Good News for Big Bang theory

On 22 Nov, Oh No wrote:

Oh, dear. a is the scale factor. That is not a measure of the distance
of observer to observed. These formulae are really garbled.

But, on Wed, Nov 1 2006 10:10 am, Oh No wrote:

As Philip said, Hubbles constant is the rate of change of the scale
factor divided by the scale factor. You may take the scale factor to be
a measure of separation between galaxies (or rather clusters) if you
like over short cosmological distances. The distance between two
galaxies is then r*a(t) where r is a constant for galaxies moving with
the cosmic fluid, and a(t) is the scale factor. Then, for small r, the
speed of separation is

s = r * adot(t)

From this, I, and Chalky, inferred that the distance d between galaxies
is r*a, and that the rate of acceleration of separation of galaxies is
r*adotdot.

If you disagree with these conclusions, please say so, and why.

Hubbles constant is H(t) = adot(t)/a(t)

In fact, Hubble's constant is defined as the rate of separation of
galaxies divided by that separation, so your definition is only true if
d does equal r*a

The acceleration (or deceleration) parameter is

q = - adotdot * a / adot^2

= - (adotdot / a ) * H^ - 2 by elementary algebra.

If you disagree with that conclusion, please say so, and why.

Furthermore, (adotdot / a ) = the rate of acceleration of separation of
galaxies / that separation

If you disagree with that further conclusion, please say so, and
explain why.

Or are you, on the other hand, now claiming that we don't actually live
in a galaxy?


I think, perhaps, it is your understanding which is garbled, not ours.


John Bell

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

Oh, dear. a is the scale factor. That is not a measure of the
distance
of observer to observed. a(t)-0 at the big bang, i.e. t=0. H_0=H(t0)
i.e now. These formulae are really garbled.

In that case, could you please explain what you, personally, mean by
the scale factor,

I would prefer to explain what the scale factor means, to any
cosmologist, if you would prefer to make a small display of manners. All
your innuendo and insults amount to is a large display of ignorance,
inappropriate to posting here. However I will explain it.

in plain English, and how you measure it.

You do not measure the scale factor, and indeed it has no absolute
value, but is indeterminate up to a factor. In early accounts of general
relativity with Einstein's closure condition, a(t) was often taken to be
the "radius of the universe", but in fact this is not required and makes
no sense in an open topology. You may easily check that the things we
measure, such as

H = adot/a and q = - adotdot * a / adot^2

have no dependency on an absolute value of a.


As Philip said, Hubbles constant is the rate of change of the scale
factor divided by the scale factor. You may take the scale factor to be
a measure of separation between galaxies (or rather clusters) if you
like over short cosmological distances. The distance between two
galaxies is then r*a(t) where r is a constant for galaxies moving with
the cosmic fluid, and a(t) is the scale factor. Then, for small r, the
speed of separation is

s = r * adot(t)

From this, I, and Chalky, inferred that the distance d between galaxies
is r*a, and that the rate of acceleration of separation of galaxies is
r*adotdot.

That is right. The distance is r*a, so if you took a larger value for a
you would simply be choosing a smaller value of r to compensate. r would
then be a relative measure of the distance between galaxies, while
a=a(t) would be a constant for all galaxies at any given time. It gives
a measure of changes of scale caused by expansion, which is why it is
called the scale factor.


The acceleration (or deceleration) parameter is

q = - adotdot * a / adot^2

= - (adotdot / a ) * H^ - 2 by elementary algebra.

If you disagree with that conclusion, please say so, and why.

Furthermore, (adotdot / a ) = the rate of acceleration of separation of
galaxies / that separation

If you disagree with that further conclusion, please say so, and
explain why.

Or are you, on the other hand, now claiming that we don't actually live
in a galaxy?

I did point out to you that H(t) has a dependency on time. It is not
equal to H0, the value of Hubble's constant in our own era.


I think, perhaps, it is your understanding which is garbled, not ours.

Take note of what I have said.



Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:

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

Oh, dear. a is the scale factor. That is not a measure of the distance
of observer to observed. a(t)-0 at the big bang, i.e. t=0. H_0=H(t0)
i.e now. These formulae are really garbled.

