Any complete standardized SN11 data out there?

sean wrote:

include the relevent +- error margin
factored in. (ie 50817 is 0.91+-0.3)
.....
50817 0.94 .95 out by +0.01

Where do you get 0.94 from?

I don't know what you mean by "include the relevant error margin factored
in". When doing a fit, the estimated error may be used to weight the data
points, but never added or subtracted.

By "out by" do you mean the amount by which the difference exceeds the
error? If so, that would be a very "original" method of data analysis.

The HST readings in the first column are
from the tables and include the relevent +- error margin
factored in. (ie 50817 is 0.91+-0.3) The second column
under `V band` is the template day times s with day
0 on the template matching day 50822 from the tables

1997eq V band template (undilated except for s)
50817 0.94 .95 out by +0.01
50824 0.88 .99 out by +0.1
50846 0.36 .36 matches
50855 0.25 .22 out by -0.03
50863 0.21 .15 out by -0.05

Are you unable to see a pattern here?

That pattern means that this is *not* the best fit.

A rough calculation shows the v band template would
only have to be dilated by 1.2 (z=0.2) to fit the table
data within error margins if all my numbers are right.

So you are trying to find the least dilation for which the template is
within the error margins for every point?

Do you not see that your method is *guaranteed* to underestimate the dilation?

Would you not object to someone finding the *greatest* dilation that fits
within those margins? That would be wrong in the opposite direction.

Your use of phrases like "a best fit within error margins" seems to imply
that you don't understand what is meant by "the best fit."

The best fitting dilation is the value for which the fit is *best*. That
means finding the set of parameters that minimize the sum of the squared
differences. The error bars are used by multiplying the differences for
each data point by a weight, that is larger for the points with smaller
error bars.

It is very laborious to do this by hand, but it is the only valid way to
estimate the parameters.

I know you will say... "but the fit above isnt within
error margins"...but I notice that quite a few of Knops
template fits are also not within the observed data error
margins by about the same amounts as my 1997eq fit to
the undilated v band template above.

Generally, especially if there are many data points, even the best fit will
not be within the error bars for every single point. Error bars are
estimates, and sometimes the actual error is larger.

The problem isn't that your fit isn't "within error margins", the problem
is that it is not the *best* fit. You are using a method guaranteed to be
biased towards smaller values, and then expecting people to trust the
unexpectedly small values you get.

There are statistical methods for determining if a set of data is
compatible with a parameter having a particular value (e.g. zero), but they
do not include anything you have used.

Generally statistics become more powerful as sample size increases, so that
all the supernovas combined can be incompatible with zero dilation, even
if no one light curve has errors small enough.

I don't think that is the case here, it looks like that one case is
inconsistent with zero. It is impossible to determine the level of
significance of that from the information provided above.

Ralph Hartley

sean, as long as you
1) insist that visual comparisons are as valid as
an actual mathematical chi squared fit, and
2) refuse to do a proper error analysis for your
readings off the graphs,
this discussion is quite pointless.

Bjorn, as long as you
1)ignore the fact that I *also* supply mathematical
(ie non visual) fits here and in my last post
2)refuse to do check more than 2 out of my 11
analysis of the graphs (both those 2 of my analysis
you did check you found to be correct after all)...
3)Refuse to comprehend that Knops best fits DO NOT
test for fits where the template is undilated
(ie for 1997eq z=0)

this discussion is indeed pointless

As I mentioned in my earlier post I calculated
that if the decay were linear then using Steves
calculations I could calculate `back` and get 14
days for a 1 magdecay from peak +1.

I remember your calculation - but IIRC it did *not*
use a *linear* decay.

It was linear but you forget . But whether
or not it is linear is irrelevent as you yourself calculate
a 14 day decay time which works out to a ratio of 14/10=1.4
As the redshift is 1.86 , by your calculations the data
suppports no time dilation by a small margin, even with
error margins applied.

simply because in the maths the variable redshift
z is always stated as 0

You make no sense at all.

