Good News for Big Bang theory

In article , "Chalky"
writes:

No. You can equate observable z to some sort of velocity ONLY at low
redshift

This is incorrect. See below for further elucidation, and references.

(and even then, it's nothing deep, more "all things are linear
to first order).

I would agree that Hubble's Law is a first order approximation, if for
no better reason than that it relates D to V to first order, with no
higher order terms present. However, that point aside, what you say is
probably only necessarily true if you wish to interpret reality
exclusively within the context of GR, AND interpret GR exclusively
within the context of the mathematical apparatus of the field equation
that Einstein published during World War 1.

If you interpret GR more generally (and, I would thus argue, more
rigorously), to mean ANY logically and mathematically viable solution
of the relativistic axioms, which is consistent with empirical
observation, then it seems to me that your argument is no longer
necessarily valid.

Velocity (change in proper distance with time) being proportional to
proper distance follows directly from homogeneous and isotropic
expansion. No physics. Neither of these quantities is observable.

At low redshift, where all distances are approximately the same, this
holds approximately for all distances.

Proof: if z tells you the velocity, is it independent
of the cosmological parameters?

Yes, at least relative to us. So what is your proof?

Let me rephrase that: If z tells you the velocity, is the VELOCITY
independent of the cosmological parameters? (The fact that z is, is
obvious, since it is an observed quantity.)

1) Hubble derived the Law from observational data, not theory.

Yes, but, as all evolutionary biologists know, origin and current
function are two different things. Also, Hubble's data were EXTREMELY
low redshift by modern standards, so he could get away with this.

Sure. But I am actually talking about something more sophisticated now.
Consequently, in the context of 2007, your argument can actually be
used to support my thesis.

4) It is thus clear to me, in the context of the above, that by
distance, Hubble estimated and meant light travel distance not 'proper'
distance.

Actually, he meant luminosity distance, but again the redshifts were so
low it didn't matter.

Although Hubble may well have used luminosity distance to arrive at his
conclusions, I seriously doubt that he could have been sloppy enough,
as a scientist, to equate luminosity distance with real distance, in
formulating his general law. Even if Hubble knew nothing about SR or
GR, he should still have known, even in the context of a Euclidean
Universe, that luminosity distance is, by definition, (1 + z) times
real distance, just from the 19th century Doppler shift formula, and
related elementary (degree course) matriculation level physics.

Actually, his redshifts were so low that it didn't matter. Do the
maths.

Although Hubble may well have used luminosity distance to arrive at his
conclusions, I seriously doubt that he could have been sloppy enough,
as a scientist, to equate luminosity distance with real distance, in
formulating his general law. Even if Hubble knew nothing about SR or
GR, he should still have known, even in the context of a Euclidean
Universe, that luminosity distance is, by definition, (1 + z) times
real distance, just from the 19th century Doppler shift formula, and
related elementary (degree course) matriculation level physics.

Why don't you read Hubble's own paper for yourself? For example,
you can find a copy of one of the first papers discussing the
distance-velocity relationship at

http://spiff.rit.edu/classes/phys240.../hub_1929.html

In this paper, he does not distinguish between the several types
of "distance" which have been discussed in this thread. I suspect
that he didn't bother because the data would not permit one to
make any distinction at that time.

Phillip Helbig---remove CLOTHES to reply wrote:

In article , "Chalky"
writes:

No. You can equate observable z to some sort of velocity ONLY at low
redshift

This is incorrect. See below for further elucidation, and references.

(and even then, it's nothing deep, more "all things are linear
to first order).

I would agree that Hubble's Law is a first order approximation, if for
no better reason than that it relates D to V to first order, with no
higher order terms present. However, that point aside, what you say is
probably only necessarily true if you wish to interpret reality
exclusively within the context of GR, AND interpret GR exclusively
within the context of the mathematical apparatus of the field equation
that Einstein published during World War 1.

If you interpret GR more generally (and, I would thus argue, more
rigorously), to mean ANY logically and mathematically viable solution
of the relativistic axioms, which is consistent with empirical
observation, then it seems to me that your argument is no longer
necessarily valid.

