Red shift and homogeneity

"George Dishman" wrote in message ...

Why shouldn't it expand? The only way it could be stopped
would be if the most distant parts were up against
something, but for an infinite universe there is always
more space beyond. The words bigger and smaller just don't
apply, it starts infinite, it expands and it is still
infinite.

If you want to take a Newtonian view, I explained to Jim
some time ago, every galaxy moves away from us to a place
recently vacated by a more distant galaxy. There is never
a galaxy that doesn't have an infinite number of more
distant galaxies already beyond it.

I think it's one of those things that needs a bit of time
for your mind to adapt to. We are not accustomed to meeting
the infinite in real life.

George


I dont find infinity hard to deal with although it is in a sense
impossible to visualiize an infinite volume. What I do is imagine a
finite universe and then just look beyond the edge.So its not
difficult. I realize it does open a pandoras box when discussing
infinity and I have been told recently that it drove a mathematician
called Cantor insane a century ago thinking about infinity. I am also
aware that some mathematicians can model different sizes of infinity
but also have been told by a reliable source that most of these
solutions are also not strictly correct or valid, in particular those
used by astronomers.

A few points I would like to make. First is the idea that different
sets of infinity can be larger or smaller. I definitely feel that
mathematicians are involved in a conceit and deceit here on this
point. Their logic is that beteween numbers 1-2 there are an infinite
amount of fractions or decimals ie 1.009785877 etc And between 1-3
there are twice as many and therefore there is a larger infinite
amount of fractions btween 1-3 than 1-2. But that doesnt work for me.
You can only have a larger amount of something if the original amount
has a value. But inbetween 1-2 and 1-3 the amounts, being both
infinite, are NOT known and therefore you cannot prove that some sets
of infinity are larger than others as neither set has a specific
calculable value or amount. One can only speculate but thats not
rigorous enough. If I was to say to you prove to me that one infinite
set is larger than another you would be unable to supply two amounts
one larger than the other as definitive proof that two infinite sets
have different values or amounts.And as both sets are infinite you
cannot supply a specific amount to either set to compare against the
other.Therefore strictly speaking dfferent infinite sets cannot have
different sizes contrary to accepted belief.

And regarding your argument about infinite space being able to expand
because there is always more space for it to expand into. I think
George that maybe your argument neglects to take into account that
your initial section of space that is expanding cannot expand into
other available parts of the universe simply because ALL other
available parts of the infinite universe are already taken in
infinitum by other spaces trying to expand.. Everywhere wants to
expand and if everywhere is already taken by space trying to expand
there is thus , in an infinite universe , no available *extra* empty
space into which any one space can expand to. Your logic is flawed
because your infinite universe is actually a finite universe within an
other empty *unoccuppied* infinite universe that isnt or cant expand
but supplies the neccesary space into which your finite universe can
expand to. Your paper experiment is a finite paper experiment. Your
sheets you use can only expand IF there is an edge to your paper or
groups of paper that beyond which have no paper. Just imagine if your
sheets of expanding paper were set into an infinity of expanding
sheets of paper. So no matter how far you go there are still always
sheets trying to expand. Where can they expand to ? The only place is
into other sheets . So in that case maybe some papers can expand but
that implies that others have to reduce to give up that extra space .
In your expanding paper universe only some sheets can expand at the
expense of others.And your original sheet cannot expand because there
is no space in the infinite universe where there is NO paper and
therefore no extra space , into which it can expand into.Your argument
assumes that somewhere in your universe an infinite amount of space
is available where there is no paper.And you admit this by saying
above... " there is always more space beyond.." What *more space* ..
empty space?

Eddingtons ballon analogy only works because his ballon is a finite
size and the only ballon in much larger airspace with no other
ballons. His balloon wouldnt expand if there was an infinity of
ballons in all directions trying to expand into ITS space.
I would like to end on a slightly ddiffernt point . If lets say your
universe could expand it also follows that the speed at which two
points in an infinitely expanding universe are expanding would have to
always increase their relative speeds from each other or accelerate
away from each other. And the farther away from each other those
points are the faster they have to move away from each other. Its odd
then that supposedly observations recently have been made that imply
that the universe expansion is accelerating. Because in your model of
an expanding BB universe it does seem that any two points would have
to accelerate away from each other to accomadate the expansion of your
universe. Interesting, but only if infinity could expand which I
dont beleive it can and only if those supernova observations correctly
imply that the universe is expanding.
Sean

"Jim Greenfield" wrote in message
om...
"George Dishman" wrote in message
...
"Jim Greenfield" wrote in message
...
"George Dishman" wrote in message
...

IIUC, the CMBR origin is claimed to be
the outer limit of the universe, originating from the BB before the
formation of the first galaxies.

Yes and no. It is the limit of how far we can see but not the
limit of the universe. It does come from before the earliest
galaxies were formed but not from further away. More on this
later.

In which discussion I will ask, why then can we not see beyond 14bly?
....

http://www.dishman.me.uk/George/Cosm...nsion/cmbr.gif

Because when you look some distance away (take it as 13.7 bly
for the moment, we can discuss definitions of distance later),
we see things as they were 13.7 by ago. Prior to that the
universe was opaque as well as glowing, like the surface of
the Sun, so no light reaches us from there. Do younot follow
the diagram above?