What! You dont understand that in a non expanding
model one doesnt dilate the template time scale
when comparing template to data?
No wonder you have problems understanding my posts.
(See below for Bjorns incomprehension of the simple
fact that when calculating the timescale of an undilated
template one doesnt dilate the template timescale!)

Yes. I've understood all along what you want to do.
But you *still* fail to understand: when doing the
chi squared analysis with s only instead of s(1+z),
the resulting s will *come out of the mathematical
analysis to be proportional to 1+z*. This
is an unavoidable *mathematical* *fact*.

You nor Knop has tried a fit to the data using only
s*z+1 where z=0 so you cant very well claim to know
what s would be in a non dilated best fit

Or maybe I should just ask you to try the
calculations yourself and replace z with 0 to see
what you get.

Not necessary. The outcome is a *mathematical* *fact*.

Where are these facts? Show them to me or show me the url
where someone else has done the maths. You cant though as
no one has ever calculated a best fit where the template
is not time dilated(z=0). Knop only does best fits where
the template is dilated proportional to z

For this one single example, yes. So what? We are
talking about a quite big amount of data here.

Yes and thats why I did all 11 SN and posted the results
in my last posts.

you have no basis for claiming that your fits are better
than the ones of Knop et al.

I only claim that a fit using an undilated v band template
fits the table data for 1997eq as well as most of Knops
best fit dilated templates fit the same data.

Show your work

I have already posted it once but here it is again...

1997eq V band template (undilated except for s)
50819 0.94 .95 out by +0.01
50824 0.88 .99 out by +0.1
50846 0.36 .36 matches
50855 0.25 .22 out by -0.03
50863 0.21 .15 out by -0.05
If you dont understand how a fit can be made between a
undilated template and table data heres how ..
Basically it uses the v band template supplied in Knop
table 2.I then multiply the template day count by s(.96)
and try several fits with different day starts for the
v band template. It works out that the first HST reading
matches day minus 3 on the undilated v band template
As the HST readings are the ones that count ( the others
have very wide error margins and fit any template) I
then match the HST day readings to the corresponding
template day reading starting with day minus 3 on the
template as day 50819 from the tables etc etc.
You`ll notice that the readings are outside the error
margins by small margins the largest being .1 for day
50824 reading. The reason why I can claim that my above
fit is as good as Knops `best fit` is that a lot of his
table data readings are also outside the data error
margins, some by as much as 0.1 and even more.
I have supplied a few examples in my last post where
Knops best fit templates are not within the table data
error margins. (One HST reading in 1998ba is outside the
table data error margins by a large margin.)
So until you can supply the maths that shows that my above
fit is incorrectly calculated the evidence above stands
as proof that no time dilation is as well supported as
time dilation. And until you can prove that none of Knops
templates are outside the table data error margins you
are only handwaving with no proof, that Knops dilated
templates fit within the data error margins

Furthermore despite being supposedly familiar with the
fitting process you seem to be unable to realize that
Knops best fits are only best fits for templates
where the timescale has been dilated by z. Therefore
a best fit where the template is dilated by 0 for all
redshifts(ie no time dilation)has not actually yet been
performed by you, Knop, Goldhaber and anyone else for
that matter. And so when you claim that "s is would
be proportional to z in an undilated best fit and the
maths show this".. you are not correct because you have
never done the maths yourself , and never seen any
maths showing this, Because no-one has ever calculated
a best fit on any of the 11 high redshift to date where
the time scale has not been dilated by z.

Sean

sean wrote:
sean, as long as you
1) insist that visual comparisons are as valid as
an actual mathematical chi squared fit, and
2) refuse to do a proper error analysis for your
readings off the graphs,
this discussion is quite pointless.


Bjorn, as long as you
1)ignore the fact that I *also* supply mathematical
(ie non visual) fits here and in my last post

Nothing you have done so far was a mathematical fit.


