Expansion-what formula for redshift?

On Thu, 05 Apr 2007 16:16:49 GMT, "Androcles"
wrote:


"John C. Polasek" wrote in message ...
On Thu, 05 Apr 2007 08:35:59 GMT, "Androcles"
wrote:


"John C. Polasek" wrote in message ...
On 4 Apr 2007 14:33:04 -0700, "Steve Willner"
wrote:


John C. Polasek wrote:
To simplify this discussion, see http://en.wikipedia.org Relativistic
Doppler effect. I believe their equation wrong.

http://en.wikipedia.org/wiki/Relativistic_Doppler looks OK to me. You
have to be very careful about what reference frame you measure things
in, but that shouldn't be a surprise.

The cosmological formulas have nothing to do with relativistic Doppler
shift. (At very small redshifts, everything is linear, and it makes
no difference what formula you use, but as soon as you get into the
non-linear range, you have to use the correct formula for whatever you
are trying to calculate.)

Things are a little tricky in Wiki which has several layers, one for
wavelength and one for frequency, the second being hard to find.
If you click Rel. Doppler effect you find the heading Rel. Dop. etc.
which has the relation for wavelength:
for WL 1+z = Lo/Le = (1+b)*gamma
OK. Next to the heading is a hyperlink Main Article Rel. Dop. etc.
which when you click it, goes to a 2d layer that is headed up as "The
Mechanism". Here their formula for Frequency redshift reduces to
for FRS fo/fe = (1-b)*gamma = 1/1+z
a new breed of z.
My intuition sensed an algebraic blunder if gamma were to shore up
both wavelength and frequency versions of z. But in fact the product
of the two expressions do equal unity.
Lofo/Lefe = (1-b^2)/(1-b^2) = (1+z)*(1/1+z)
So we have algebraic integrity, but it's a sticking point, hard to
assimilate, that gamma can increase the frequency as it does the
wavelength. The fact is that in both cases gamma is shoring up not z
but 1+z or for frequency, shoring up 1/1+z.
That clears it up for me, and I hope, for you. Intuition capitulates
to mathematics.


There is no gamma, ignorant lazy incompetent ****head.

It's their gamma, not mine.

I *proved* gamma doesn't exist.

Don't blame me for gamma, as I have told you that I myself don't use
gamma. My theory completely replaces relativity and has an equivalent
that makes sense.

I was just checking Wiki's math, which proved self-consistent. Their
redshift/luminosity formula could still be wrong, so the current
search for dark energy might be misdirected.
For your information, gamma is the Lorentz transform upside down, but
you probably don't believe in it either, although you appended quite a
bit of Einstein, whether bragging or complaining I couldn't tell.

Your shaky grasp of the inverse square law, as well as your
predilection for analyzing in terms of train-lengths reveals much
about your level of mathematical sophistication, so you might think
about couching your objections in a less bombastic fashion.
John Polasek

"John C. Polasek" wrote in message ...
On Thu, 05 Apr 2007 16:16:49 GMT, "Androcles"
wrote:


"John C. Polasek" wrote in message ...
On Thu, 05 Apr 2007 08:35:59 GMT, "Androcles"
wrote:


"John C. Polasek" wrote in message ...
On 4 Apr 2007 14:33:04 -0700, "Steve Willner"
wrote:


John C. Polasek wrote:
To simplify this discussion, see http://en.wikipedia.org Relativistic
Doppler effect. I believe their equation wrong.

http://en.wikipedia.org/wiki/Relativistic_Doppler looks OK to me. You
have to be very careful about what reference frame you measure things
in, but that shouldn't be a surprise.

The cosmological formulas have nothing to do with relativistic Doppler
shift. (At very small redshifts, everything is linear, and it makes
no difference what formula you use, but as soon as you get into the
non-linear range, you have to use the correct formula for whatever you
are trying to calculate.)

