Cosmic acceleration rediscovered

The following post was banned from sci.astro.research, sans notice (as
usual).
==========================

"Phillip Helbig---remove CLOTHES to reply"

wrote in message ...
In article , "Lars Wahlin"
writes:

A few years ago data from the Ia Supernova Cosmology Project found that
Hubble's law is not linear but changes in a nonlinear fashion at large
distances, i.e. The universe is accelerating.

This is just plain wrong. Hubble's Law says that recession velocity is
proportional to distance.

The "Hubble's law" to which you are referring is a theoretical construct.
Hubble's data connects distance with redshift -- not with recession
velocity.

This is actually quite trivial, since this is
the only relation which allows a homogeneous and isotropic universe to
remain so.

Your assumption has nothing to do with the discussion of the Hubble
relation. And it may have nothing to do with the real universe.

However, both the distance and velocity are not observable.

The distance is observable. The redshift is observable. The assumption
that velocity is the only contribution to redshift is pure theory (not
observable). Just like the last time this was discussed on this N.G.

http://www.google.com/groups?selm=10....supernews.com

Hubble's actual discovery was the linear apparent-magnitude--redshift
relation.

Carl Wirtz' discovery was the empirical redshift-distance relation in 1924
(pre Cepheid variable identification).

Hubble gave us the distance - redshift relation. He used Cepheid variable
stars to set the distance. And it is apparently linear for galaxies with
resolveable Cepheids. Again, just like it was discussed before in this N.G.
http://www.google.com/groups?selm=mt...tar.bris.ac.uk

FOR LOW REDSHIFT, one can use the former as a measure of
distance and the latter as a measure of velocity. However, this
relation is almost always observed whatever the cosmological parameters,
and is just a consequence of the fact that "things are linear to first
order".

In other words, "Hubble's Law" is by definition linear.

Argument-by-definition is not valid in the scientific method.

That you, and other theorists, like to assume that the distance-redshift
relationship is purely linear does not constrain the real universe. The
effect you are looking at may not be linear ... it may simply be the first
part of an exponential function.

What you mean is that a departure from this linearity is observed at
higher redshift, which indicates an expanding universe.

It only indicates an expanding universe if your assumption is true. Which
is not a given.

Well, this was actually
suggested long ago by Karachentsev .Commun. Buyrakan Obs. 39 96. (1967),
Ozernoy,Zh. Eksper. Teor. Fiz (Letters) 10, 394 (=JETP Letters 10 251),
(1969), de Vacouleurs, Publ. Astron. Pacific 83, 113 (1971) and
verified theoretically by myself (Wahlin, Astrophysics and space Science
74, 157 (1981)).

As Bill Press said in 1995, someone knows the value of the Hubble
constant to 1%---we just don't know who that person is.

Totally irrelevant.

I am not aware
of ANY observation-based arguments for an accelerating universe before
the 1990s which still stand up today. Sure, some people made some
observations and drew some conclusions. Maybe by chance the conclusions
were even correct. But it was just luck. Make a thousand predictions,
and one might be right.

Like your conclusion that the distance - redshift relation might be linear?
Unfortunately, this assumption will no longer 'stand up today.' The
supernovae data blew it away.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

"greywolf42" wrote in message
...
"George Dishman" wrote in message
...

....
Linearity is not assumed,

A false statement. It *IS* explicitly assumed. As demonstrated above and
in the references provided (which you snipped).

it is related to anisotropy
and homogeneity which again can be measured (though
not easily).

Meaning such have never been measured, merely assumed.

How much data do you need before an assumption becomes
a measured result? Peebles lists some of the evidence
in "Principals of Physical Cosmology". Take a look at
Figure 3.10, Condon's 1991 map of bright radio sources,
for example.

What you mean is that a departure from this linearity is observed at
higher redshift, which indicates an expanding universe.

It only indicates an expanding universe if your assumption is true.
Which is not a given.

It indicates a time variation of the coefficient in
the law.

But only if your assumption is true. Which is the question.

You mean only if the evidence isn't misleading us ;-)

Perhaps "Hubble 'constant'" was a poor choice
of name (with hindsight).

The term itself is not the issue under discussion.