2)refuse to do check more than 2 out of my 11
analysis of the graphs (both those 2 of my analysis
you did check you found to be correct after all)...

I rely on the ability of Knop et al. to do a proper
data analysis.


3)Refuse to comprehend that Knops best fits DO NOT
test for fits where the template is undilated
(ie for 1997eq z=0)

How often do I need to repeat that if the fit is done
without the factor 1+z, the result will be that s is
proportional to 1+z, i.e. one will *also* see time dilation?
This is a *mathematical* *fact*, totally independent of
any *physical* assumptions, provided that the same data is used.

It is only you who refuses to comprehend here.



this discussion is indeed pointless

Indeed.

[snip]


Bye,
Bjoern

Bjorn, as long as you
1)ignore the fact that I *also* supply mathematical
(ie non visual) fits here and in my last post

Nothing you have done so far was a mathematical fit.

You obviously dont know what a fit is if you think
that comparing the day values from a template (dilated
or not but multiplied by s and normalized to unity or 1)
with the appropriate day values from the observed
data is not a fit. Its not a chi squared `best fit` but
its a fit and its done mathematically with numbers.It
couldnt be done any other way but mathematically.
Your problem is you are trying to equate the term
"mathematically" with "chi squared best fit" If you
think that the only calculation that can be called
"mathematical" is a chi squared best fit then you
had better talk to someone in the maths department
at your university as they will totally disagree with
you

2)refuse to do check more than 2 out of my 11
analysis of the graphs (both those 2 of my analysis
you did check you found to be correct after all)...

I rely on the ability of Knop et al. to do a proper
data analysis.

We were discussing whether or not a peak+1 to peak+2
mag decay showed time dilation or not and not whether
if Knops data analysis was correct. This is a good
example of where you avoid admitting my analysis is
correct (seeing as you have confirmed that 2 of my 11
are correct already) by changing the subject and making
a completely irrelevent comment about Knops best fit
calculations. An analogy would be if I were to say
the sky is blue and you respond by saying " I rely
on the heidelberg city council to work out the best
day to collect the rubbish" .. hoping that other
readers to the newsgroup will take this as proof that
the sky isnt blue.


3)Refuse to comprehend that Knops best fits DO NOT
test for fits where the template is undilated
(ie for 1997eq z=0)

How often do I need to repeat that if the fit is done
without the factor 1+z, the result will be that s is
proportional to 1+z, i.e. one will *also* see time
dilation? This is a *mathematical* *fact*, totally
independent of any *physical* assumptions, provided
that the same data is used.
It is only you who refuses to comprehend here.

You havent done the calculations for this which is
why you cant supply the calculations to back up your
claim above. Nor in fact have you ever *seen* any
mathematical proof to back up your claim as Knop has
not ever tried a best fit where z is always 0.
For instance in your statement above you claim that
where z=0 in the calculation s*(1+z), s is always
proportional to z. But if in the calculations of a non
dilated model z is always 0 regardless of redshift then
surely s is always the same as it is always, at any
redshift, multiplied by 1. S could only be proportional
to redshift if z were variable in the calculation. But
as you have to admit in the non dilation calculation
this is not the case as z is always 0.
You dont even understand basic maths if you think
that where z=0, s will vary when multiplied by 1+z.
How can any value change when multiplied by 1?
Sean

sean wrote:
Bjorn, as long as you
1)ignore the fact that I *also* supply mathematical
(ie non visual) fits here and in my last post


Nothing you have done so far was a mathematical fit.


You obviously dont know what a fit is if you think
that comparing the day values from a template (dilated
or not but multiplied by s and normalized to unity or 1)
with the appropriate day values from the observed
data is not a fit. Its not a chi squared `best fit` but
its a fit and its done mathematically with numbers.
It couldnt be done any other way but mathematically.
Your problem is you are trying to equate the term
"mathematically" with "chi squared best fit"

That's the standard meaning in science.


