John (Liberty) Bell
external usenet poster
 
Posts: 242
Default Galactic Evolution (was: Still lower noise radio astronomy )

Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake Joseph Lazio
"J(B" =3D=3D John (Liberty) Bell =

writes:

JB John (Liberty) Bell wrote:
I think I've posted previously a reference to a paper that claimed
that Type II supernovae are difficult to detect beyond z ~ 0.5. The
most distant Type Ia supernova is about 1.7, IIRC.

Yes, that's right. SN1997ff is at z=3D1.755. In the Riess gold set the=

re
are only nine useful data points above z=3D1. Current surveys like the
Supernova Legacy Survey aren't even looking above about z=3D1, because=

of
measurement problems and risk of statistical bias in the data. We have
to wait for SNAP which should turn up hundreds, or even thousands of SN
at red shifts up to 2.


The reference (ApJ, 649, 563-569, 2006) provided by

(http://groups.google.com/group/sci.a..._frm/thread/1a
777a781e67a3a2/#)
indicates that there is no conclusive _observational_ evidence of q
becoming positive at z0.5.


That leads to a post by you, not by Rob.


No. It leads to a thread started by me which contains various postings
by Rob.

If you provide a complete ref,
with author and preferably arxiv, I will look at it.


The ref. provided by Rob was ApJ, 649, 563-569, 2006. I found the paper
by checking the contents of the most recent issues of the Journal. This
paper is less than 2 months old.
Authors: Charles Shapiro and Michael S. Turner . The ref. given by The
Astrophysical Journal at the top of the paper is 649:563-569, 2006
=A9 2006Date: Oct. 1 2006

Although, actually
The cosmological parameters are pretty well tied down by supernova
observations, and that should tie q=3Dq(t) down too. The only thing is, q
is used in a series expansion, which we don't much use any more, and it
makes not a lot of sense to use q(t) for any purpose I can think of.
What is usually discussed is q0=3Dq(t0), i.e. now.

If you are aware of different information, please clarify, with
appropriate references.

No, that is where I think we do have a problem. It's early days, and a=

ll
the data is too preliminary to be sure, but galaxy evolution models do
not tie in well with the age of the universe, when one looks at galaxi=

es
at z=3D6 and above. There are even large galaxies at z=3D10, though the
image we get of them is a bit inconclusive in terms of saying what kind
of stars they contain.


A reference for this too, would also be appreciated

#
I already gave you references in response to the above mentioned post.

I would refer you to two review papers in Natu

Glazebrook K. et. al., 2004, Nature, 430, 181-184.
http://www.pha.jhu.edu/~kgb/MiscPub/...iii-nature.pdf

Cimatti. et. al., 2004, Old Galaxies in the Young Universe, Nature, 430,
184-188. astro-ph/0407131


I had already read the first paper and the abstract of the second.
Neither support your assertion of large galaxies at z=3D10.

The first paper covers z =3D~ 0.5 to 2.

The second paper describes 4 galaxies at 1.6z1.9

I'll let you search arxiv yourself for galaxies around z=3D10. I don't
think there are many found so far.


I am only aware of 1, which was subsequently discredited. That is why I
asked you for your references.


John Bell
  #114  
Old November 23rd 06, 11:39 AM posted to sci.astro.research
John (Liberty) Bell
external usenet poster
 
Posts: 242
Default Galactic Evolution (was: Still lower noise radio astronomy )

John (Liberty) Bell wrote:

Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake Joseph Lazio
"J(B" =3D=3D John (Liberty) Bell =

writes:

JB John (Liberty) Bell wrote:
I think I've posted previously a reference to a paper that claimed
that Type II supernovae are difficult to detect beyond z ~ 0.5. The
most distant Type Ia supernova is about 1.7, IIRC.

Yes, that's right. SN1997ff is at z=3D1.755. In the Riess gold set the=

re
are only nine useful data points above z=3D1. Current surveys like the
Supernova Legacy Survey aren't even looking above about z=3D1, because=

of
measurement problems and risk of statistical bias in the data. We have
to wait for SNAP which should turn up hundreds, or even thousands of SN
at red shifts up to 2.

The reference (ApJ, 649, 563-569, 2006) provided by

(http://groups.google.com/group/sci.a..._frm/thread/1a
777a781e67a3a2/#)
indicates that there is no conclusive _observational_ evidence of q
becoming positive at z0.5.


That leads to a post by you, not by Rob.


No. It leads to a thread started by me which contains various postings
by Rob.

If you provide a complete ref,
with author and preferably arxiv, I will look at it.