Like your conclusion that the distance - redshift relation might be
linear? Unfortunately, this assumption will no longer
'stand up today.' The supernovae data blew it away.

Methinks thou trollst! You know better than that.

Not in the least. The nonlinear effect was predicted years ago.

Hubble Distance was defined years ago too, yet
you talk as if you had never heard of it. (The
link is my other reply if you really haven't.)

George

"George Dishman" wrote in message
...

"greywolf42" wrote in message
...
"George Dishman" wrote in message
...

...
Linearity is not assumed,

A false statement. It *IS* explicitly assumed. As demonstrated above
and in the references provided (which you snipped).

it is related to anisotropy
and homogeneity which again can be measured (though
not easily).

Meaning such have never been measured, merely assumed.

How much data do you need before an assumption becomes
a measured result?

At least one *direct* measurement in support, and *no* results contrary. The
supernova data are contrary to the linear assumption, however. They fit on
an exponential curve.

Peebles lists some of the evidence in "Principals of Physical Cosmology".

But none of those address the specific issue under discussion. (If you
disagree, please provide the specifics. Not simply a vague allusion.)

Take a look at
Figure 3.10, Condon's 1991 map of bright radio sources,
for example.

This does not address the issue of linearity of the Hubble graph.

What you mean is that a departure from this linearity is observed
at
higher redshift, which indicates an expanding universe.

It only indicates an expanding universe if your assumption is true.
Which is not a given.

It indicates a time variation of the coefficient in
the law.

But only if your assumption is true. Which is the question.

You mean only if the evidence isn't misleading us ;-)

No, I mean if you can only think along the lines of one theory. The
evidence is the variation from linearity on the Hubble curve, shown by the
supernovae. *You* are ignoring the evidence.

Perhaps "Hubble 'constant'" was a poor choice
of name (with hindsight).

The term itself is not the issue under discussion.

Like your conclusion that the distance - redshift relation might be
linear? Unfortunately, this assumption will no longer
'stand up today.' The supernovae data blew it away.

Methinks thou trollst! You know better than that.

Not in the least. The nonlinear effect was predicted years ago.

Hubble Distance was defined years ago too, yet
you talk as if you had never heard of it. (The
link is my other reply if you really haven't.)

??? The "Hubble Distance" is not germaine to the assumption of linearity of
the Hubble curve.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

"greywolf42" wrote in message
...
"George Dishman" wrote in message
...

...
Linearity is not assumed,

A false statement. It *IS* explicitly assumed. As demonstrated above
and in the references provided (which you snipped).

it is related to anisotropy
and homogeneity which again can be measured (though
not easily).

Meaning such have never been measured, merely assumed.

How much data do you need before an assumption becomes
a measured result?

At least one *direct* measurement in support,

By definition that is impossible since distant observations
are of the past. An indirect measurement is given below.

and *no* results contrary. The
supernova data are contrary to the linear assumption, however.

Sorry, that's simply not true. Learn the definition
of the Hubble Distance and you will see why.

They fit on
an exponential curve.

Perhaps, but it would be an exponential function of
time while the Hubble Law is linear with distance
at a given time. The two are not incompatible.

Peebles lists some of the evidence in "Principals of Physical
Cosmology".

But none of those address the specific issue under discussion. (If you
disagree, please provide the specifics. Not simply a vague allusion.)

They specifically address whether the universe is
homogenous and isotropic which leads to linearity
as a function of distance at a common time.

Take a look at
Figure 3.10, Condon's 1991 map of bright radio sources,
for example.

This does not address the issue of linearity of the Hubble graph.

It addresses the linearity of the Hubble Law, not
a plot of redshift versus _observable_ distance.

What you mean is that a departure from this linearity is
observed
at
higher redshift, which indicates an expanding universe.

It only indicates an expanding universe if your assumption is
true.
Which is not a given.

It indicates a time variation of the coefficient in
the law.

But only if your assumption is true. Which is the question.

You mean only if the evidence isn't misleading us ;-)

No, I mean if you can only think along the lines of one theory. The
evidence is the variation from linearity on the Hubble curve, shown by the
supernovae. *You* are ignoring the evidence.

No, I understand that there are two separate
dependencies which you are conflating. The
supernova data provides information about
the time dependency while evidence relating
to homogeneity relates to the spatial
dependence.