If you
think that the only calculation that can be called
"mathematical" is a chi squared best fit then you
had better talk to someone in the maths department
at your university as they will totally disagree with
you

We are talking about science here, not about what
mathematicians think what a fit is generally.


2)refuse to do check more than 2 out of my 11
analysis of the graphs (both those 2 of my analysis
you did check you found to be correct after all)...


I rely on the ability of Knop et al. to do a proper
data analysis.


We were discussing whether or not a peak+1 to peak+2
mag decay showed time dilation or not and not whether
if Knops data analysis was correct.

If Knop's data analysis is correct, such a crude
method won't reveal much.


This is a good
example of where you avoid admitting my analysis is
correct

Err, I pointed out several times that your values seem
to be correct, but as long as you omit a proper discussion
of error margins, your analysis doesn't mean much.


[snip strange analogy]


3)Refuse to comprehend that Knops best fits DO NOT
test for fits where the template is undilated
(ie for 1997eq z=0)


How often do I need to repeat that if the fit is done
without the factor 1+z, the result will be that s is
proportional to 1+z, i.e. one will *also* see time
dilation? This is a *mathematical* *fact*, totally
independent of any *physical* assumptions, provided
that the same data is used.
It is only you who refuses to comprehend here.


You havent done the calculations for this which is
why you cant supply the calculations to back up your
claim above.

I do not *have* to do the calculations, since the result
is obvious to anyone who understands chi squared fitting!


Nor in fact have you ever *seen* any
mathematical proof to back up your claim as Knop has
not ever tried a best fit where z is always 0.

Err, I base my claim on my knowledge of chi squared fitting.
See below.


For instance in your statement above you claim that
where z=0 in the calculation s*(1+z), s is always
proportional to z.

That's a very strange way of rewording what I actually
said.


But if in the calculations of a non
dilated model z is always 0 regardless of redshift then
surely s is always the same as it is always, at any
redshift, multiplied by 1.

No, it isn't. You still do not understand chi squared
fitting.


S could only be proportional
to redshift if z were variable in the calculation.

z is available *in the data*. It's entirely irrelevant
for the result if I include it explicitly in the calculation or not.


But as you have to admit in the non dilation calculation
this is not the case as z is always 0.
You dont even understand basic maths if you think
that where z=0, s will vary when multiplied by 1+z.

No, it's you who does not understand chi squared fitting.


How can any value change when multiplied by 1?

I do not claim that it does.

Let's look at an example. Let's say that we have five
SNs, at redshift 0.1, 0.4, 0.5, 1.0, and 1.4. Let's
also say that a chi-squared fit using the measured
data and the factor 1+z in the formula to which is
fitted, the results for s will be, say, 1.1, 0.98, 1.05,
0.97, 1.0 etc. (s is always close to 1).

I claim that it is an inevitable mathematical fact then
that if I do a chi-squared fit using the same data,
but without the factor 1+z in the formula to which is fitted,
the results for s will be 1.21, 1.47, 1.372, 1.575 and 2.4.
I.e. the s which comes out of the chi-squared fit will
be proportional to 1+z (within some small error margins).

Again, for the 10th time: it is an inevitable mathematical
fact that this result will come out. It can't be any other
result - due to the math of chi squared fitting.



Bye,
Bjoern

Bjorn wrote

If Knop's data analysis is correct, such a crude
method won't reveal much.

When Steve Wilmner first suggested using the method
you refer to above you didnt think it was crude at
the time.
Now that my analysis using this method supports no
time dilation you change your mind and say that
Steves recommended method is too crude.
And assuming Knops data analysis is correct it still
does not alter the fact that his analysis has a
very narrow range and only tests the data against
a dilated template. If he were to do a proper
scientifically acceptable analysis he would have at
least also tested the data against a non time
dilated template to provide what could be called a
control test. As he didnt his paper cannot claim
to rule out a non expanding model of the universe.
Furthermore as I have already pointed out, there are
numerous inconsistencies and mistakes in his analysis
and using a series of single fits to the data I have
shown that at the very least a best fit of an
undilated template fits the data as well as Knops
best fit of a dilated template.You wave your hands
but offer no concrete proof to refute my findings.