Velocity (change in proper distance with time) being proportional to
proper distance follows directly from homogeneous and isotropic
expansion. No physics. Neither of these quantities is observable.

That is half of the reason why I no longer use such metaphysical
concepts myself. The other half of the reason is that such de facto
unobservable abstractions tempt one back down the slippery slope
towards formulating a field equation which collapses repeatedly into
paradoxical singularities, just like Einstein's preliminary effort was
soon found to do.

I now prefer to understand observable reality in terms of things which
are themselves observable, such as real measuring devices, and real
events. This would seem to have the advantage of being both logical,
and empirically scientific.

Proof: if z tells you the velocity, is it independent
of the cosmological parameters?

Yes, at least relative to us. So what is your proof?

Let me rephrase that: If z tells you the velocity, is the VELOCITY
independent of the cosmological parameters?

YES. That velocity, for at least the lion's share of the visible
universe, IS independent of the cosmological parameters that are
required to give EFE any semblance of credibility, on that scale. This
should come as no surprise to anybody. The effects of known matter had
to be boosted by a factor of about 7 via the introduction of the
speculative concept of dark matter, just to explain galactic rotation
curves in the context of EFE. This, along with the contribution of
extragalactic dark matter, has now been dwarfed by the still more
exotic speculation of dark energy, just to explain the observational
evidence of accelerating expansion. An empirical scientist (or cynic),
could thus now claim with perfect justifiication that the current EFE
cosmological model is now driven by ~ 97% speculative metaphysics, and
only ~ 3% the locally verified physics of known matter. Einstein
exhorted us to think locally. It looks to me like the devotees of the
concordance model decided not to listen.

1) Hubble derived the Law from observational data, not theory.

Yes, but, as all evolutionary biologists know, origin and current
function are two different things. Also, Hubble's data were EXTREMELY
low redshift by modern standards, so he could get away with this.

Sure. But I am actually talking about something more sophisticated now.
Consequently, in the context of 2007, your argument can actually be
used to support my thesis.

4) It is thus clear to me, in the context of the above, that by
distance, Hubble estimated and meant light travel distance not 'proper'
distance.

Actually, he meant luminosity distance, but again the redshifts were so
low it didn't matter.

Although Hubble may well have used luminosity distance to arrive at his
conclusions, I seriously doubt that he could have been sloppy enough,
as a scientist, to equate luminosity distance with real distance, in
formulating his general law. Even if Hubble knew nothing about SR or
GR, he should still have known, even in the context of a Euclidean
Universe, that luminosity distance is, by definition, (1 + z) times
real distance, just from the 19th century Doppler shift formula, and
related elementary (degree course) matriculation level physics.

Actually, his redshifts were so low that it didn't matter. Do the
maths.

I agree that it didn't matter for the arithmetic then. It doesn't even
matter for the corresponding arithmetic now, since magnitude deviations
from what an inertial model would predict, are interpreted in terms of
ratios of predicted distance (or more accurately, flux) at the same z.
However, it does matter for understanding what is physically going on
out there. Hubble should have had an adequate grasp of such basic
natural philosophy to appreciate the difference between luminosity
distance and physical distance. Consequently, if he had actually
INTERPRETED the data to mean that recession velocity was proportional
to luminosity distance, he would have said so, instead of defining the
law as he did.

The same is equally true now for "Chalky's Law"
(http://www.1stlight.org/z8.asp#CL).


Chalky

Thus spake Oh No
Thus spake Chalky
Phillip Helbig---remove CLOTHES to reply wrote:

This law, now christened 'Chalky's Law' by John, was formally defined,
copyright protected, and published, at
http://www.1stlight.org/z8.asp#CL , at the precise start of 2007
(Greenwich Mean Time).

I don't see any curve fitting on your site at all. For a start you
haven't even plotted a curve, let alone shown a chi^2 test, so you can't
claim a better fit. Fortunately I happen to have a fitting program into
which I can very easily plug Chalky's law. Rather amusingly, far from
being a fit to the data, Chalky's law doesn't even lie on the graph.
Whereas, for 225 points of the combined Riess04 and Astier Data sets the
standard model produces a best fit chi^2 value of 212.5 and the
teleconnection produces a best fit of 210.8 (both excellent fits, btw),
Chalky's law gives a best fit of
chi^2 = 4,363,667.