The ref. provided by Rob was ApJ, 649, 563-569, 2006. I found the paper
by checking the contents of the most recent issues of the Journal. This
paper is less than 2 months old.
Authors: Charles Shapiro and Michael S. Turner . The ref. given by The
Astrophysical Journal at the top of the paper is 649:563-569, 2006
=A9 2006Date: Oct. 1 2006

Although, actually
The cosmological parameters are pretty well tied down by supernova
observations, and that should tie q=3Dq(t) down too. The only thing is, q
is used in a series expansion, which we don't much use any more, and it
makes not a lot of sense to use q(t) for any purpose I can think of.
What is usually discussed is q0=3Dq(t0), i.e. now.

If you are aware of different information, please clarify, with
appropriate references.

No, that is where I think we do have a problem. It's early days, and a=

ll
the data is too preliminary to be sure, but galaxy evolution models do
not tie in well with the age of the universe, when one looks at galaxi=

es
at z=3D6 and above. There are even large galaxies at z=3D10, though the
image we get of them is a bit inconclusive in terms of saying what kind
of stars they contain.

A reference for this too, would also be appreciated

#
I already gave you references in response to the above mentioned post.

I would refer you to two review papers in Natu

Glazebrook K. et. al., 2004, Nature, 430, 181-184.
http://www.pha.jhu.edu/~kgb/MiscPub/...iii-nature.pdf

Cimatti. et. al., 2004, Old Galaxies in the Young Universe, Nature, 430,
184-188. astro-ph/0407131


I had already read the first paper and the abstract of the second.
Neither support your assertion of large galaxies at z=3D10.

The first paper covers z =3D~ 0.5 to 2.

The second paper describes 4 galaxies at 1.6z1.9

I'll let you search arxiv yourself for galaxies around z=3D10. I don't
think there are many found so far.


I am only aware of 1, which was subsequently discredited. That is why I
asked you for your references.


Technical addendum.

In the above posting of Wed, Nov 22 2006 4:27 pm, the Astrophysical
Journal copyright symbol was corrupted to =A9. This is understandable
since it is an 8 bit character code, not 7 bit ascii. However, each
instance of =, including those quoted, was also corrupted, this time to
=3D. The reason for this is less obvious. (I found in a later posting
that this second corruption can be supressed by typing = over every
displayed =, before posting the response.)

John Bell

[Mod. note: MIME encoding (http://en.wikipedia.org/wiki/Mime) has this
effect. It can be avoided by posting in plain ASCII only, which is why
I continue to encourage posters to be careful to do so -- mjh]
  #115  
Old November 23rd 06, 06:46 PM posted to sci.astro.research
Oh No
external usenet poster
 
Posts: 433
Default Galactic Evolution (was: Still lower noise radio astronomy )

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake Joseph Lazio

JB John (Liberty) Bell wrote:
I think I've posted previously a reference to a paper that claimed
that Type II supernovae are difficult to detect beyond z ~ 0.5. The
most distant Type Ia supernova is about 1.7, IIRC.

Yes, that's right. SN1997ff is at z=3D1.755. In the Riess gold set the=

re
are only nine useful data points above z=3D1. Current surveys like the
Supernova Legacy Survey aren't even looking above about z=3D1, because=

of
measurement problems and risk of statistical bias in the data. We have
to wait for SNAP which should turn up hundreds, or even thousands of SN
at red shifts up to 2.

The reference (ApJ, 649, 563-569, 2006) provided by

(http://groups.google.com/group/sci.a..._frm/thread/1a
777a781e67a3a2/#)
indicates that there is no conclusive _observational_ evidence of q
becoming positive at z0.5.


The ref. provided by Rob was ApJ, 649, 563-569, 2006. I found the paper
by checking the contents of the most recent issues of the Journal. This
paper is less than 2 months old.
Authors: Charles Shapiro and Michael S. Turner . The ref. given by The
Astrophysical Journal at the top of the paper is 649:563-569, 2006
=A9 2006Date: Oct. 1 2006


This paper takes the non-standard step of dispensing with the Friedmann
equation. Not something I would be inclined to do, since the Friedmann
equation is itself based on well established physics. The most I would
consider reasonable is to allow the cosmological constant Lambda to vary
in time. This is done in a somewhat arcane group of theories often
called "quintescence". Of course if one does take a step like this then
one is no longer working within the context of a mainstream GR
cosmology, and obviously that opens up the possibility that q is not
determined at all times by the current data. However, there is an
immediate problem that, in this case, the amount of data is so little
that it is very difficult to come to any physics conclusions at all.
Mostly these theories are being tested by looking for supernova at z1,
because that is where we are best able to collect data with which to
test them. Other projects are underway, but I believe they are mostly in
early design and build stage. As I understand, at the moment there is no
evidence for varying Lambda. If you are talking about such theories
outside of standard cosmology, you should make your context plain.