This is a good
example of where you avoid admitting my analysis is
correct

Err, I pointed out several times that your values seem
to be correct, but as long as you omit a proper
discussion of error margins, your analysis doesn't mean
much.

Even *with* error margins added the analysis supports
no dilation much better than dilation . For instance
lets look at YOUR analysis of 14 days +- 3 days for
1997ek. 14/10=1.4. As 1997ek is 1.86 that puts
YOUR reading with YOUR error margins marginally
closer to no dilation , even with error margins
applied. In fact your reluctance to not analyse the
other 9 SN is due to the fact that you know the numbers
will on average support no dilation more strongly
than dilation.

I do not *have* to do the calculations, since the result
is obvious to anyone who understands chi squared fitting!

Post the (correct) maths here on this newsgroup
to back up your claims and dont pretend to know results
of calculations that you have never seen or made.

For instance in your statement above you claim that
where z=0 in the calculation s*(1+z), s is always
proportional to z.

That's a very strange way of rewording what I actually
said.

Only strange if you dont understand the physics.

But if in the calculations of a non
dilated model z is always 0 regardless of redshift
then surely s is always the same as it is always,
at any redshift, multiplied by 1.

No, it isn't.

Ahh! See here is a good example of your inability to
understand the physics implicit in our discussion.
You problem is you are labouring under the delusion
that a non expanding non BB universe is still
expanding.
You mistakenly think that to do a chi squared fit of
a non dilated template one has to still dilate the
template timescale!

S could only be proportional
to redshift if z were variable in the calculation.

z is available *in the data*. It's entirely
irrelevant for the result if I include it
explicitly in the calculation or not.

Here is yet another example of how you are unable
to comprehend that a chi squared calculation of a
non dilated template explicitly does not dilate
the template.
So it is the opposite of what you claim above.
It is *entirely relevent* for the result if z is
included in the calculation or not. If it is then the
calculation tests for dilation (as Knop does). If it
isnt (and repaced by 0 in all instances)then the
calculation tests for no dilation.

Let's look at an example. Let's say that we have
five SNs, at redshift 0.1, 0.4, 0.5, 1.0, and 1.4.
Let's also say that a chi-squared fit using the
measured data and the factor 1+z in the formula to
which is fitted, the results for s will be, say,
1.1, 0.98, 1.05,0.97, 1.0 etc. (s is always close
to 1).

I claim that it is an inevitable mathematical fact
then that if I do a chi-squared fit using the same
data,but without the factor 1+z in the formula to
which is fittedthe results for s will be 1.21, 1.47,
1.372, 1.575 and 2.4.
I.e. the s which comes out of the chi-squared fit
will be proportional to 1+z (within some small
error margins).

Above is an excellent example of how you seem unable
to understand that in a non expanding, non BB model
of the universe one does not make chi squared
calculations where the template timescale is
DILATED by z.
Lets take your first example of an SN of redshift 0.1
with an s value of 1.1. In a chi squared fit where
the template is *NOT DILATED* z will be written as
0 (as the time scale of a template in a non dilated
model is never expanded nor compressed.) So the
correct maths will then be 1+z * s ..or
1+0 * 1.1 = 1.1
Yet your maths is so off that you incorrectly
substitute 0 with 0.1 which gives you the incorrect
result of 1.21.
Where did the z value of 0.1 come from? Dont forget,
we are calculating for a NON DILATED template.
And to correct all the other 4 mistakes you make
above here are the correct calculations...
z+1 * 0.98 or... 0+1 * .98 = 0.98 ..no change in s
z+1 * 1.05 or... 0+1 * 1.05= 1.05 .. "
z+1 * 0.97 or... 0+1 * 0.97= 0.97 .. "
z+1 * 1.0 or... 0+1 * 1.0 = 1.0 .. "
As you can see, contrary to what you believe,a correct
calculation shows that s is not proportional to z in
a non dilated model. Furthermore if you were to
actually do a chi squared fitting you would find
that a chi squared best fit of an undilated template
would fit the data at least as well as a dilated
template.