In that case, could you please explain what you, personally, mean by
the scale factor,

I would prefer to explain what the scale factor means, to any
cosmologist, if you would prefer to make a small display of manners. All
your innuendo and insults amount to is a large display of ignorance,
inappropriate to posting here.

? How did you get to that from his above quoted sentence?

However I will explain it.

in plain English, and how you measure it.

You do not measure the scale factor, and indeed it has no absolute
value, but is indeterminate up to a factor. In early accounts of general
relativity with Einstein's closure condition, a(t) was often taken to be
the "radius of the universe", but in fact this is not required and makes
no sense in an open topology. You may easily check that the things we
measure, such as

H = adot/a and q = - adotdot * a / adot^2

have no dependency on an absolute value of a.

Which is why I, personally, see absolutely no point in your insistence
on translating things which have real model independent physical
meaning locally (r, r dot and r dot dot) into things which do not (a, a
dot and a dot dot). This merely allows you to then claim (under the
Galactic Evolution discussion), that things which have real physical
meaning do not, and can therefore only be adequately understood and
evaluated within the context of a Friedmann cosmology. There is a well
known name for this technique, when applied more generally by, for
example, religious charlatans. It is called mystification.

As Philip said, Hubbles constant is the rate of change of the scale
factor divided by the scale factor. You may take the scale factor to be
a measure of separation between galaxies (or rather clusters) if you
like over short cosmological distances. The distance between two
galaxies is then r*a(t) where r is a constant for galaxies moving with
the cosmic fluid, and a(t) is the scale factor. Then, for small r, the
speed of separation is

s = r * adot(t)

From this, I, and Chalky, inferred that the distance d between galaxies
is r*a, and that the rate of acceleration of separation of galaxies is
r*adotdot.

That is right. The distance is r*a, so if you took a larger value for a
you would simply be choosing a smaller value of r to compensate. r would
then be a relative measure of the distance between galaxies, while
a=a(t) would be a constant for all galaxies at any given time.

What? That appears to be the exact opposite of your above quoted
definition!

Let me paraphrase them and put them closer together, so that you, too,
can then see the difference:

1: " The distance between two galaxies is r*a where r is a constant
for all galaxies at any given time, and a is the scale factor."

2: " The distance between two galaxies is r*a where a is a constant
for all galaxies at any given time, and r is a measure of the distance
between them."

No wonder the shifting sands of your definitions and subsequent
objections, don't seem to make much sense.

It gives
a measure of changes of scale caused by expansion, which is why it is
called the scale factor.

The acceleration (or deceleration) parameter is

q = - adotdot * a / adot^2

= - (adotdot / a ) * H^ - 2 by elementary algebra.

If you disagree with that conclusion, please say so, and why.

Furthermore, (adotdot / a ) = the rate of acceleration of separation of
galaxies / that separation

If you disagree with that further conclusion, please say so, and
explain why.

Or are you, on the other hand, now claiming that we don't actually live
in a galaxy?

I did point out to you that H(t) has a dependency on time. It is not
equal to H0, the value of Hubble's constant in our own era.


I think, perhaps, it is your understanding which is garbled, not ours.

Take note of what I have said.

Take note of what I have said, in response.


Chalky.

Thus spake Chalky
Oh No wrote:

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

Oh, dear. a is the scale factor. That is not a measure of the distance
of observer to observed. a(t)-0 at the big bang, i.e. t=0. H_0=H(t0)
i.e now. These formulae are really garbled.

In that case, could you please explain what you, personally, mean by
the scale factor,

I would prefer to explain what the scale factor means, to any
cosmologist, if you would prefer to make a small display of manners. All
your innuendo and insults amount to is a large display of ignorance,
inappropriate to posting here.

? How did you get to that from his above quoted sentence?

Because these are mathematical definitions, which are made rigorously
and with absolute objectivity and which are accepted as such by all
relativists and cosmologists. The constant suggestions that I only have
a personal understanding of them is tantamount to an accusation of
incompetence.

However I will explain it.

in plain English, and how you measure it.