Things are a little tricky in Wiki which has several layers, one for
wavelength and one for frequency, the second being hard to find.
If you click Rel. Doppler effect you find the heading Rel. Dop. etc.
which has the relation for wavelength:
for WL 1+z = Lo/Le = (1+b)*gamma
OK. Next to the heading is a hyperlink Main Article Rel. Dop. etc.
which when you click it, goes to a 2d layer that is headed up as "The
Mechanism". Here their formula for Frequency redshift reduces to
for FRS fo/fe = (1-b)*gamma = 1/1+z
a new breed of z.
My intuition sensed an algebraic blunder if gamma were to shore up
both wavelength and frequency versions of z. But in fact the product
of the two expressions do equal unity.
Lofo/Lefe = (1-b^2)/(1-b^2) = (1+z)*(1/1+z)
So we have algebraic integrity, but it's a sticking point, hard to
assimilate, that gamma can increase the frequency as it does the
wavelength. The fact is that in both cases gamma is shoring up not z
but 1+z or for frequency, shoring up 1/1+z.
That clears it up for me, and I hope, for you. Intuition capitulates
to mathematics.


There is no gamma, ignorant lazy incompetent ****head.

It's their gamma, not mine.

I *proved* gamma doesn't exist.

Don't blame me for gamma, as I have told you that I myself don't use
gamma. My theory completely replaces relativity and has an equivalent
that makes sense.

Oh, I see... You are a crackpot with his own theory.


I was just checking Wiki's math, which proved self-consistent.

How ridiculous. You have no idea what "self-consistent" means.

Which of these statements do you agree with and which are consistent
with each other?

1) Frustra fit per plura, quod fieri potest per pauciora.
It is vain to do with more what can be done with less.
-- William of Ockham circa 1288 - 1348

2) We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. -- Sir Isaac Newton, 1643 - 1727

3) Everything should be as psychotic as possible, but not simpler. --Albert Einstein 1879 - 1955

4) "But the ray moves relatively to the initial point of k, when measured in the stationary system, with the velocity c-v" --Albert Einstein 1879 - 1955

5) "It follows, further, that the velocity of light c cannot be altered by composition with a velocity less than that of light." --Albert Einstein 1879 - 1955


You cannot answer, of course, you'll just pour out more word salad.


Their
redshift/luminosity formula could still be wrong, so the current
search for dark energy might be misdirected.
For your information, gamma is the Lorentz transform upside down, but
you probably don't believe in it either, although you appended quite a
bit of Einstein, whether bragging or complaining I couldn't tell.

For your information, 1/gamma = 1/1 = gamma, whether you are
stalling, trolling or just plain stupid I can't tell.



Your shaky grasp of the inverse square law,

How ridiculous. You inability to comprehend a beam can converge as
well as diverge (or even exist as a beam) demonstrates there is more
than one inverse square law. Ever started a fire with a magnify glass,
****head?
http://www.campfiredude.com/i/magnifying-glass.jpg



as well as your
predilection for analyzing in terms of train-lengths reveals much
about your level of mathematical sophistication,

ALL units of distance are ARBITRARY, ****head. That's
why we have miles and kilometres, metres and yards, inches
and centimetres.
What's so wrong about a train length as a unit of distance?
Horses win races by a length or even by a nose after they've run
a furlong, which is 10 chains, and a chain is 22 yards, the length
between wickets on a cricket pitch. 8 furlongs to the mile, ****head.

Your predilection for ignoring a proof and calling it "sophistry"
without bothering to study or attempt to fault it (as if you could)
betrays your utmost incompetence.


so you might think
about couching your objections in a less bombastic fashion.

Look in the mirror for an arrogant bombastic crackpot with his own theory.
The level of your mathematical sophistication has never gone beyond
7th grade.
"My intuition sensed an algebraic blunder" -- Polasek.
My PROOF of an algebraic blunder you call "sophistry".
Your "intuition" is ****ed, along with your "opinions".

"JCP" == John C Polasek writes:

JCP There is a big effort to determine dark energy's effects, based
JCP only on the fact that Super Novae at high z appear to be fainter
JCP than the redshift calculations show, i.e. if the redshift shows z
JCP = 3, the luminosities appear fainter than expected for z =3.

The luminosities of supernovae was the first clue to dark energy. It
is no longer the "only" datum we have. Observations of the cosmic
microwave background, surveys of galaxies, clusters of galaxies, and a
couple of other data sets now all point to the need for some kind of
dark energy, which would drive an expansion.

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.

JCP I could not find any reference that cited their formulation. Wiki
JCP shows L = L0(1+z)*gamma. Also sqrt(1+z)/sqrt(1-z). What is the
JCP formula used by the dark energy investigators?

Check Ned Wright's calculator, URL:
http://www.astro.ucla.edu/~wright/CosmoCalc.html , and associated
documentation.