Again, for the 10th time: it is an inevitable
mathematical fact that this result will come out. It
can't be any other result - due to the math of chi
squared fitting.

Thats 10 times you are wrong then.As I have shown
above it is an inevitable fact that you dont
understand the maths behind a chi squared fit of an
undilated template.
If you did you would not have made the inevitable
mathematical mistakes in your calculations above.

Incidentally I notice that the SWIFT team has declined
to release the lightcurve and spectrum of grb 050117.
Is it because they have found that there is no redshift?
Sean www.gammarayburst.com

In article ,
"sean" you writes:
Even *with* error margins added the analysis supports
no dilation much better than dilation .

The above poster is the only one to reach this conclusion. The
analysis by Knop et al., as Bjoern and others have pointed out,
demonstrates the presence of time dilation because 's' is nearly
constant. In a much simpler way, my comparison of 1997ek and 1995D
(done several ways and posted in detail) also found time dilation
obvious in the data.

I've invited "Sean" to post his analysis (not just his conclusion)
for 1997ek and 1995D, but so far he has not done so. Until such an
analysis is posted, all we have are unsupported assertions.

--
Steve Willner Phone 617-495-7123
Cambridge, MA 02138 USA
(Please email your reply if you want to be sure I see it; include a
valid Reply-To address to receive an acknowledgement. Commercial
email may be sent to your ISP.)

sean wrote:
Bjorn wrote


If Knop's data analysis is correct, such a crude
method won't reveal much.


When Steve Wilmner first suggested using the method
you refer to above you didnt think it was crude at
the time.

The point is simply that it is crude *compared to*
the amount of mathematical effort and rigour which Knop
et al. (and also other research groups) have used.


Now that my analysis using this method supports no
time dilation you change your mind and say that
Steves recommended method is too crude.

Err, so far the results are consistent both with
"time dilation" and "no time dilation". So saying that
this method supports "no time dilation" is rather premature.


And assuming Knops data analysis is correct it still
does not alter the fact that his analysis has a
very narrow range

What do you mean here?


and only tests the data against a dilated template.
If he were to do a proper
scientifically acceptable analysis he would have at
least also tested the data against a non time
dilated template to provide what could be called a
control test. As he didnt his paper cannot claim
to rule out a non expanding model of the universe.

*sigh*

This argument was addressed many times now,


Furthermore as I have already pointed out, there are
numerous inconsistencies and mistakes in his analysis

Err, no. You *claim* that there are inconsistences
and mistakes. But these claims are merely based on your
misunderstandings of the method used, as explained time
after time by Steve, me and others.



and using a series of single fits to the data I have
shown that at the very least a best fit of an
undilated template fits the data as well as Knops
best fit of a dilated template.

There was e.g. a good post by Ralph Hartley on exactly
this point, already 19 days ago, which you entirely ignored so far.


You wave your hands
but offer no concrete proof to refute my findings.

I have pointed out several errors in your reasoning
already.



This is a good
example of where you avoid admitting my analysis is
correct


Err, I pointed out several times that your values seem
to be correct, but as long as you omit a proper
discussion of error margins, your analysis doesn't mean
much.


Even *with* error margins added the analysis supports
no dilation much better than dilation. For instance
lets look at YOUR analysis of 14 days +- 3 days for
1997ek. 14/10=1.4. As 1997ek is 1.86 that puts
YOUR reading with YOUR error margins marginally
closer to no dilation , even with error margins
applied.

Yes, that's one single example. What about the 10 others
in Knop's paper? Do you expect me to do all the work,
analysing all of them using proper error margins?