Perhaps "Hubble 'constant'" was a poor choice
of name (with hindsight).

The term itself is not the issue under discussion.

Like your conclusion that the distance - redshift relation might
be
linear? Unfortunately, this assumption will no longer
'stand up today.' The supernovae data blew it away.

Methinks thou trollst! You know better than that.

Not in the least. The nonlinear effect was predicted years ago.

Hubble Distance was defined years ago too, yet
you talk as if you had never heard of it. (The
link is my other reply if you really haven't.)

??? The "Hubble Distance" is not germaine to the assumption of linearity
of
the Hubble curve.

The Hubble Law, which is believed to be linear, is a
corelation with the Hubble Distance. How can you discuss
whether it is linear or not without first knowing how
that distance is defined?

George

"g" == greywolf42 writes:

g Then why do you constantly ignore the possibility that the
g redshift-distance relation is an exponential curve?

Do the data support such a notion?

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

"Joseph Lazio" wrote in message
...
"g" == greywolf42 writes:

g Then why do you constantly ignore the possibility that the
g redshift-distance relation is an exponential curve?

Do the data support such a notion?

Yes.

For a quick reference, see Perlmutter, Figure 3, Physics Today, April 2003,
"Supernovae, Dark Energy, and the Accelerating Universe".
http://www.slac.stanford.edu/econf/C...perlmutter.pdf

Just notice that instead of "accelerating universe" and "decelerating
universe" (which require a linear assumption), one should read: "exponential
redshift-distance relation" and "inverse exponential redshift-distance
relation," respectively. Pure Hubble constant (linear assumption) lies on
the straight line.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

"George Dishman" wrote in message
...

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

{snip higher levels}

There are two
unknowns at work, how redshift varies with location and
how it varies with time.

You manifest the fallacy of the excluded middle. There are more than
two options.

There are an infinite number of options, I said
"two unknowns".

What you provided are two theories, not unknowns. The latter term denotes a
constant to be solved for.

And once again, you are assuming that the redshift-distance
relation is a constant (at a given time and place). The other option is
that the redshift-distance relation does not vary with location or time.
But simply is not a straight line.

We can only directly observe a
sample through that, a diagonal so to speak.

Again, it is only a 'diagonal' if you first assume a line.

That line is simply the relation between distance and
the age of the galaxies we observe, not an assumption
of linearity.

The "age of the galaxies" that you claim is determined based upon a distance
that is calculated using the Hubble Law ... which is a linear assumption.

You are
giving the impression that you think one-dimensionally
and cannot see the bigger picture, which I doubt.

The classic ad hominem fallacy.

"which I doubt"

????

If you are serious, I suggest you start by understanding
the definition of distance used in the Hubble Law:

Followed by the classic special plead fallacy.

http://www.astro.ucla.edu/~wright/cosmo_02.htm#md

It explains the Hubble Distance.

No, it doesn't even mention the Hubble distance. Did you mean the "Hubble
law distance" term that Ned uses? That's not the same as the Hubble
distance. At least according to
http://www.astro.ufl.edu/~guzman/ast...project01.html
(See parallel post for references and details.)

How can you discuss
the law if you don't know the definition of the
quantities it relates?

"Hubble's Law" is not defined using Hubble distance. Misner, Thorne and
Wheeler do just fine discussing the Hubble Law and cosmology. And they
don't use the term "Hubble Distance." The Hubble distance is a theoretical
distance number that is calculated *from* the Hubble Law. (See parallel
post for references and details.)

You might then understand Phillip's comments.

Repeat the classic special plead fallacy. I understand both Phillip and
you just fine, thanks. Note that it is Phillip who is cutting out
responses that he doesn't want to deal with.

Or perhaps he dropped aspects that you cannot
discuss because you don't understand the basic
definitions.

The classic special plead fallacy. But the use of terminology is an
irrelevant issue. Let's get back to physics.

Why are you so fixated

Fixated? I mentioned it once purely in the context of
the source of the term.

You've used it at least a dozen times in the thread. I'm not talking
about the word use. I'm talking about the assumption that you
keep making.

The evidence supports it so far.