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On Apr 27, 7:20 am, Joseph Lazio wrote:
"JCP" == John C Polasek writes:

JCP There is a big effort to determine dark energy's effects, based
JCP only on the fact that Super Novae at high z appear to be fainter
JCP than the redshift calculations show, i.e. if the redshift shows z
JCP = 3, the luminosities appear fainter than expected for z =3.

The luminosities of supernovae was the first clue to dark energy. It
is no longer the "only" datum we have. Observations of the cosmic
microwave background, surveys of galaxies, clusters of galaxies, and a
couple of other data sets now all point to the need for some kind of
dark energy, which would drive an expansion.

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.

JCP I could not find any reference that cited their formulation. Wiki
JCP shows L = L0(1+z)*gamma. Also sqrt(1+z)/sqrt(1-z). What is the
JCP formula used by the dark energy investigators?

Check Ned Wright's calculator, URL:http://www.astro.ucla.edu/~wright/CosmoCalc.html, and associated
documentation.

--
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No means no, stop rape. |http://patriot.net/%7Ejlazio/
sci.astro FAQ athttp://sciastro.astronomy.net/sci.astro.html

JP:
Thank you Joseph (Lt., sir). It appears from Ned Wright's article Part
2, that the redshift formula I asked about is 1+z = exp(v/c), which I
had not seen before, and not the relativistic Doppler formulation. I
raise the point that this exp(v/c) might not be correct since it must
depend on the (still-not-defined) model of the universe, so that at
the higher z's, the luminosity discrepancy could show up. An algebraic
solution is a more attractive solution than to postulate a sudden
expansion due to "dark energy".
At v/c of 0.8, Ned has z = 1.226, the relativistic Doppler is 2.0 and
I have an expression z = 1.584, 29% greater than Ned's. Is this 29% at
beta of 0.8 in the direction of explaining the discrepancy?
What is there about the CMB that says sudden expansion, or dark
energy?

"JCP" == John C Polasek writes:

JCP On Apr 27, 7:20 am, Joseph Lazio
JCP wrote:

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.

JCP I could not find any reference that cited their formulation. Wiki
JCP shows L = L0(1+z)*gamma. Also sqrt(1+z)/sqrt(1-z). What is the
JCP formula used by the dark energy investigators?

Check Ned Wright's calculator,
URL:http://www.astro.ucla.edu/~wright/CosmoCalc.html, and
associated documentation.

JCP It appears from Ned Wright's article Part 2, that the redshift
JCP formula I asked about is 1+z = exp(v/c), which I had not seen
JCP before, and not the relativistic Doppler formulation.

Upon a bit further reflection, perhaps the best answer I could have
given is to consult with the people who did the work. Adam Riess
(2000, http://adsabs.harvard.edu/abs/2000PASP..112.1284R ) summarizes
how the results are obtained. Briefly, one determines the magnitude
of the SN Ia. After appropriate correction, the distance modulus of a
SN Ia is m - M = 25 + 5 log D_L, where D_L is the luminosity
distance. In equation (3) of this paper, he then gives the expression
for the luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for more
details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] *
sinn{ sqrt(|\Omega_k|) * integral_0^z dz
sqrt[(1+z)^2(1+z\Omega_m) - z(2+z)\Omega_\Lambda]}

Here
H_0 = Hubble constant
\Omega_m = matter density in terms of the critical density
\Omega_\Lambda = dark energy density in terms of the critical density
\Omega_k = 1 - \Omega_m - \Omega_\Lambda
sinn = sinh for \Omega_k = 0
sin for \Omega_k = 0


JCP What is there about the CMB that says sudden expansion, or dark
JCP energy?

Consider the Universe just before the CMB is created. It is a
plasma, so it can support waves. Waves have the property that they
can create regions of higher and lower density. When the CMB is
created, i.e., when the plasma becomes neutral, those high and low
density regions persist, and we see them today as regions of slightly
hotter or colder temperature in the CMB. Based on the properties of
the Universe (such as the density of the plasma at the time of
recombination), we can predict how large those hot/cold regions should
appear on the sky and how hot and cold they should be. These
predictions depend upon quantities like the density of the plasma, the
distance to where the CMB is being created, and the like.

By comparing measurements of the CMB, like those from the WMAP
satellite, with the models, one can then determine how much matter and
dark energy is required to reproduce the observations.