Although the paper says that there is only week *observational* evidence
of past deceleration, such deceleration is a feature of a standard GR
cosmology, and it concludes that "none of the kinematic models studied
here have revealed robust features about cosmic acceleration that differ
from LambdaCDM or wCDM. Moreover, none of the kinematic models fit the
data significantly better".

I'll let you search arxiv yourself for galaxies around z=3D10. I don't
think there are many found so far.


I am only aware of 1, which was subsequently discredited. That is why I
asked you for your references.


I had said that the data was too thin to use. It does not altogether
surprise me if the observation has been discredited. I gather the
moderator gave references earlier in the thread.


Regards

--
Charles Francis
substitute charles for NotI to email
  #116  
Old November 24th 06, 09:39 AM posted to sci.astro.research
Chalky
external usenet poster
 
Posts: 219
Default Galactic Evolution (was: Still lower noise radio astronomy )

Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake "John (Liberty) Bell"
Oh No wrote:

Thus spake Joseph Lazio

JB John (Liberty) Bell wrote:
I think I've posted previously a reference to a paper that claimed
that Type II supernovae are difficult to detect beyond z ~ 0.5. The
most distant Type Ia supernova is about 1.7, IIRC.

Yes, that's right. SN1997ff is at z=3D1.755. In the Riess gold set the=

re
are only nine useful data points above z=3D1. Current surveys like the
Supernova Legacy Survey aren't even looking above about z=3D1, because=

of
measurement problems and risk of statistical bias in the data. We have
to wait for SNAP which should turn up hundreds, or even thousands of SN
at red shifts up to 2.

The reference (ApJ, 649, 563-569, 2006) provided by

(http://groups.google.com/group/sci.a..._frm/thread/1a
777a781e67a3a2/#)
indicates that there is no conclusive _observational_ evidence of q
becoming positive at z0.5.


The ref. provided by Rob was ApJ, 649, 563-569, 2006. I found the paper
by checking the contents of the most recent issues of the Journal. This
paper is less than 2 months old.
Authors: Charles Shapiro and Michael S. Turner . The ref. given by The
Astrophysical Journal at the top of the paper is 649:563-569, 2006
=A9 2006Date: Oct. 1 2006


This paper takes the non-standard step of dispensing with the Friedmann
equation.


This is not strictly true. The paper takes the "non standard" step of
examining the astronomical data objectively, for what it is.

The authors DO examine the data in the context of the best fit EFE
model. However, they also examine the data in the context of radically
different models too, which puts the evidence into perspective.

In particular, I draw your attention to Figure 1, and my discussion
with John Bell under the subtitle "Better News for Big bang Theory".
You will note from the text of the paper, that the displayed step
function gives as good a match to the data, as does EFE (also displayed
in that figure). You will also note from my discussion with John, that
when I tanslated his predicted cosmic acceleration into the more
commonly used acceleration parameter q, this gave rise to a predicted
asymptotically decreasing q function as z got progressively lower.

Thirdly, please note, from figure 1, that a best fit asymptotic
function does appear to represent something mid way between the best
fit step function, and the best fit EFE function at low z.

Not something I would be inclined to do,


That is clear from your own approach to the unification of QM and GR.

since the Friedmann
equation is itself based on well established physics.


By the same token, 90 years ago, you would not have been inclined to
examine the orbital anomaly of Mercury in the context of EFE, since
Newtonian physics was then the well established physics, whereas EFE
was not.

This is not a personal attack, since the vast majority of physicists at
that time, were of the same opinion. There was one notable exception,
however, who mounted an expedition to test Einstein's predicted
doubling of the Newtonian bending of starlight grazing the Sun, during
a solar eclipse. The rest is history (and that is what got EFE
recognised).

The most I would
consider reasonable is to allow the cosmological constant Lambda to vary
in time.


And how is that reasonable? As Phillip Helbig pointed out, a constant
is, by definition, constant. There is no way that such a varying lambda
can be predicted from Einstein's foundations of the theory.

This is done in a somewhat arcane group of theories often
called "quintescence". Of course if one does take a step like this then
one is no longer working within the context of a mainstream GR
cosmology, and obviously that opens up the possibility that q is not
determined at all times by the current data. However, there is an
immediate problem that, in this case, the amount of data is so little
that it is very difficult to come to any physics conclusions at all.
Mostly these theories are being tested by looking for supernova at z1,
because that is where we are best able to collect data with which to
test them. Other projects are underway, but I believe they are mostly in
early design and build stage. As I understand, at the moment there is no
evidence for varying Lambda. If you are talking about such theories
outside of standard cosmology, you should make your context plain.