Then let's discuss the evidence, shall we? Instead of going off on snide
tangents.

on a "constant of proportionality," to the exclusion of
the beginning of an exponential function?

Apparently it's my turn to expand your mind, they are not
exclusive.

Then why do you constantly ignore the possibility that the
redshift-distance relation is an exponential curve?

An exponential function of what?

Distance. As I have stated many times.

I have already
said that an exponential versus time is what I
expect as dark energy becomes dominant.

I know you keep repeating this irrelevancy. But that assumes a linear
distance relation.

The recession velocity at any given cosmic age
can be proportional to the Hubble distance while the
'constant of proportionality' in that relation could
vary exponentially with time.

(*^*^%^ I am not talking about variations with time.
Or with variations in space.

No, but everybody else is.

??? At the date and time of your post, no one other than you and me posted
in this sci.astro thread. Lt. Lazio added a one question post this morning
("Do the data support such a notion?").

You are talking about
the relation between observable distance and
observable red-shift which is a combination of
the two dependencies, the Hubble Law and a(t).

Only if you first assume the Hubble law is absolute *Truth*.

The relation between the observable redshift and the observable distance
simply *IS*. It is not dependent upon a popular theory (the Hubble Law).

In fact if you put the most likely measured values into
GR, current theory says that is exactly what will happen
as dark energy becomes dominant.

The measured values of what?

Of the constants in GR.

The constants in GR are the speed of gravity and the value 8 pi (conversion
to Newtonian gravitational constant). GR is not Relativistic Cosmology, but
Relativistic cosmology contains GR. The Big Bang theory is not Relativistic
Cosmology, but the current BB theory contains Relativistic Cosmology.

I presume you mean the "constants" in the Big Bang theory. Please specify
which ones you are talking about.

Better yet, please focus on the parallel post. Maybe I've found a way to
get the message across.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

"George Dishman" wrote in message
...

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

"greywolf42" wrote in message
...

{snip higher levels}

How much data do you need before an assumption becomes
a measured result?

At least one *direct* measurement in support,

By definition that is impossible since distant observations
are of the past. An indirect measurement is given below.

I suspect you are making things more difficult for yourself. Direct does
not mean that it must happen simultaneously with some other event. If this
were the case, there would never be a direct observation of anything,
anywhere.

and *no* results contrary. The
supernova data are contrary to the linear assumption, however.

Sorry, that's simply not true. Learn the definition
of the Hubble Distance and you will see why.

The classic special plead fallacy. I know the definition of the Hubble
distance, thanks. Even though MTW doesn't even bother with the term.

The Hubble distance is a theoretical derivative number. One starts with the
observed local value of the redshift-distance relation. Then one assumes
that the r-d relation is explicitly linear -- this is called the "Hubble
Law." One then derives a "Hubble time" (according to MTW, p. 709) by
"linearly extrapolating to zero separation on the basis of the expansion
rate observed today." One then determines the "Hubble distance" by
multiplying the speed of light by the Hubble time.
http://www.astro.ufl.edu/~guzman/ast...project01.html


They fit on an exponential curve.

Perhaps, but it would be an exponential function of
time

No. What makes you insist on assuming spatial linearity?

while the Hubble Law is linear with distance
at a given time. The two are not incompatible.

We aren't discussing the "Hubble Law". Of course the Hubble Law is
linear with distance at a given time! That's because it assumes
linearity!

We are discussing the *basis* for the theoretical Hubble Law. Specifically,
the redshift-distance relationship.

Peebles lists some of the evidence in "Principals of Physical
Cosmology".

But none of those address the specific issue under discussion. (If you
disagree, please provide the specifics. Not simply a vague allusion.)

They specifically address whether the universe is
homogenous and isotropic which leads to linearity
as a function of distance at a common time.

That is an incorrect conclusion. As noted before, a steady-state universe
could be both homegenous and isotropic, and STILL not have a linear function
of redshift versus distance (at common time). The linear assumption is a
completely separate assumption, limited to the Big Bang theory.

And you still haven't provided the specific reference (page) or excerpt.

Take a look at
Figure 3.10, Condon's 1991 map of bright radio sources,
for example.

This does not address the issue of linearity of the Hubble graph.