I wondered if I had been a little unfair on Chalky. He might have been
expected to do a bit better than that. Then I noticed that there was an
error in the units of Chalky's law. In fact if you multiply by the speed
of light, and also optimise for errors in Hubble's constant, you get

chi^2 = 209.5.

Actually quite good for a naive law even if it does have no physics
justification. In fact it is quite interesting to see how good a fit can
be obtained by a simple quadratic law, since it gives you an idea as to
how close the physical models are to an optimum fit.


I know chalky is more interested in the Riess06 data, and I needed to
run the tests anyway.

Not withstanding the possible calibration problems which still exist in
the cleaned up data (particularly the HZSST data set), I find for the
Gold06 set with 182 SN

Standard Teleconnection Chalky
Chi^2 158.75 156.67 158.38
Omega 0.34 2.01 n/a

So I win this time, but its a close thing. Chalky still beats the
standard model. I'm struck by how close to Omega=2 the teleconnection
comes out. I don't know any reason for that.

For the silver set, which contains SN for which the spectral
determination is less clear, but which contains 285 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

Chalky wins again, but this is the data which he designed his law to
fit. A big warning is present in these figures. The cleaned up 06 data
gave a chi^2 value a bit less than the number of data points. That is
what one expects for valid data if the error margins are slightly
generous, as they should be. But here the value of chi^2 is
substantially above the number of data points. In fact, so much higher
that it goes right off chi^2 table.

http://people.msoe.edu/~jorgense/ChiSquare_Table.pdf#search='Percentage%
20po

So the only thing we say on the basis of the silver set is that it
contains invalid data with rather more than 99.5% certainty.


Regards

--
Charles Francis
substitute charles for NotI to email

Thus spake Oh No
I know chalky is more interested in the Riess06 data, and I needed to
run the tests anyway.

Not withstanding the possible calibration problems which still exist in
the cleaned up data (particularly the HZSST data set), I find for the
Gold06 set with 182 SN

Standard Teleconnection Chalky
Chi^2 158.75 156.67 158.38
Omega 0.34 2.01 n/a

So I win this time, but its a close thing. Chalky still beats the
standard model. I'm struck by how close to Omega=2 the teleconnection
comes out. I don't know any reason for that.

For the silver set, which contains SN for which the spectral
determination is less clear, but which contains 285 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

Chalky wins again, but this is the data which he designed his law to
fit.

It is usual in problems of this sort to remove outliers which can
reasonably be suspected of being false data. This data is particularly
suspect, since it is potentially contaminated from another type of
supernova. The larger chi^2 values which have most influence on the fit
are also the most likely to be false data. In addition all the errors as
given include a constant error due to peculiar velocities. I felt it
justifiable to exclude points outside of a 99% confidence limit. There
should normally be less three points in a sample the size of the silver
set, but there are eleven silver (one had chi^240!) and three gold.
Since the bulk of those will not be type 1A supernova, it is reasonable
think that others in both sets may be also not type 1A. This leaves a
sample of 270 points for the silver set, for which spectral
determination is less clear.

Standard Teleconnection Chalky
Chi^2 223.94 219.31 218.73
Omega 0.327 1.997 n/a

Chalky still wins, but only just. The influence of dodgy data starts to
become clear though as the margins is much reduced.

When the three outliers are removed from the gold set the result, for
179df is

Standard Teleconnection Chalky
Chi^2 139.12 136.54 139.27
Omega 0.342 2.05 n/a

The standard model now pips Chalky to second place, while the
teleconnection increases its lead in the gold set, which is the highest
quality data. Interesting that the gradually increasing prediction for
Omega with better quality data is starting to push the standard model
toward a timescale problem. With Omega=0.34 the age of the universe
comes out at 12.8 Gyears, 0.8 Gyrs less than the best age of the Milky
way from beryllium abundances. I think the margin is about 1Gyr, so not
quite a timescale problem yet.