--
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No means no, stop rape. | http://patriot.net/%7Ejlazio/
sci.astro FAQ at http://sciastro.astronomy.net/sci.astro.html

On 09 May 2007 06:29:44 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On Apr 27, 7:20 am, Joseph Lazio
JCP wrote:

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.

JCP I could not find any reference that cited their formulation. Wiki
JCP shows L = L0(1+z)*gamma. Also sqrt(1+z)/sqrt(1-z). What is the
JCP formula used by the dark energy investigators?

Check Ned Wright's calculator,
URL:http://www.astro.ucla.edu/~wright/CosmoCalc.html, and
associated documentation.

JCP It appears from Ned Wright's article Part 2, that the redshift
JCP formula I asked about is 1+z = exp(v/c), which I had not seen
JCP before, and not the relativistic Doppler formulation.

Upon a bit further reflection, perhaps the best answer I could have
given is to consult with the people who did the work. Adam Riess
(2000, http://adsabs.harvard.edu/abs/2000PASP..112.1284R ) summarizes
how the results are obtained.
I found the abstract but am not entitled to see the article. It looks
all quite abstruse but I found some material of interest.
Below, 5 log D_L implies 5th power of range which seems curious
especially since D_L should be unitless in order to take the log.

Briefly, one determines the magnitude
of the SN Ia. After appropriate correction, the distance modulus of a
SN Ia is m - M = 25 + 5 log D_L, where D_L is the luminosity
distance. In equation (3) of this paper, he then gives the expression
for the luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for more
details:
In this definition of D_L it looks like D_L = R_0 = c/H0 = cT
stretched by 1+z in real meters x sine (fn(z, Wk, Wm, WL)). It never
becomes unitless. It must be that luminosity distance is normalized to
the cT radius.
D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] *
sinn{ sqrt(|\Omega_k|) * integral_0^z dz
sqrt[(1+z)^2(1+z\Omega_m) - z(2+z)\Omega_\Lambda]}
Since H0, Wm and WL are undetermined, the problem seems
underspecified, together with the manifold appearances of 1+z, 2+z,
z(2+z), it looks more like my original question was underspecified.
Here
H_0 = Hubble constant
\Omega_m = matter density in terms of the critical density
\Omega_\Lambda = dark energy density in terms of the critical density
\Omega_k = 1 - \Omega_m - \Omega_\Lambda
sinn = sinh for \Omega_k = 0
sin for \Omega_k = 0


JCP What is there about the CMB that says sudden expansion, or dark
JCP energy?

Consider the Universe just before the CMB is created. It is a
plasma, so it can support waves. Waves have the property that they
can create regions of higher and lower density. When the CMB is
created, i.e., when the plasma becomes neutral, those high and low
density regions persist, and we see them today as regions of slightly
hotter or colder temperature in the CMB. Based on the properties of
the Universe (such as the density of the plasma at the time of
recombination), we can predict how large those hot/cold regions should
appear on the sky and how hot and cold they should be. These
predictions depend upon quantities like the density of the plasma, the
distance to where the CMB is being created, and the like.

By comparing measurements of the CMB, like those from the WMAP
satellite, with the models, one can then determine how much matter and
dark energy is required to reproduce the observations.
I have a replacement for the CMB and the Big Bang. Objectively, it is
hard to see how you can make strong arguments about anything from
examination of the "tie-dyed sky" (just a little levity).
Thank you again for your kind attention.
John Polasek

"JCP" == John C Polasek writes:

JCP On 09 May 2007 06:29:44 -0400, Joseph Lazio
JCP wrote:

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.
[...]
Upon a bit further reflection, perhaps the best answer I could
have given is to consult with the people who did the work. Adam
Riess (2000, http://adsabs.harvard.edu/abs/2000PASP..112.1284R )
summarizes how the results are obtained.

JCP I found the abstract but am not entitled to see the article.

Note that the arXiv version should be freely accessible.

JCP It looks all quite abstruse but I found some material of
JCP interest. Below, 5 log D_L implies 5th power of range which
JCP seems curious especially since D_L should be unitless in order to
JCP take the log.