It addresses the linearity of the Hubble Law, not
a plot of redshift versus _observable_ distance.

On the contrary, a simple review of my prior posts in this thread shows that
the issue *IS* the evidence supporting this assumption: the observational
plot of redshift versus distance. The Hubble Law -- per se -- is a
theoretical construct, which is -- by definition -- linear. And no one has
ever denied or implied that the theory is not linear.

Here is the initial exchange, from
http://www.google.com/groups?selm=pD...ewsgroup s.co
m

Phillip Helbig:
"Hubble's Law says that recession velocity is proportional to distance."

greywolf42:
"The 'Hubble's law' to which you are referring is a theoretical
construct. Hubble's data connects distance with redshift -- not with
recession velocity."

{Of course, that's likely the reason that Phillip refused to let this reply
to his post get onto sci.astro.research.}

(aside)
===========================
Let's try this with math, instead of words. As we seem to be talking past
one another. For the moment, let us ignore possible changes with time.

The standard Hubble Law is of the form:
V = H D
Where D is the distance in Mpc, V is the recessional velocity in kps, and
the Hubble constant is given in units of kps/Mpc. This equation is
explicitly linear. "H" is assumed to be constant throughout the universe.

Now let us convert this back to approximate redshift units (approximations
are fine, because the value of H is not claimed to better precision than
about +- 20%) -- since the data is all in redshift ... not velocity:
delta lambda / lambda = H' D.

Since delta lambda over lambda is dimensionless, the units for H' would be
Mpc^-1. Where H' = H / c. [The conversion (at least at resolvable Cepheid
distance) is straightforward doppler effect: delta lambda / lamda = v / c.]

Both equations are the same observable effect. Both are explicitly linear,
as written. Now, let us examine a simple exponential version:

delta lambda / lambda = 1 - exp(-mu D)
delta lambda / lambda = mu D + (mu D)^2 / 2 - ......

At near distances (like those of resolvable Cepheid stars), there is no way
to distinguish the linear from the exponential change. At substantial
distances (like those of the newer supernovae data), however, the higher
order terms in the approximation are no longer negligible.

So, I could as easily use:
delta lambda / lambda = 1 - exp(-H' D)


In the case of the linear assumptions, the supernovae data must be addressed
through an additional, ad hoc, cosmological term. In the case of the
exponential fit, no additional cosmological term is needed.
===========================

{snip higher levels}

You mean only if the evidence isn't misleading us ;-)

No, I mean if you can only think along the lines of one theory. The
evidence is the variation from linearity on the Hubble curve, shown by
the supernovae. *You* are ignoring the evidence.

No, I understand that there are two separate
dependencies which you are conflating.

No. You are not addressing the point at issue. You are stuck in a linear
theory. I am addressing the observational data.

The
supernova data provides information about
the time dependency while evidence relating
to homogeneity relates to the spatial
dependence.

Only if you first assume linearity of the Hubble *DATA*.

{snip higher levels}

Hubble Distance was defined years ago too, yet
you talk as if you had never heard of it. (The
link is my other reply if you really haven't.)

??? The "Hubble Distance" is not germaine to the assumption of linearity
of the Hubble curve.

The Hubble Law, which is believed to be linear, is a
corelation with the Hubble Distance. How can you discuss
whether it is linear or not without first knowing how
that distance is defined?

Well, Misner, Thorne, and Wheeler do an admirable job of discussing
cosmology and Hubble's law (and the Hubble time) without ever mentioning the
"Hubble Distance."

Again, we aren't talking about the Hubble Distance at all. The "Hubble Law"
(both theory and term) was created long before there was a concept or term
"Hubble Distance."

But we are talking about the *data* in the redshift-distance relation.

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}

[Reposting as this seems to have got lost]

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

"greywolf42" wrote in message
...

{snip higher levels}

I'm going to do some major snipping and some rearranging
too, these posts are becoming entirely swamped by side
issues. I guess you may feel I have altered the context
but it's difficult to avoid if this is to be a readable
reply.