You do not measure the scale factor, and indeed it has no absolute
value, but is indeterminate up to a factor. In early accounts of general
relativity with Einstein's closure condition, a(t) was often taken to be
the "radius of the universe", but in fact this is not required and makes
no sense in an open topology. You may easily check that the things we
measure, such as

H = adot/a and q = - adotdot * a / adot^2

have no dependency on an absolute value of a.

Which is why I, personally, see absolutely no point in your insistence
on translating things which have real model independent physical
meaning locally (r, r dot and r dot dot) into things which do not (a, a
dot and a dot dot).

Yes, but then you also have no understanding of differential geometry.
You would do better to try to learn about its mathematical structure
rather than criticise before understanding. If r is defined, as we have
been doing, using global coordinates so that for objects moving with the
cosmic fluid r is constant (see below for elucidation) and the actual
distances are

x = r * a

and the things you are interested in are x,

xdot = r*adot
xdotdot = r*adotdot

Then we can make global statements about all cosmological distances by
talking about a, adot and adotdot, whereas you could only make
statements about a particular cosmological distance between two objects
by talking about x, xdot and xdotdot. Moreover, since these statements
are equally true no matter what actual value of a(t) is used, the
absolute value of a(t) has no physical meaning and is irrelevant, and we
are free to set a particular value if we find it convenient to do so.


This merely allows you to then claim (under the
Galactic Evolution discussion), that things which have real physical
meaning do not, and can therefore only be adequately understood and
evaluated within the context of a Friedmann cosmology. There is a well
known name for this technique, when applied more generally by, for
example, religious charlatans. It is called mystification.

As Philip said, Hubbles constant is the rate of change of the scale
factor divided by the scale factor. You may take the scale factor to be
a measure of separation between galaxies (or rather clusters) if you
like over short cosmological distances. The distance between two
galaxies is then r*a(t) where r is a constant for galaxies moving with
the cosmic fluid, and a(t) is the scale factor. Then, for small r, the
speed of separation is

s = r * adot(t)

From this, I, and Chalky, inferred that the distance d between galaxies
is r*a, and that the rate of acceleration of separation of galaxies is
r*adotdot.

That is right. The distance is r*a, so if you took a larger value for a
you would simply be choosing a smaller value of r to compensate. r would
then be a relative measure of the distance between galaxies, while
a=a(t) would be a constant for all galaxies at any given time.

What? That appears to be the exact opposite of your above quoted
definition!

Let me paraphrase them and put them closer together, so that you, too,
can then see the difference:


1: " The distance between two galaxies is r*a where r is a constant
for all galaxies at any given time, and a is the scale factor."

2: " The distance between two galaxies is r*a where a is a constant
for all galaxies at any given time, and r is a measure of the distance
between them."

No wonder the shifting sands of your definitions and subsequent
objections, don't seem to make much sense.

Certainly that helps me to see where your misunderstanding lies, but in
neither case is it a paraphrase of what I have said, and that is why it
makes no sense to you. I will try and state it more plainly.

Given any pair of galaxies moving with the cosmic fluid, r is a measure
of the separation between them and is constant in time. In general, a
different pair of galaxies will have a different value of r.

The scale factor a=a(t) varies in time, and is the same for any pair of
galaxies at cosmic time t. It is a measure of the expansion of the
universe.




Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:
Certainly that helps me to see where your misunderstanding lies, but in
neither case is it a paraphrase of what I have said, and that is why it
makes no sense to you. I will try and state it more plainly.

Given any pair of galaxies moving with the cosmic fluid, r is a measure
of the separation between them and is constant in time. In general, a
different pair of galaxies will have a different value of r.

The scale factor a=a(t) varies in time, and is the same for any pair of
galaxies at cosmic time t. It is a measure of the expansion of the
universe.

But all you are doing here is separating something which is real, which
I will call R, into two things which are abstractions, for your
convenience, within a particular cosmological model.

hence R=r.a

By arbitrarily defining r as constant you thus translate f1(R)/f2(R)
into f1(a)/f2(a)

So what?