And what about the analysis by Riess et al, where time
dilation was found with *18 standard deviations* certainty?


In fact your reluctance to not analyse the
other 9 SN is due to the fact that you know the numbers
will on average support no dilation more strongly
than dilation.

Don't make wild guesses about my motives. I tell you
right out why I don't do the work: because I rely on
the ability of Knop et al. do to proper data analysis,
and I think that anyone who disputes that has the burden
of proof on *his* shoulders.


I do not *have* to do the calculations, since the result
is obvious to anyone who understands chi squared fitting!


Post the (correct) maths here on this newsgroup
to back up your claims and dont pretend to know results
of calculations that you have never seen or made.

I already told you the basic math necessary for chi squared
fitting weeks ago.

You have not shown that you understood it so far.



[snip quibbling about words]


But if in the calculations of a non
dilated model z is always 0 regardless of redshift
then surely s is always the same as it is always,
at any redshift, multiplied by 1.


No, it isn't.


Ahh! See here is a good example of your inability to
understand the physics implicit in our discussion.
You problem is you are labouring under the delusion
that a non expanding non BB universe is still
expanding.

*sigh* No. No. No. No. No.

This has nothing at all to do with *physics*. This is
simply, only, exclusively, about the *math* of data
analysis.

Despite lots of explanations, you *still* fail to
understand that!


You mistakenly think that to do a chi squared fit of
a non dilated template one has to still dilate the
template timescale!

*sigh* No. No. No. No. No.

Read again what I actually wrote. *Nowhere* I talked
about using a dilated template.

The *only* thing that I include is the factor "s".
Do you suggest that we leave out that factor, too,
in the chi squared fit? Or what?



S could only be proportional
to redshift if z were variable in the calculation.


z is available *in the data*. It's entirely
irrelevant for the result if I include it
explicitly in the calculation or not.


Here is yet another example of how you are unable
to comprehend that a chi squared calculation of a
non dilated template explicitly does not dilate
the template.

No, that has nothing at all to do with my actual
argument. *Nowhere* did I say that a dilated template
has to be used.

Read again what I actually wrote. Try to understand it
this time.


So it is the opposite of what you claim above.
It is *entirely relevent* for the result if z is
included in the calculation or not.

No, it is not. If I don't include z explicitly in
the formula to which is fitted, i.e. if I use only
s instead of s*(1+z), then the fit will tell me that
s is proportional to 1+z (provided that I use the
same data). For the 10th time: that is a *mathematical*
fact, entirely indepedent of the *physics*.


If it is then the
calculation tests for dilation (as Knop does). If it
isnt (and repaced by 0 in all instances) then the
calculation tests for no dilation.

Wrong.

The fit tells you by what factor the template has to
be stretched until it fits the data. If you use
s*(1+z) in the formula to which you fit, s comes out
to be roughly constant, equal to 1, as Knop et al. and
others have shown. It is then a *mathematical fact*,
*completely independent of the physics*, that a fit
using only s will give the result that s is proportional
to 1+z.

This has been pointed out to you at least 20 times now!


Let's look at an example. Let's say that we have
five SNs, at redshift 0.1, 0.4, 0.5, 1.0, and 1.4.
Let's also say that a chi-squared fit using the
measured data and the factor 1+z in the formula to
which is fitted, the results for s will be, say,
1.1, 0.98, 1.05,0.97, 1.0 etc. (s is always close
to 1).


I claim that it is an inevitable mathematical fact
then that if I do a chi-squared fit using the same
data,but without the factor 1+z in the formula to
which is fittedthe results for s will be 1.21, 1.47,
1.372, 1.575 and 2.4.
I.e. the s which comes out of the chi-squared fit
will be proportional to 1+z (within some small
error margins).


Above is an excellent example of how you seem unable
to understand that in a non expanding, non BB model
of the universe one does not make chi squared
calculations where the template timescale is
DILATED by z.