I must emphasise that it is not possible to draw any firm conclusion
from these results. They are much too close to call. In terms of odds
this represents something like 10:9 in favour of the teleconnection, and
it should be pretty obvious that the result is fairly sensitive to
variations in the sample. Nonetheless I find it encouraging that every
way I split the data (I have tried other splits based on the teams which
collected data), I get a very similar picture, that the teleconnection
is marginally preferred to the standard model. Chalky's law behaves as
one would expect of a law constructed to fit data - the optimum law for
any given data set is always going to produce a better fit than the true
law, but when applied to a different data set, that is no longer the
case.




Regards

--
Charles Francis
substitute charles for NotI to email




Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:

Thus spake Oh No
Thus spake Chalky
Phillip Helbig---remove CLOTHES to reply wrote:

This law, now christened 'Chalky's Law' by John, was formally defined,
copyright protected, and published, at
http://www.1stlight.org/z8.asp#CL , at the precise start of 2007
(Greenwich Mean Time).

I don't see any curve fitting on your site at all. For a start you
haven't even plotted a curve, let alone shown a chi^2 test, so you can't
claim a better fit. Fortunately I happen to have a fitting program into
which I can very easily plug Chalky's law. Rather amusingly, far from
being a fit to the data, Chalky's law doesn't even lie on the graph.
Whereas, for 225 points of the combined Riess04 and Astier Data sets the
standard model produces a best fit chi^2 value of 212.5 and the
teleconnection produces a best fit of 210.8 (both excellent fits, btw),
Chalky's law gives a best fit of
chi^2 = 4,363,667.

I wondered if I had been a little unfair on Chalky. He might have been
expected to do a bit better than that. Then I noticed that there was an
error in the units of Chalky's law. In fact if you multiply by the speed
of light,

Poor Chalky. He got jibed for leaving the c in his formulae, and then
gets in hot water again, for then using natural units, as previously
advised, when publishing his Law.

and also optimise for errors in Hubble's constant, you get

chi^2 = 209.5.

Actually quite good for a naive law even if it does have no physics
justification.

Actually, its physics justification was its whole raison d'etre, which
is why we wanted to get this particular prediction published asap, in
2007 (without waiting for the pretty graphs).

In fact it is quite interesting to see how good a fit can
be obtained by a simple quadratic law, since it gives you an idea as to
how close the physical models are to an optimum fit.


I know chalky is more interested in the Riess06 data, and I needed to
run the tests anyway.

Not withstanding the possible calibration problems which still exist in
the cleaned up data (particularly the HZSST data set), I find for the
Gold06 set with 182 SN

Standard Teleconnection Chalky
Chi^2 158.75 156.67 158.38
Omega 0.34 2.01 n/a

So I win this time, but its a close thing. Chalky still beats the
standard model. I'm struck by how close to Omega=2 the teleconnection
comes out. I don't know any reason for that.

For the silver set, which contains SN for which the spectral
determination is less clear, but which contains 285 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

Chalky wins again,

Most gracious of you. You actually won on the first throw, but I guess
Chalky did win overall, since he didn't change Omega, which is
irrelevant, in context.

but this is the data which he designed his law to
fit.

Not so. He derived his law from theory. We had the devils own job
reinterpreting the original prediction in a way that could be seen as
consistent with the way the data has been presented by astronomers
(i.e. in the context of EFE). When Chalky got it, he then tested the
Law against the full 290 supernova data set that had been already
(helpfully) been statistically analysed by Ned Wright. Most of these
were gold. (Ned's reference here is:
http://braeburn.pha.jhu.edu/~ariess/R06/sn_sample )

A big warning is present in these figures. The cleaned up 06 data
gave a chi^2 value a bit less than the number of data points. That is
what one expects for valid data if the error margins are slightly
generous, as they should be. But here the value of chi^2 is
substantially above the number of data points. In fact, so much higher
that it goes right off chi^2 table.

http://people.msoe.edu/~jorgense/ChiSquare_Table.pdf#search='Percentage%
20po

So the only thing we say on the basis of the silver set is that it
contains invalid data with rather more than 99.5% certainty.

Yes, but the importance of that invalid data (which may be just one Sn)
gets watered down more, the more samples one includes in the set. On
this argument, including the silver set as Ned and Chalky did, is
probably still better than excluding it.