I could equally well arbitrarily define a as constant and r as
variable, for my own convenience, within the context of a different
cosmological model, to obtain
f1(R)/f2(R) = f1(r)/f2(r)

Who would be the wiser, in terms of what this actually means in terms
of astronomical observations?

Consequently I now rephrase
my original question as follows:

If we take your definitions of both q and Ho to be initially defined in
terms of a purely abstract algebraic function a, and then consider the
two possible definitions of that purely abstract function a to mean:

1) the distance R from us to any particular galaxy (in accordance with
Hubble's definition)
2) the scale factor of the universe (now), in accordance with your
definition,

What are the differences, if any, between these two definitions?

Since I don't want to drag this out, I will now
explain what the real difference is, in plain English.

Definition 1 is physically meaningful because:

A It defines both q and Ho in terms that can be physically observed and
measured.

B It thus provides us with a realistic tool for the empirical
astronomical task of measuring, interpreting, and mapping the 4
dimensional dynamism of the universe that we observe in practice.

Definition 2 is physically meaningless because:

A It defines both q and Ho in terms that cannot be physically observed
and measured.

B It thus provides us with a completely unrealistic tool for for the
empirical astronomical task of measuring, interpreting, and mapping the
4 dimensional dynamism of the universe that we observe in practice,
now, since it is impossible to observe (now) any part of the universe
that
exists (now) at any distance that is further away from us than the
noses on the end of our faces. This is because of the well known fact
that the speed of light is less than infinity.

Consequently, this definition is extremely model dependent and thus
almost useless for any comparative evaluation of different
cosmological models, in the light of hard observed astronomical
evidence.

It is, therefore, quite a good tool for perpetuating the process of
mystification, identified by Chalky in his posting of Sat, Nov 25 2006
8:35 am, and nothing more, in the context we are currently discussing.


John Bell
http://global.accelerators.co.uk
(Change John to Liberty to bypass anti-spam email filter)

[Mod. note: quoted text trimmed -- mjh]

Thus spake "John (Liberty) Bell"
Oh No wrote:
Certainly that helps me to see where your misunderstanding lies, but in
neither case is it a paraphrase of what I have said, and that is why it
makes no sense to you. I will try and state it more plainly.

Given any pair of galaxies moving with the cosmic fluid, r is a measure
of the separation between them and is constant in time. In general, a
different pair of galaxies will have a different value of r.

The scale factor a=a(t) varies in time, and is the same for any pair of
galaxies at cosmic time t. It is a measure of the expansion of the
universe.

But all you are doing here is separating something which is real, which
I will call R, into two things which are abstractions, for your
convenience, within a particular cosmological model.

Quite. Its not difficult.

hence R=r.a

By arbitrarily defining r as constant you thus translate f1(R)/f2(R)
into f1(a)/f2(a)

So what?

I could equally well arbitrarily define a as constant and r as
variable, for my own convenience, within the context of a different
cosmological model, to obtain
f1(R)/f2(R) = f1(r)/f2(r)

Who would be the wiser, in terms of what this actually means in terms
of astronomical observations?

I don't suppose anyone would be any wiser. If one wants to communicate
it is generally better to follow accepted definitions, whereever
possible.

Consequently I now rephrase
my original question as follows:

If we take your definitions of both q and Ho to be initially defined in
terms of a purely abstract algebraic function a, and then consider the
two possible definitions of that purely abstract function a to mean:

1) the distance R from us to any particular galaxy (in accordance with
Hubble's definition)
2) the scale factor of the universe (now), in accordance with your
definition,

What are the differences, if any, between these two definitions?

The big difference is that variation in R contains an entirely random
element of peculiar motion, which makes it quite useless as a basis for
statistical analysis or for the study of properties of the universe as a
whole.

Definition 1 is physically meaningful because:

A It defines both q and Ho in terms that can be physically observed and
measured.

It also defines them incorrectly according to any useful cosmology, and
gives a different definition from that you would find by using a
different galaxy. You cannot even find a value for q0 by looking at only
one galaxy. You need a sample over a range of redshifts, and then you
will get a different value by using a different sample.

B It thus provides us with a realistic tool for the empirical
astronomical task of measuring, interpreting, and mapping the 4
dimensional dynamism of the universe that we observe in practice.