First let's get the topic clear. You said:

We aren't discussing the "Hubble Law". Of course the Hubble Law is
linear with distance at a given time! That's because it assumes
linearity!

and you give this reference:

Here is the initial exchange, from
http://www.google.com/groups?selm=pD...wsgroup s.com

Phillip Helbig:
"Hubble's Law says that recession velocity is proportional to distance."

greywolf42:
"The 'Hubble's law' to which you are referring is a theoretical
construct. Hubble's data connects distance with redshift -- not with
recession velocity."

However, that is only part of the exchange: Here is the whole
quote from Lars and Phillip:

"Phillip Helbig---remove CLOTHES to reply"

wrote in message ...
In article , "Lars Wahlin"
writes:

A few years ago data from the Ia Supernova Cosmology Project found
that
Hubble's law is not linear but changes in a nonlinear fashion at large
distances, i.e. The universe is accelerating.

This is just plain wrong. Hubble's Law says that recession velocity is
proportional to distance.

To me it is clear that Lars was referring to the
relationship between observed redshift and distance,
which is non-linear, while Phillip is clearly referring
to the relationship between recession speed and distance
at a particluar epoch which is linear as discussed below.

So when you say "We aren't discussing the 'Hubble Law'.",
I have to disagree, and when you say

But the use of terminology is an
irrelevant issue. Let's get back to physics.

I also think what started this is that Lars and Phillip
were talking about different relationships, though each
might consider it to be "The Hubble Law".

Now you also said above "Of course the Hubble Law is linear
with distance at a given time! That's because it assumes
linearity!" and you seem to confirm that opinion he

The Hubble distance is a theoretical derivative number. One starts with
the
observed local value of the redshift-distance relation. Then one assumes
that the r-d relation is explicitly linear -- this is called the "Hubble
Law." ...

Again you seem to be implying linearity is purely an
assumption.

They specifically address whether the universe is
homogenous and isotropic which leads to linearity
as a function of distance at a common time.

That is an incorrect conclusion. As noted before, a steady-state universe
could be both homegenous and isotropic, and STILL not have a linear
function
of redshift versus distance (at common time). The linear assumption is a
completely separate assumption, limited to the Big Bang theory.

You were correct when you said "One starts with the
observed local value of the redshift-distance relation."
but the assumption is that this is due to expansion over
local scales. If the universe is homogenous then you can
imagine a slice through the universe at a given epoch to
be tiled with regions all similar to the local area we
can observe and linearity of velocity with distance then
follows if the universe is homogeneous and isotropic but
ONLY at a given epoch, i.e. over a surface of uniform
cosmic age. I'm sure you follow, the logic is trivial.

Linearity itself is therefore not an assumption but a
consequence of the cosmological principle plus the
observed linearity at small scales.

Incidentally, in a homegenous and isotropic steady-state
universe, the relationship between speed and distance is
still linear but with a constant of proportionality with
the value zero.

Let's try this with math, instead of words. As we seem to be talking past
one another. For the moment, let us ignore possible changes with time.

I agree, that's a sensible approach.

The standard Hubble Law is of the form:
V = H D
Where D is the distance in Mpc, V is the recessional velocity in kps, and
the Hubble constant is given in units of kps/Mpc. This equation is
explicitly linear. "H" is assumed to be constant throughout the universe.

You cited this page

http://www.astro.ufl.edu/~guzman/ast...project01.html

but ignored this fundamental definition:

"The Hubble constant H_0 is the constant of proportionality
between recession speed v and distance d in the expanding
Universe;

v = H_0 d

The subscripted "0" refers to the present epoch because in
general H changes with time."

Since you obviously read the page and quoted parts, I again
get the impression you deliberately ignored this definition
since it clearly repeats what I have been pointing out to
you all along.

Now let us convert this back to approximate redshift units (approximations
are fine, because the value of H is not claimed to better precision than
about +- 20%) -- since the data is all in redshift ... not velocity:
delta lambda / lambda = H' D.

Since delta lambda over lambda is dimensionless, the units for H' would be
Mpc^-1. Where H' = H / c. [The conversion (at least at resolvable
Cepheid
distance) is straightforward doppler effect: delta lambda / lamda = v /
c.]

Both equations are the same observable effect. Both are explicitly
linear,
as written. Now, let us examine a simple exponential version:

delta lambda / lambda = 1 - exp(-mu D)
delta lambda / lambda = mu D + (mu D)^2 / 2 - ......