Actually though, the numbers don't add up. I counted 290 Snae
altogether in Ned's set, which, quoting from ref.

"To match primary fits in Riess et al. 2007 (astro-ph/0611572)
Please cite Riess et al. 2007 (astro-ph/0611572).

1) Discard all SNe Ia with z0.0233
2) Discard all SNe with quality='Silver'
This should leave 182 SNe Ia."

That looks like 100 silvers to me, in their analysis..

(Your revised response was most gracious and welcome, and I am sure
that Chalky will agree.)

Perhaps you could now also try throwing the whole lot in the number
cruncher together, and see what you come up with.


Regards

John

Oh No wrote:
Thus spake Oh No
Thus spake Chalky

This law, now christened 'Chalky's Law' by John, was formally defined,
copyright protected, and published, at
http://www.1stlight.org/z8.asp#CL , at the precise start of 2007
(Greenwich Mean Time).

for 225 points of the combined Riess04 and Astier Data sets the
standard model produces a best fit chi^2 value of 212.5 and the
teleconnection produces a best fit of 210.8 (both excellent fits, btw),
Chalky's law optimise for errors in Hubble's constant, you get
chi^2 = 209.5.

And what is that optimised value for Ho? (so we can check that
prediction too)

Let us take your above 225 points as set A, your next 182 point (gold
set) as set B and your final 285 point (silver set) as set C. You get:

Model: Chalky's Law EFE Teleconnection No. of Data Points
chi^2 A: 209.5 212.5 210.8 225
chi^2 B: 158.38 158.75 156.67 182
chi^2 C: 383.05 393.49 387.55 285

That is three tests out of three which confirm that Chalky's Law is
more accurate than EFE. Ditto for your teleconnection model.

Now let us get more ambitious.
What do you find for:

(D) the 290 point (mostly gold) set used by Ned Wright and adopted by
Chalky? (http://braeburn.pha.jhu.edu/~ariess/R06/sn_sample)

(E) the entire ~ 570? point (complete) set using the whole ~204? gold,
285 silver, and ~ 81? Astier supernovae, without preference or
prejudice?

Given the models are so close thus far, any peculiar motion at low z,
or otherwise duff data elsewhere, should affect all 3 runners
similarly.


Regards, John

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

Thus spake Oh No
Thus spake Chalky
Phillip Helbig---remove CLOTHES to reply wrote:

This law, now christened 'Chalky's Law' by John, was formally defined,
copyright protected, and published, at
http://www.1stlight.org/z8.asp#CL , at the precise start of 2007
(Greenwich Mean Time).

I don't see any curve fitting on your site at all. For a start you
haven't even plotted a curve, let alone shown a chi^2 test, so you can't
claim a better fit. Fortunately I happen to have a fitting program into
which I can very easily plug Chalky's law. Rather amusingly, far from
being a fit to the data, Chalky's law doesn't even lie on the graph.
Whereas, for 225 points of the combined Riess04 and Astier Data sets the
standard model produces a best fit chi^2 value of 212.5 and the
teleconnection produces a best fit of 210.8 (both excellent fits, btw),
Chalky's law gives a best fit of
chi^2 = 4,363,667.

I wondered if I had been a little unfair on Chalky. He might have been
expected to do a bit better than that. Then I noticed that there was an
error in the units of Chalky's law. In fact if you multiply by the speed
of light,

Poor Chalky. He got jibed for leaving the c in his formulae, and then
gets in hot water again, for then using natural units, as previously
advised, when publishing his Law.

It can be important simply to state what you mean. But I do feel a bit
guilty and have to apologise. It should have occurred to me to think of
this sooner. As it was, I posted too quickly. Sorry about that, Chalky.

and also optimise for errors in Hubble's constant, you get

chi^2 = 209.5.

Actually quite good for a naive law even if it does have no physics
justification.

Actually, its physics justification was its whole raison d'etre, which
is why we wanted to get this particular prediction published asap, in
2007 (without waiting for the pretty graphs).

I may be able to email you some before too long.

In fact it is quite interesting to see how good a fit can
be obtained by a simple quadratic law, since it gives you an idea as to
how close the physical models are to an optimum fit.