It provides something completely useless for that purpose. What you are
talking of is the empirical value of q or H0, both of which are given
with error bounds and which are subject to change over time. For those
to be useful empirical measures, you must first have a theoretical
definition which one seeks to determine through measurement.

Definition 2 is physically meaningless because:

A It defines both q and Ho in terms that cannot be physically observed
and measured.

That is completely false. The definitions have been designed so as to
give measurable quantities.

B It thus provides us with a completely unrealistic tool for for the
empirical astronomical task of measuring, interpreting, and mapping the
4 dimensional dynamism of the universe that we observe in practice,
now, since it is impossible to observe (now) any part of the universe
that
exists (now) at any distance that is further away from us than the
noses on the end of our faces. This is because of the well known fact
that the speed of light is less than infinity.

This is arbitrary nonsense. You should really learn just a little bit
about cosmology and astrophysicists before making a fool of yourself
here.

Consequently, this definition is extremely model dependent and thus
almost useless for any comparative evaluation of different
cosmological models, in the light of hard observed astronomical
evidence.

Obviously the values of H0 and q0 are model dependent. General
relativity allows a range of possible models, and the experimental
determination of H0 and q0 enables us to choose between them. That is
how astrophysicists have arrived at the currently favoured "Concordance"
model, with CDM and Lambda~0.7. In practice, as has been said, q0 is
part of a series expansion which was intended for manual analysis based
on galaxies at low red shift. That analysis was inconclusive and has
long been superceded by the observation of supernovae at redshifts
approaching and greater than 1, and the use of computers for more
accurate analysis.



Regards

--
Charles Francis
substitute charles for NotI to email

"John (Liberty) Bell" wrote in message
...
.....

[regarding scale factor]

It is, therefore, quite a good tool for perpetuating the process of
mystification, identified by Chalky in his posting of Sat, Nov 25 2006
8:35 am, and nothing more, in the context we are currently discussing.

This seems to be getting far more complex than is necessary.

Consider three galaxies at distances of 10 MPc, 20 MPc and
30 MPc at some cosmic time t0. At some later time t1, they
are found to be at 11 MPc, 22 MPc and 33 MPc. The distance
each has moved is 1 MPc, 2 MPc and 3 MPc respectively. The
speeds similarly vary pro rata with the range. However I
can easily say that each is 10% farther away, or that the
distance has increased by a factor of 1.1 in each case.

That ratio is the "scale factor" and is called a(t) so if
a(t0)=1.0 then a(t1)=1.1. It seems to me that the use of
a(t) simplifies discussions because it can be used to
characterise any model without worrying about distances and
speeds for individual galaxies.

George

Thus spake George Dishman
"John (Liberty) Bell" wrote in message
...
....

[regarding scale factor]

It is, therefore, quite a good tool for perpetuating the process of
mystification, identified by Chalky in his posting of Sat, Nov 25 2006
8:35 am, and nothing more, in the context we are currently discussing.

This seems to be getting far more complex than is necessary.

Consider three galaxies at distances of 10 MPc, 20 MPc and
30 MPc at some cosmic time t0. At some later time t1, they
are found to be at 11 MPc, 22 MPc and 33 MPc. The distance
each has moved is 1 MPc, 2 MPc and 3 MPc respectively. The
speeds similarly vary pro rata with the range. However I
can easily say that each is 10% farther away, or that the
distance has increased by a factor of 1.1 in each case.

That ratio is the "scale factor" and is called a(t) so if
a(t0)=1.0 then a(t1)=1.1. It seems to me that the use of
a(t) simplifies discussions because it can be used to
characterise any model without worrying about distances and
speeds for individual galaxies.

Yes. The added complications are that each of the three galaxies will
have a peculiar motion superimposed on the Hubble expansion, so the
observed ratios are not expected to be perfect, and that in practice we
allow a0=a(t0) to be an arbitrary constant, so that what we actually use
in equations is

a(t0)/a0 = 1 and a(t1)/a0 = 1.1 etc.