No, neither I nor John have been looking at such 'arcane' (one might
even say revisionist) approaches to cosmology and relativity theory.
IMO they lack elegance, and are more reminiscent, in their historical
context, to adding further epicycles to the Ptolemaic model of the
Universe, before Copernicus, Galileo, Brahe, Kepler, and Newton came
along.

John has already explained to you, first at sci.physics.research (over
6 months ago), and then again here, that his job is to examine the
consequences of a newer (as yet unpublished) solution of relativistic
field theory, in the context of compatibility with both modern
astronomical evidence and known (proven) physics. You still seem
unwilling to accept that.

Although the paper says that there is only week *observational* evidence
of past deceleration, such deceleration is a feature of a standard GR
cosmology,


Yes. I only computed the situation at low z, since the situation at
high z is far less clear cut.

It is, however, the situation at low z that we can examine most
fruitfully at present, because this is the area where the divergence
between these models is greatest. You can confirm that, simply by
looking at Figure 1 of the paper.

and it concludes that "none of the kinematic models studied
here have revealed robust features about cosmic acceleration that differ
from LambdaCDM or wCDM. Moreover, none of the kinematic models fit the
data significantly better".


Agreed, but they did not examine the predicted asymptotic function.
They did say, however, that the step function was as good a fit as EFE
(which you should find astonishing, given your preconceptions). And our
predicted asymptotic function does seem to lie between those two
extremes over the vast majority of the range where statistically
meaningful astronomical data is available.

Such a new statistical examination looks to me like it could well make
an excellent starting point for a further groundbreaking astronomical
paper. I sincerely hope that some bright young (academic)
astrophysicist has enough sense to try it out, and then publish his (or
her) findings.


Chalky.
  #117  
Old November 24th 06, 02:39 PM posted to sci.astro.research
Oh No
external usenet poster
 
Posts: 433
Default Galactic Evolution (was: Still lower noise radio astronomy )

Thus spake Chalky
Oh No wrote:

The ref. provided by Rob was ApJ, 649, 563-569, 2006. I found the paper
by checking the contents of the most recent issues of the Journal. This
paper is less than 2 months old.
Authors: Charles Shapiro and Michael S. Turner . The ref. given by The
Astrophysical Journal at the top of the paper is 649:563-569, 2006
=A9 2006Date: Oct. 1 2006


This paper takes the non-standard step of dispensing with the Friedmann
equation.


This is not strictly true.


No, that is strictly true and is clearly stated in the paper.

The paper takes the "non standard" step of
examining the astronomical data objectively, for what it is.


If one were really to do that the data would be just a bunch of numbers,
and nothing could be said of it at all. There is no such thing as
science without assumptions, for example a basic assumption that reality
exists independent of our perceptions, or the assumption that it obeys
laws which are always and everywhere the same as encapsulated in the
general principle of relativity. It is trivially obvious that if you
drop that assumption you will be able to say very little about any data
from distant astronomical objects, so to start making a song and dance
about it, and to suggest that the analysis given under general
relativity is in some way unscientific because of it, is not only
thoroughly offensive, but plain ignorant because actually there is a
good deal of scientific work, both theoretical and observational, which
does look into well defined ways in which the assumption can be varied.

The authors DO examine the data in the context of the best fit EFE
model. However, they also examine the data in the context of radically
different models too, which puts the evidence into perspective.


A better perspective would be to understand the structure of General
Relativity based on differential geometry, to understand the EFE, and
the derivation of Friedmann's equation and to know just what assumptions
are involved, and in what manner it is reasonable to vary them.

Not something I would be inclined to do,


That is clear from your own approach to the unification of QM and GR.


Indeed I have varied a much more subtle and less robust assumption in
GR, while retaining the EFE and Friedmann's equation, and I have found a
statistically better fit to the data than standard for a model with no
cosmological constant at all, let alone a variable one.

since the Friedmann
equation is itself based on well established physics.


By the same token, 90 years ago, you would not have been inclined to
examine the orbital anomaly of Mercury in the context of EFE, since
Newtonian physics was then the well established physics, whereas EFE
was not.