I know chalky is more interested in the Riess06 data, and I needed to
run the tests anyway.

Not withstanding the possible calibration problems which still exist in
the cleaned up data (particularly the HZSST data set), I find for the
Gold06 set with 182 SN

Standard Teleconnection Chalky
Chi^2 158.75 156.67 158.38
Omega 0.34 2.01 n/a

So I win this time, but its a close thing. Chalky still beats the
standard model. I'm struck by how close to Omega=2 the teleconnection
comes out. I don't know any reason for that.

For the silver set, which contains SN for which the spectral
determination is less clear, but which contains 285 points

Standard Teleconnection Chalky
Chi^2 393.49 387.55 383.05
Omega 0.32 1.985 n/a

Chalky wins again,

Most gracious of you. You actually won on the first throw, but I guess
Chalky did win overall, since he didn't change Omega, which is
irrelevant, in context.

There I cannot agree with you. It's true that chalky does not have free
parameters, but the rate of change of expansion is determined by
gravitational force. The more dense matter is in the universe the more
rapidly Hubble expansion slows down, and that is what is being
determined in these tests. This would be true even in a Newtonian theory
of gravity.

but this is the data which he designed his law to
fit.

Not so. He derived his law from theory. We had the devils own job
reinterpreting the original prediction in a way that could be seen as
consistent with the way the data has been presented by astronomers
(i.e. in the context of EFE). When Chalky got it, he then tested the
Law against the full 290 supernova data set that had been already
(helpfully) been statistically analysed by Ned Wright. Most of these
were gold. (Ned's reference here is:
http://braeburn.pha.jhu.edu/~ariess/R06/sn_sample )

That is also the data I used.

A big warning is present in these figures. The cleaned up 06 data
gave a chi^2 value a bit less than the number of data points. That is
what one expects for valid data if the error margins are slightly
generous, as they should be. But here the value of chi^2 is
substantially above the number of data points. In fact, so much higher
that it goes right off chi^2 table.

http://people.msoe.edu/~jorgense/ChiSquare_Table.pdf#search='Percentage%
20po

So the only thing we say on the basis of the silver set is that it
contains invalid data with rather more than 99.5% certainty.

Yes, but the importance of that invalid data (which may be just one Sn)
gets watered down more, the more samples one includes in the set. On
this argument, including the silver set as Ned and Chalky did, is
probably still better than excluding it.

I have posted a follow-up on the results of removing the most
questionable points.

Actually though, the numbers don't add up. I counted 290 Snae
altogether in Ned's set, which, quoting from ref.

Actually we have both made a mistake. The set is from Riess's site (note
URL includes ariess). I loaded it into my text editor and have 292 lines
of data which I pasted into my application. I failed to check that my
application then counted these lines correctly, and actually had a bug
which I have now found. Thanks for that. The bug only affected the count
of the number of data points, not the values of chi^2 or the predicted
values of Omega.

"To match primary fits in Riess et al. 2007 (astro-ph/0611572)
Please cite Riess et al. 2007 (astro-ph/0611572).

1) Discard all SNe Ia with z0.0233
2) Discard all SNe with quality='Silver'
This should leave 182 SNe Ia."

That looks like 100 silvers to me, in their analysis..

In fact I count (with the corrected program) 206 gold points and 86
silver points. I used all of these for the full analysis (like Ned I am
not sure that it is really right to drop points z0.023. I can't see
that it will do much harm either. Maybe it is safer to drop them. For
the gold set analysis I pasted the data from

arXiv:astro-ph/0612653v1

which has already been restricted to 182 points of gold set data with
z=0.023

In respect of that paper, btw, I also tried removing the 6 points of
HZSST data which they mark as questionable, and also, I tried removing
all the HZSST data on the ground that if that much of it is questionable
then it all is. I did not feel this made any great difference to the
results and did not think that I would share their conclusions, so in
the end I decided to include all the HZSST data. I confess, my analysis
was not as thorough as theirs. Had I thought it was going to support
their position I would have continued it, but the problems appeared to
me to be to do with individual data in different sets, not with any
particular set taken as a whole. The HZSST data does have a wider spread
than other sets, but it also has wider error margins for individual
points and so has less affect on a chi^2 test than better sets. Their
analysis was based on predictions for changes in Lambda, and I
personally doubt the validity of that enquiry. If either the
teleconnection or Chalky's law turns out to be correct, it would show up
in an analysis like that as apparently incompatible data sets.