*sigh* Nowhere in the above did I say that one uses a
template dilated by z for the analysis.

Read again what I actually wrote. Try to understand it
this time.


Lets take your first example of an SN of redshift 0.1
with an s value of 1.1. In a chi squared fit where
the template is *NOT DILATED* z will be written as
0 (as the time scale of a template in a non dilated
model is never expanded nor compressed.) So the
correct maths will then be 1+z * s ..or
1+0 * 1.1 = 1.1

Err, this math has nothing at all to do with the fitting
procedure. No one *calculates* what the dilating factor
should be by using (1+z)*s = (1+0)*s. The *fitting algorithm*
*itself* tells us what stretching of the time scale is needed
in order for the best fit.


I'll try again with the same example.

First, the case *with* 1+z, i.e. we make a fit to the formula
I(t) = Imax * ( fR((t-tmax)/s(1+z)) + b ).
In the example I mentioned above, fitting the SN with z=0.1
to this formula gave s = 1.1. Let's write for abbreviation
w = s*(1+z), then obviously w = 1.21. Agreed?

In other words, if we do a fit to the formula
I(t) = Imax * ( fR((t-tmax)/w) + b ),
then the fit will tell us that w has to be 1.21. Still agreed?

Now the second case, with z=0 in the fitting formula. I.e.
we use the formula
I(t) = Imax * ( fR((t-tmax)/s) + b )
for the fit. Now, the fitting algorithm obviously does not
care for the name of variables. It is entirely irrelevant
if there is an "s" or a "w" in the formula - the result
is obviously the same. Hence if we do a fit to this formula,
the result will be s = 1.21. q.e.d.


If you disagree with the above, I recommend to you that
you educate yourself on chi squared fitting. Or perhaps
ask any physicist or mathematician if there is an error
in the reasoning I presented here.


Yet your maths is so off that you incorrectly
substitute 0 with 0.1 which gives you the incorrect
result of 1.21.

No, I don't. You still do not understand chi squared
fitting.


Where did the z value of 0.1 come from?

From the data. The fitting algorithm told us, when
using the first formula, that we need an s of 1.1 for
the best fit to the data. I.e. that we need a w of 1.21 for the best
fit to the data. The obvious conclusion then is if we use the second
formula in the fit, the algorithm will tell us that we need
an s of 1.21 for the best fit to the data.


Dont forget,
we are calculating for a NON DILATED template.

Indeed. That's why I use only s, not s*(1+z), in the
second formula.

[snip more of irrelevant math]


As you can see, contrary to what you believe,a correct
calculation shows that s is not proportional to z in
a non dilated model.

The problem is that these calculations have nothing at
all to do with chi squared fitting. They are entirely ad hoc and simply
make no sense in this connection.


Furthermore if you were to
actually do a chi squared fitting you would find
that a chi squared best fit of an undilated template
would fit the data at least as well as a dilated
template.

The data says otherwise. If a non-time dilated template
would fit the data better, the fitting algorithm would
have told us that s is proportional to 1/(1+z), not that
it is roughly constant.

You are still arguing against mathematical facts. That's
a bad idea.

BTW, that's yet another point which has been explained
to you at least 10 times now.


Again, for the 10th time: it is an inevitable
mathematical fact that this result will come out. It
can't be any other result - due to the math of chi
squared fitting.


Thats 10 times you are wrong then.

I beg to differ.

Hint: I have already done chi squared fits in my career.
Even already in my lab work. I *know* how they work.
Don't you think it's more likely that it is *you* who
is wrong here? May I remind you that just a few weeks ago,
you did not even know what "chi squared fit" actually means?


As I have shown
above it is an inevitable fact that you dont
understand the maths behind a chi squared fit of an
undilated template.

You have shown above only that you don't understand
chi squared fitting.


If you did you would not have made the inevitable
mathematical mistakes in your calculations above.

There were no mistakes. Your math has nothing to do
with chi squared fitting.



[snip]

Bye,
Bjoern