This is the standard definition of the distance modulus, which follows
from the definition of magnitude. The apparent magnitude is the
brightness of the object at its distance D_L. The absolute magnitude
is its brightness if it were at a distance of 10 pc. With the inverse
square law, we have

m - M = 2.5 log[(D_L/10 pc)^2]
= 5 log(D_L/10 pc)
= 5 log D_L - 5

One additional step is required to get it to the form I quote below.
Riess was quoting distances in Mpc, not pc. Thus,

m - M = 2.5 log[({D_L*10^6 pc}/10 pc)^2]
= 5 log([D_L*10^6 pc]/10 pc)
= 5 log D_L + 30 - 5
= 5 log D_L + 25

for D_L expressed in Mpc.


Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M =
25 + 5 log D_L, where D_L is the luminosity distance. In equation
(3) of this paper, he then gives the expression for the luminosity
distance in terms of cosmological parameters. I'll reproduce it
the best that I can here, but consult the paper for more
details:

JCP In this definition of D_L it looks like D_L = R_0 = c/H0 = cT
JCP stretched by 1+z in real meters x sine (fn(z, Wk, Wm, WL)). It
JCP never becomes unitless. It must be that luminosity distance is
JCP normalized to the cT radius.

I think this is addressed by my comments above.

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) - z(2+z)\Omega_\Lambda]}

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each SN
Ia, I have two observables: its redshift z and its apparent magnitude
m. It appears that the absolute magnitude M of SN Ia is essentially
constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts, then
we can try to solve for the unknown quantities \Omega_m, H_0, and
\Omega_\Lambda.


--
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On 10 May 2007 06:57:17 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On 09 May 2007 06:29:44 -0400, Joseph Lazio
JCP wrote:

JCP This has been attributed to early sudden expansion of the
JCP universe, an unlikely circumstance but it could be they are
JCP simply using the wrong formula for redshift.
[...]
Upon a bit further reflection, perhaps the best answer I could
have given is to consult with the people who did the work. Adam
Riess (2000, http://adsabs.harvard.edu/abs/2000PASP..112.1284R )
summarizes how the results are obtained.

JCP I found the abstract but am not entitled to see the article.

Note that the arXiv version should be freely accessible.

JCP It looks all quite abstruse but I found some material of
JCP interest. Below, 5 log D_L implies 5th power of range which
JCP seems curious especially since D_L should be unitless in order to
JCP take the log.

This is the standard definition of the distance modulus, which follows
from the definition of magnitude. The apparent magnitude is the
brightness of the object at its distance D_L. The absolute magnitude
is its brightness if it were at a distance of 10 pc. With the inverse
square law, we have

m - M = 2.5 log[(D_L/10 pc)^2]
= 5 log(D_L/10 pc)
= 5 log D_L - 5

One additional step is required to get it to the form I quote below.
Riess was quoting distances in Mpc, not pc. Thus,

m - M = 2.5 log[({D_L*10^6 pc}/10 pc)^2]
= 5 log([D_L*10^6 pc]/10 pc)
= 5 log D_L + 30 - 5
= 5 log D_L + 25

for D_L expressed in Mpc.


Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M =
25 + 5 log D_L, where D_L is the luminosity distance. In equation
(3) of this paper, he then gives the expression for the luminosity
distance in terms of cosmological parameters. I'll reproduce it
the best that I can here, but consult the paper for more
details:

JCP In this definition of D_L it looks like D_L = R_0 = c/H0 = cT
JCP stretched by 1+z in real meters x sine (fn(z, Wk, Wm, WL)). It
JCP never becomes unitless. It must be that luminosity distance is
JCP normalized to the cT radius.

I think this is addressed by my comments above.

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) - z(2+z)\Omega_\Lambda]}

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each SN
Ia, I have two observables: its redshift z and its apparent magnitude
m. It appears that the absolute magnitude M of SN Ia is essentially
constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts, then
we can try to solve for the unknown quantities \Omega_m, H_0, and
\Omega_\Lambda.
Joseph:
An interim note:
The magnitude algebra (2.512*log) must be OK, but the redshift usage
is new to me. With 2-plus omegas, I'd say there's quite a bit of room
for algebraic error (my original balk) in finding that the SN's are
dimmer than their z. I'll work on it later. I have equipment trouble.
I have my own theory about some of this. For example if you take
deSitter's critical density 3H2/8piG = Muni/Voluni and let R = cT and
T = 1/H you'll find equality is nicely satisfied if there is constant
creation at c^3/G. It's in Ch. 13 of my book Dual Space theory. It
doesn't end there. It seems legitimate.
John Polasek

"JCP" == John C Polasek writes:

JCP On 10 May 2007 06:57:17 -0400, Joseph Lazio
JCP wrote:

Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M
= 25 + 5 log D_L, where D_L is the luminosity distance. In
equation (3) of this paper, he then gives the expression for the
luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for
more details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
z(2+z)\Omega_\Lambda]}

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each
SN Ia, I have two observables: its redshift z and its apparent
magnitude m. It appears that the absolute magnitude M of SN Ia is
essentially constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts,
then we can try to solve for the unknown quantities \Omega_m, H_0,
and \Omega_\Lambda.