That said, there is always a risk of incompatibility between different
sets when using unhomogeneous data. If two instruments are not
calibrated correctly together then we will get a much higher chi^2 than
we should, and also spurious predictions for Omega. Nonetheless, Riess
has done a lot of work to make sure the data is correctly calibrated,
and I see no particular reason as yet to think that work should be
rejected.

(Your revised response was most gracious and welcome, and I am sure
that Chalky will agree.)

Perhaps you could now also try throwing the whole lot in the number
cruncher together, and see what you come up with.

More on that in answer to your next post.


Regards

--
Charles Francis
substitute charles for NotI to email

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

This law, now christened 'Chalky's Law' by John, was formally defined,
copyright protected, and published, at
http://www.1stlight.org/z8.asp#CL , at the precise start of 2007
(Greenwich Mean Time).

for 225 points of the combined Riess04 and Astier Data sets the
standard model produces a best fit chi^2 value of 212.5 and the
teleconnection produces a best fit of 210.8 (both excellent fits, btw),
Chalky's law optimise for errors in Hubble's constant, you get
chi^2 = 209.5.

And what is that optimised value for Ho? (so we can check that
prediction too)

It's not possible to calculate H0 from this data on its own. A value of
H0 is already built into the magnitude figures. This cancels out of the
fits.

This may be slightly different for Chalky's law. One of the fitting
parameters is the absolute magnitude of a type 1A supernova. Varying
that is equivalent to varying Hubble's constant. To be fair on all three
models I allowed that to vary in all cases. It comes out that the
absolute magnitude is almost identical for the teleconnection and the
standard model, but is slightly less for Chalky's law - by just under
0.08 mag. It is possible that there is other info on nearby supernovae
that puts this difference outside margins of error, but that takes me
beyond my current level of knowledge. If constrained to use a value
closer to that of the standard model, Chalky's law could get pushed out
of contention.

Let us take your above 225 points as set A, your next 182 point (gold
set) as set B and your final 285 point (silver set) as set C. You get:

Model: Chalky's Law EFE Teleconnection No. of Data Points
chi^2 A: 209.5 212.5 210.8 225
chi^2 B: 158.38 158.75 156.67 182
chi^2 C: 383.05 393.49 387.55 285

That is three tests out of three which confirm that Chalky's Law is
more accurate than EFE. Ditto for your teleconnection model.

Incidentally the teleconnection does use the EFE, and also Friedmann's
equation. It only differs from the standard model in predictions
concerning cosmological redshift. The impact of this difference is quite
dramatic, however. Instead of an infinite universe with accelerating
expansion and cold dark matter, it comes up with an "Einstein preferred"
closed, finite universe with no cosmological constant and no cold dark
matter.

Now let us get more ambitious.
What do you find for:

(D) the 290 point (mostly gold) set used by Ned Wright and adopted by
Chalky? (http://braeburn.pha.jhu.edu/~ariess/R06/sn_sample)

As explained in previous post, I was actually using 292 points from this
set, which I counted incorrectly.

(E) the entire ~ 570? point (complete) set using the whole ~204? gold,
285 silver, and ~ 81? Astier supernovae, without preference or
prejudice?

The complete set is actually the 292 points we have used. This includes
the original Reiss04 gold and silver sets, the entire Astier set, plus,
26 (iirc) new HST points. The 225 points I used before consists of the
original Reiss04 gold set, less (iirc) 3 outliers together with the
Astier set less two outliers also discarded by Astier. These outliers
are now included as silver points (i.e. don't fit Riess's spectroscopy
criteria for type 1A supernovae), as are a number of other Astier
points.

Many of the points in Riess's original set have been recalibrated for
the new 06 set, and he has also calibrated the Astier data to the other
sets, which I had done separately. He has made other small adjustments
to the Astier data which I don't know about. He is much more expert on
this data and how it is collected and preprocessed than I am. I think we
have to take the new gold and silver sets as being the most complete and
accurate data available so far.