I really think you need to understand the physics involved before you
make that kind of judgement. Newton's law of gravity was always an
unexplained phenomenon, as was his *assumption* of an absolute
background space. These things were well understood by the great
mathematical physicists, Leibniz, Gauss, Riemann, and it was on their
painstaking and inspirational work and thought over two hundred years
that Einstein based both the special and general theory of relativity.

This is not a personal attack, since the vast majority of physicists


In matters of the theoretical advance of science, such as those due to
Newton and Einstein, the vast majority of physicists have very little to
say. They come along afterwards and check the detail through experiment.
But to understand the insights involved in generating the theory, it
would be wiser to look only at what was said by great mathematicians.

The most I would
consider reasonable is to allow the cosmological constant Lambda to vary
in time.


And how is that reasonable? As Phillip Helbig pointed out, a constant
is, by definition, constant.


That is a matter of semantics.

There is no way that such a varying lambda
can be predicted from Einstein's foundations of the theory.


There is also no way that constant lambda can be predicted from
Einstein's foundations. There is not even any way that any lambda at all
can be predicted from the foundations of the theory. Nor, for that
matter, is there any other theory, in particle physics for example, that
can predict lambda or a value for it.

This is done in a somewhat arcane group of theories often
called "quintescence". Of course if one does take a step like this then
one is no longer working within the context of a mainstream GR
cosmology, and obviously that opens up the possibility that q is not
determined at all times by the current data. However, there is an
immediate problem that, in this case, the amount of data is so little
that it is very difficult to come to any physics conclusions at all.
Mostly these theories are being tested by looking for supernova at z1,
because that is where we are best able to collect data with which to
test them. Other projects are underway, but I believe they are mostly in
early design and build stage. As I understand, at the moment there is no
evidence for varying Lambda. If you are talking about such theories
outside of standard cosmology, you should make your context plain.


No, neither I nor John have been looking at such 'arcane' (one might
even say revisionist) approaches to cosmology and relativity theory.
IMO they lack elegance, and are more reminiscent, in their historical
context, to adding further epicycles to the Ptolemaic model of the
Universe, before Copernicus, Galileo, Brahe, Kepler, and Newton came
along.


I am inclined to agree with that. Not just Lambda, but CDM, Inflation,
the unresolved problems between quantum theory and general relativity,
all point to the need for a radical shift in our accepted paradigms.

John has already explained to you, first at sci.physics.research (over
6 months ago), and then again here, that his job is to examine the
consequences of a newer (as yet unpublished) solution of relativistic
field theory, in the context of compatibility with both modern
astronomical evidence and known (proven) physics. You still seem
unwilling to accept that.


It is true that I am unwilling to accept that anyone who shows as little
understanding of mathematics in general, or of general relativity in
particular, can be equipped to do such a job. Also, as a great deal of
work has gone into finding solutions of relativistic field theory, by
mathematicians who are equipped for the job, I am sceptical that there
really is such a thing as an unpublished solution of the sort you appear
to be suggesting (not withstanding recent, genuine, published solutions
such as those of Bekenstein and Moffat). If this is a solution, it
should be publishable in its own right, even without data analysis.
Otherwise anyone is likely to suspect that it is based on an errors, or
makes assumptions outside of relativistic field theory which may well
not make sense.

Mathematically constructing a new solution of relativistic field theory
is extremely difficult. It took Bekenstein years, and Moffat had the
benefit of following his work. Even early solutions, Schwarzschild,
Friedmann Cosmologies, were carried out by mathematicians of exceptional
ability. But I have been explaining to you and John very basic stuff;
the meaning of the scale factor, the meaning of curvature. The prospect
that you could really be talking of a new unpublished solution appears
to be practically zero.

and it concludes that "none of the kinematic models studied
here have revealed robust features about cosmic acceleration that differ
from LambdaCDM or wCDM. Moreover, none of the kinematic models fit the
data significantly better".


Agreed, but they did not examine the predicted asymptotic function.
They did say, however, that the step function was as good a fit as EFE
(which you should find astonishing, given your preconceptions).


Not at all. Given the quality of the data, I would expect all sorts of
things to fit it once you drop Friedmann's equation. That is precisely
why I find it unimpressive - the very opposite of astonishing. It is
very easy to drop scientific assumptions and get arbitrary functions to
fit data. Leibniz even furnished a proof that there are always an
infinite number of ways to do that. What is much harder and far more
subtle is to do what Einstein did, and replace scientific assumptions
with, better, more rigorous, and more scientific, assumptions, and then
to demonstrate a better fit with data. The ability to do that is what
made him a genius. Don't expect me to believe that anyone can do it who
can't even understand what Einstein said.


Regards

--
Charles Francis
substitute charles for NotI to email
 




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