JCP An interim note: The magnitude algebra (2.512*log) must be OK,
JCP but the redshift usage is new to me. With 2-plus omegas, I'd say
JCP there's quite a bit of room for algebraic error (my original
JCP balk) in finding that the SN's are dimmer than their z.

Not sure what you mean by "2-plus omegas." The fitting assumes that
there is one value for \Omega_m, one value for \Omega_\Lambda, and one
value for H_0. That's the point of doing the fitting: To take the
measured values of m and z for the SN Ia and find the appropriate
values for the two different \Omega.

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups have
performed these kinds of measurements and conducted the fits. They
reach similar conclusions, giving confidence that there has not been
an error in the computer programs used to do the fitting.

--
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On 14 May 2007 06:45:50 -0400, Joseph Lazio
wrote:

"JCP" == John C Polasek writes:

JCP On 10 May 2007 06:57:17 -0400, Joseph Lazio
JCP wrote:

Briefly, one determines the magnitude of the SN Ia. After
appropriate correction, the distance modulus of a SN Ia is m - M
= 25 + 5 log D_L, where D_L is the luminosity distance. In
equation (3) of this paper, he then gives the expression for the
luminosity distance in terms of cosmological parameters. I'll
reproduce it the best that I can here, but consult the paper for
more details:

D_L = c(1 + z)/[H_0 sqrt{|\Omega_k|}] * sinn{ sqrt(|\Omega_k|) *
integral_0^z dz sqrt[(1+z)^2(1+z\Omega_m) -
z(2+z)\Omega_\Lambda]}

I had suspected a faulty calculation of redshift to account for
expansion, and my trepidations are not at all relieved by the above
expression. At the least I would question what model could produce
(1+z)^2*(1+z)Omega_k? Or even z(2+z)*Omega_lambda?
Just to evaluate the limit case of zero dark matter and no dark
energy, omega_k then would become unity and the expression seems to
reduce to
DL = c(1+z)/H_0*sin(integral (1+z)dz) =
c(1+z)/H_0*sin(z + z^2/2) =
cT(1+z)* sin(z + z^2/2)
But then it doesn't support the case for z = 0. Up to the sine term we
have cT stretched by 1+z, OK so far, but then the sine term imposes an
irreparable penalty it seems to me. I've probably made a simple
mistake. I am still of the opinion that redshift is being misapplied
somehow, leading to suspicion of sudden expansion.

JCP Since H0, Wm and WL are undetermined, the problem seems
JCP underspecified, together with the manifold appearances of 1+z,
JCP 2+z, z(2+z), it looks more like my original question was
JCP underspecified.

Well, that's the point of conducting the observations. For each
SN Ia, I have two observables: its redshift z and its apparent
magnitude m. It appears that the absolute magnitude M of SN Ia is
essentially constant.

For any given SN Ia, you're right, the problem is underspecified.
Once we have many observations of SN Ia, at different redshifts,
then we can try to solve for the unknown quantities \Omega_m, H_0,
and \Omega_\Lambda.

JCP An interim note: The magnitude algebra (2.512*log) must be OK,
JCP but the redshift usage is new to me. With 2-plus omegas, I'd say
JCP there's quite a bit of room for algebraic error (my original
JCP balk) in finding that the SN's are dimmer than their z.

Not sure what you mean by "2-plus omegas."
I meant that you have 3 omegas, with the omeag_k being the one's-
complement of the sum of the other two.
The fitting assumes that
there is one value for \Omega_m, one value for \Omega_\Lambda, and one
value for H_0. That's the point of doing the fitting: To take the
measured values of m and z for the SN Ia and find the appropriate
values for the two different \Omega.

The "algebraic error" statement simply doesn't make sense. All of
these calculations are done on computers. Two different groups have
performed these kinds of measurements and conducted the fits. They
reach similar conclusions, giving confidence that there has not been
an error in the computer programs used to do the fitting.