At near distances (like those of resolvable Cepheid stars), there is no
way
to distinguish the linear from the exponential change. At substantial
distances (like those of the newer supernovae data), however, the higher
order terms in the approximation are no longer negligible.

The variation of H(t) with t is also no longer negligible.

So, I could as easily use:
delta lambda / lambda = 1 - exp(-H' D)

No, instead of the constant value H', you need to use
H(t) and integrate the effect over the lookback time.

The converse (finding the time from z) is mentioned
in equation (29) of:
http://www.astro.ufl.edu/~guzman/ast...project01.html

In the case of the linear assumptions, the supernovae data must be
addressed
through an additional, ad hoc, cosmological term. In the case of the
exponential fit, no additional cosmological term is needed.

That is not true, you are oversimplifying by ignoring
the variation of H(t) at high redshift. This produces
non-linearity even when there is a linear relationship
with distance at any given epoch.

George

"George Dishman" wrote in message
...
[Reposting as this seems to have got lost]

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
...

"greywolf42" wrote in message
. ..
"George Dishman" wrote in message
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"greywolf42" wrote in message
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{snip higher levels}

I'm going to do some major snipping and some rearranging
too, these posts are becoming entirely swamped by side
issues. I guess you may feel I have altered the context
but it's difficult to avoid if this is to be a readable
reply.

Fair enough. I've had to do this from time to time with other posts, and
posters.

First let's get the topic clear. You said:

We aren't discussing the "Hubble Law". Of course the Hubble Law is
linear with distance at a given time! That's because it assumes
linearity!

and you give this reference:

Here is the initial exchange, from

http://www.google.com/groups?selm=pD...ewsgroup s.co
m

Phillip Helbig:
"Hubble's Law says that recession velocity is proportional to distance."

greywolf42:
"The 'Hubble's law' to which you are referring is a theoretical
construct. Hubble's data connects distance with redshift -- not with
recession velocity."

However, that is only part of the exchange: Here is the whole
quote from Lars and Phillip:

"Phillip Helbig---remove CLOTHES to reply"

wrote in message ...
In article , "Lars Wahlin"
writes:

A few years ago data from the Ia Supernova Cosmology Project found
that Hubble's law is not linear but changes in a nonlinear fashion
at
large distances, i.e. The universe is accelerating.

This is just plain wrong. Hubble's Law says that recession velocity
is proportional to distance.

To me it is clear that Lars was referring to the
relationship between observed redshift and distance,
which is non-linear, while Phillip is clearly referring
to the relationship between recession speed and distance
at a particluar epoch which is linear as discussed below.

So when you say "We aren't discussing the 'Hubble Law'.",
I have to disagree,

That's one heck of a roundabout and turbid way of "clarifying" the topic!

What exactly are you disagreeing with? Do you understand the difference
between Hubble's data and the "Hubble law?"

and when you say

But the use of terminology is an
irrelevant issue. Let's get back to physics.

I also think what started this is that Lars and Phillip
were talking about different relationships, though each
might consider it to be "The Hubble Law".

That was part of my point, thanks.

The Hubble Law is explicitly theoretical, not observational. I was
attempting to clarify.

Now you also said above "Of course the Hubble Law is linear
with distance at a given time! That's because it assumes
linearity!" and you seem to confirm that opinion he

The Hubble distance is a theoretical derivative number. One starts with
the
observed local value of the redshift-distance relation. Then one assumes
that the r-d relation is explicitly linear -- this is called the "Hubble
Law." ...

Again you seem to be implying linearity is purely an
assumption.

Actually, I've stated so explicitly, several times. I'm not simply implying
it.

They specifically address whether the universe is
homogenous and isotropic which leads to linearity
as a function of distance at a common time.

That is an incorrect conclusion. As noted before, a steady-state
universe could be both homegenous and isotropic, and STILL
not have a linear function of redshift versus distance
(at common time). The linear assumption is a completely
separate assumption, limited to the Big Bang theory.

You were correct when you said "One starts with the
observed local value of the redshift-distance relation."
but the assumption is that this is due to expansion over
local scales.

It doesn't matter what ad hoc explanation you make to back up the linear
assumption. The assumption of a linear relationship is still an assumption.