Regards

--
Charles Francis
substitute charles for NotI to email

Oh No wrote:

The big difference is that variation in R contains an entirely random
element of peculiar motion, which makes it quite useless as a basis for
statistical analysis or for the study of properties of the universe as a
whole.


This has been a rather amazing discussion for several reasons, and I
offer the following nonsequitor to add a little levity to the gravity,
and to check my own understanding of standard cosmological ideas.

Axiom I: We are *here* only discussing the physics within the
observable universe.

We have good reason to think that we are witnessing a global expansion
of spacetime.

However, fully bound systems (galaxies, small galactic groups and
tightly bound galactic clusters) do *not* participate in this global
expansion of spacetime. By this I mean that they do not expand along
with the background S-T, or in other words, they do not change in size
with time.

Bound systems on lower scales (say stellar or atomic systems) are also
"immune" from this global expansion.

The bound galactic systems have considerable random motions ("peculiar"
velocities) that also are distinct from, and in addition to, the global
expansion.

What I am wondering is: Is what I have been assuming is standard
astrophysics for many years shared by most astrophysicists? Are we all
on the same page? If not, what other conceptual framework would modify
these four statements, and how?

I feel like I am groping towards something without knowing exactly
where I'm going, except that the idea of parts of nature expanding
while other parts clearly do not expand is an intriguing idea.

Robert L. Oldershaw


[Mod. note: out of date but still relevant:
http://math.ucr.edu/home/baez/physic..._universe.html
-- mjh]

Thus spake "
Oh No wrote:

The big difference is that variation in R contains an entirely random
element of peculiar motion, which makes it quite useless as a basis for
statistical analysis or for the study of properties of the universe as a
whole.


This has been a rather amazing discussion for several reasons, and I
offer the following nonsequitor to add a little levity to the gravity,

:-)

and to check my own understanding of standard cosmological ideas.

Axiom I: We are *here* only discussing the physics within the
observable universe.

Not really. The physics applies within the observable universe, but
general relativity is global - it assumes that local laws of physics are
the same for all observers, and implicitly assumes that they would be
the same for an observer outside of what is for us the observable
universe. More specifically, homogeneity and isotropy are assumed for
Friedmann cosmologies, and in these the quantity a(t) (or a(t)/a0 if one
must) applies globally at any given cosmic time (time on a geodesic from
the big bang).

People do try relaxing homogeneity and isotropy assumptions, but it
seems a bit meaningless to do so when it only alters predictions outside
the observable universe, and I don't know of any successful theory which
has done so with observable results - e.g. a couple were mentioned
recently on s.a.r. and Ted Bunn was able to tell us that they have been
eliminated experimentally.

So for the most part this discussion has been, from my point of view at
least, within the context of standard cosmology and discusses global
properties. I would flag it whenever that is not the case, but I don't
usually see the need to preface everything I say with "in standard
cosmology".

We have good reason to think that we are witnessing a global expansion
of spacetime.

A stack of very good reasons.

However, fully bound systems (galaxies, small galactic groups and
tightly bound galactic clusters) do *not* participate in this global
expansion of spacetime. By this I mean that they do not expand along
with the background S-T, or in other words, they do not change in size
with time.

Yes. This is, of course, also a prediction of general relativity
(prediction in the sense of logically derivable from first principles,
not, of course, that the derivation preceded the observation).

Bound systems on lower scales (say stellar or atomic systems) are also
"immune" from this global expansion.

Yes.

The bound galactic systems have considerable random motions ("peculiar"
velocities) that also are distinct from, and in addition to, the global
expansion.

Yes.

What I am wondering is: Is what I have been assuming is standard
astrophysics for many years shared by most astrophysicists? Are we all
on the same page? If not, what other conceptual framework would modify
these four statements, and how?

sounds like you are basically on the same page.

I feel like I am groping towards something without knowing exactly
where I'm going, except that the idea of parts of nature expanding
while other parts clearly do not expand is an intriguing idea.

[Mod. note: out of date but still relevant:
http://math.ucr.edu/home/baez/physic..._universe.html
-- mjh]

I don't think I can do better than that by way of general explanation.



Regards

--
Charles Francis
substitute charles for NotI to email