Neither set is perfect. Just by looking at the data statistically, it
seems to me the bulk of silver points are type 1A. OTOH quite a few are
not. Certainly, by applying his spectroscopy condition Riess removes
almost all the points which lie away from the curves (all three curves),
and that is a good indication that his criterion works. He removes some
points also which are close to the curves. These may or may not be type
1A. I suspect quite a few of them are type 1A, but the quality of
observation was not good enough to be sure.

Including wrong data in a chi^2 test in general has much more affect
than discounting right data, so it seems to me that it is better to go
with the gold set than the silver one. I've been reviewing what I did
yesterday and it still seems to me that the Gold set is not perfect. I
think there is an underlying distribution which is tighter than first
appears to be the case, but it is difficult to see how to establish
this. It may be impossible to establish in any convincing way after
allowing for random factors. I still think it is right to take out the
one point beyond 3sigma for the distribution (99.9%) but I can't really
justify taking out the two others beyond 99%. One might expect two
points beyond that level anyway. Also, when I looked more carefully I
realised that removing one of those points was unfair on Chalky, because
it wasn't beyond 99% from his curve. The result, for 181 data points,
slightly reduces the teleconnection's lead and moves Chalky firmly back
into second place.

Standard Teleconnection Chalky
Chi^2 150.75 148.34 149.78
Omega 0.334 1.997 n/a


Given the models are so close thus far, any peculiar motion at low z,
or otherwise duff data elsewhere, should affect all 3 runners
similarly.

All three curves are very close, and a lot of very accurate data will be
needed to distinguish them. With around 180 points you really want a
difference of about 20 in the value of chi^2 to say anything approaching
conclusive.

Potentially, with a lot of data, Chalky's law can be distinguished from
the other two in the range z0.4. Unfortunately they don't seem to be
looking much in that range at the moment. We could do with more recent,
(more accurate), LR supernovae. The teleconnection and the standard laws
are almost indistinguishable right up to z=1. It really needs a lot of
data above z=1.5 to have a chance of distinguishing it. Above z=1,
Chalky's law lies between the teleconnection and the standard model,
perhaps a little closer to the teleconnection up to about z=2.

The data we need will come. SNAP is being designed to find thousands of
supernovae at up to about z=2. We just have to wait - about ten years I
think.


Regards

--
Charles Francis
substitute charles for NotI to email

Potentially, with a lot of data, Chalky's law can be distinguished from
the other two in the range z0.4. Unfortunately they don't seem to be
looking much in that range at the moment. We could do with more recent,
(more accurate), LR supernovae.

The SDSS Supernova Search team has found quite a few
low-redshift SNe over the past two years. Let me do a hasty
estimate ... of order 140 Type Ia during the 2005 season and
of order 200 Type Ia during the 2006 season. Only a fraction
of these events has really frequent followup, which is necessary
to determine the peak magnitudes, but it's better than chopped
liver :-) You can find more information at

http://sdssdp47.fnal.gov/sdsssn/sdsssn.html

but I suspect you won't find a nice table with observed
peak magnitudes; the team is still working on the data
reduction and analysis. Several team members are presenting
posters at next week's AAS meeting, so watch your local
news sources for tidbits. You could also look at the AAS meeting
website, which will make some presentations available after
they have been made, I think. See special session 32,
"The SDSS Supernova Survey":

http://www.abstractsonline.com/viewer/viewSession.asp


The teleconnection and the standard laws
are almost indistinguishable right up to z=1. It really needs a lot of
data above z=1.5 to have a chance of distinguishing it. Above z=1,
Chalky's law lies between the teleconnection and the standard model,
perhaps a little closer to the teleconnection up to about z=2.

The data we need will come. SNAP is being designed to find thousands of
supernovae at up to about z=2. We just have to wait - about ten years I
think.

Hmmmm ... the usual SNAP simulations go up to z=1.7 or so, not
z=2.0,
but that's basically the plan. I may be a bit pessimistic, but ten
years
might take us to the launch, not the final results being published :-(

Michael Richmond