If the universe is homogenous then you can
imagine a slice through the universe at a given epoch to
be tiled with regions all similar to the local area we
can observe and linearity of velocity with distance then
follows if the universe is homogeneous and isotropic but
ONLY at a given epoch, i.e. over a surface of uniform
cosmic age. I'm sure you follow, the logic is trivial.

The assumption *is* trivial.

Linearity itself is therefore not an assumption but a
consequence of the cosmological principle plus the
observed linearity at small scales.

Uh, no. The assumption came first. Then the "cosmological principle" was
built upon the edifice of the linear assumption. You can see the linear
assumption explicitly in Hubble's original graph. Velocity versus distance.
When Hubble's data was redshift vs. distance.

Incidentally, in a homegenous and isotropic steady-state
universe, the relationship between speed and distance is
still linear but with a constant of proportionality with
the value zero.

Only if you assume the Big-bang relationship, that redshift is ever and
always only due to doppler shift or expansion.

Let's try this with math, instead of words. As we seem to be talking
past one another. For the moment, let us ignore possible changes
with time.

I agree, that's a sensible approach.

The standard Hubble Law is of the form:
V = H D
Where D is the distance in Mpc, V is the recessional velocity in kps,
and the Hubble constant is given in units of kps/Mpc. This equation
is explicitly linear. "H" is assumed to be constant throughout the
universe.

You cited this page

http://www.astro.ufl.edu/~guzman/ast...project01.html

but ignored this fundamental definition:

"The Hubble constant H_0 is the constant of proportionality
between recession speed v and distance d in the expanding
Universe;

v = H_0 d

The subscripted "0" refers to the present epoch because in
general H changes with time."

I did not ignore it.

Since you obviously read the page and quoted parts, I again
get the impression you deliberately ignored this definition
since it clearly repeats what I have been pointing out to
you all along.

It was irrelevant to the issue at hand. The addition of this wrinkle
affects the mathematical issue not at all.

Now let us convert this back to approximate redshift units
(approximations are fine, because the value of H is not claimed to
better precision than about +- 20%) -- since the data is
all in redshift ... not velocity:
delta lambda / lambda = H' D.

Since delta lambda over lambda is dimensionless, the units for H' would
be Mpc^-1. Where H' = H / c. [The conversion (at least at resolvable
Cepheid distance) is straightforward doppler effect:
delta lambda / lamda = v / c.]

Both equations are the same observable effect. Both are explicitly
linear, as written. Now, let us examine a simple exponential version:

delta lambda / lambda = 1 - exp(-mu D)
delta lambda / lambda = mu D + (mu D)^2 / 2 - ......

At near distances (like those of resolvable Cepheid stars), there is no
way to distinguish the linear from the exponential change. At
substantial distances (like those of the newer supernovae data),
however, the higher order terms in the approximation are no
longer negligible.

The variation of H(t) with t is also no longer negligible.

Only if you assume that H is always linear. Sure, you can make this
assumption. But it's not the only one available.

So, I could as easily use:
delta lambda / lambda = 1 - exp(-H' D)

No, instead of the constant value H', you need to use
H(t) and integrate the effect over the lookback time.

Only if the value changes with time. Which isn't the only option.

The converse (finding the time from z) is mentioned
in equation (29) of:
http://www.astro.ufl.edu/~guzman/ast...project01.html

Yes, I know. But this is irrelevant to the point under discussion.

In the case of the linear assumptions, the supernovae data must be
addressed through an additional, ad hoc, cosmological term.
In the case of the exponential fit, no additional cosmological term is
needed.

That is not true,

On the contrary, it is explicitly true. This is called "dark energy" or the
"cosmological constant."

you are oversimplifying by ignoring
the variation of H(t) at high redshift.

I did not "ignore" your assumption of time-dependence. Because it is used
solely to get around the linear distance dependence that I am discussing.

This produces
non-linearity even when there is a linear relationship
with distance at any given epoch.

Yes. But the fact that you can arbitrarily add an ad hoc time-dependence to
a linear term; does not mean that a non-linear term is just as valid.

Why do you avoid acknowledging that a nonlinear term is even conceivable?

--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}