How is this?
I marked adjacent boxes ABCDEF on my graph paper. Then I moved B one
space. But red shift indicates that when F was at position B (before
expansion) it was moving a lot faster (say 2 squares in the same
interval- which is of course exagerated). Now when I do this exercise
a few more times, using all the letters, I find that density of ABCD,
is less than CDEF (larger spread)

Suppose you marked every third square with a letter on your
first sheet. That becomes every fourth square on the second
sheet. Now suppose we align B like this:

A B C D E F
A B C D E F

No. My letters spread as A B C D E F

You confused me by saying "adjacent boxes". Anyway, the
problem is that your pattern is not homogenous. We are
considering whether something originally homogenous
remains so, so you have to start with them equally
spaced.

(exagerated, but in yor spread, B is travelling the same speed as F,

If B and F were moving at the same speed, the distance
between them would remain constant.

which is not red shift observed)

Here are the speeds:

A B C D E F
A B C D E F
A: | one quare left, speed = -1
B: | hasn't moved, speed = 0
C: | one square right, speed = 1
D: | two squares, speed = 2
E: | three squares, speed = 3
F: | four squares, speed = 4


Clearly the letters more distant from B seem to be moving
faster. C is moving at speed 1, D at 2 and so on. Now think
of that as two groups, ABC and DEF, and think of the change
as being composed of two effects, motion and expansion of
the groups. Group ABC has not moved as a whole since the
speeds are 1 to the left, 0 and 1 to the right, average 0.
The group is expanding since A and C are moving away from
B at speed 1 in opposite directions.

Group DEF on the other hand is moving at speed 3, 2 for D,
3 for E and 4 for F so 3 on average. DEF is also expanding
because D is moving away from E at speed 1 to the left while
F is moving at speed 1 to the right.

The key here is that both groups are expanding at the same
rate, 1 square in the interval for A/C and D/F even though
group DEF is moving rapidly but group ABC is not.

Now align E:

A B C D E F
A B C D E F

This time it is group ABC that is moving rapidly to the left
while group DEF is static. In fact it doesn't matter what
letter you align, A and C will be expanding away from B in
exactly the same way that D and F are expanding away from E.

The density has gone down for 0.33 letters per square to
0.25 letters per square everywhere and no choice of alignment
will affect that.

I think that you have placed your galaxies at distances dictated by c,

No, I have made them homogenous, i.e. an equal number per
unit of distance, at a given instant in time.

but have changed your observation points (from galaxy to galaxy)
INSTANTLY.

There is no observation point, this is a map of the universe
at one particular instant. To calculate what we would observe
you have to take multiple such slices.

This has allowed the appearance that the view would be the
same anywhere,

No, it is a _model_ that says galaxies are actually distributed
evenly (equal density at large scales) at any instant, it does
not describe the appearance at all.

when if the relocation was done similarly to the
arriving images (at c), I don't think your spread of maintained
homogeneity stands up.

Homogeneity doesn't refer to appearance, it refers to the
instantaneous distribution that we _infer_ from the observations.

So I am afraid that I still have this (belief?) that an expansion,
considering ALL the universe, by default would cause a change in
homogeneity.

Try to imagine your piece of paper as just a fraction of the
whole. No matter how big it is it is no different anywhere to
what you see on your sample. Think of a letter as far away as
you can imagine, the letters adjacent to it will be expanding
away from it by 1 square in the interval and the density in
that region has gone down from 0.33 to 0.25.

If it was 0.33 everywhere and it is now 0.25 everywhere,
homogeneity has been preserved.

Other posters refer to light being at a different velocity when the
universe was 'smaller', which is claimed to upset this view.

There has been speculation about that but nothing believable.
The possibility exists so people do tests to look for any
variation when the opportunity arises but so far it is mainly
cranks pushing their own ideas.

Also that
the expansion of space drags the galaxies along, rather than them
travelling through space. You might have to try convincing me along
those lines, in order to overcome my current skepticism ref expansion.

If you ever become conversant with GR, I will have to backtrack
on some of what I am saying. Until then, I feel it is better to
explain it in terms you understand, as close to Newtonian physics
as I can manage. However, I will be open about this and suggest
you read the following threads. These are experts who know the
subject well, the question is not the theory but how to explain
it:

http://makeashorterlink.com/?V5C032776

http://makeashorterlink.com/?U2D051776

These guys seem to chuck out the Doppler red shift for cosmological
scales.

I told you I would be open, I am not trying to sell you a
line, I am giving you the opportunity to see for yourself
what the present state of play is.

What Ted Bunn is arguing is that the two approaches are
equivalent given an appropriate change of coordinate
system. The different descriptions are just different
ways of looking at the same physics. The discussion is
really about whether using Doppler shift is useful or
confusing. Given that you don't know GR, I feel we have
no choice but to use the Doppler version, then try to
relate that to the relativistic description after you
learn at least the basics of SR.

We spent considerable time in a certain railway station which
was supposed to be very sound evidence for BB per this very Doppler
red shift............

The essence is that the different ways of explaining it can
be considered equivalent under certain circumstances.

George

I'm afraid that I am still with Sean on this (or vice versa), in that
the term "expanding infinity" is oxymoronic and contradictory.

Then you are still thinking of infinity as unimaginably big but
still finite. There is a fundamental difference between the two
and I can't really help much more on that, but it is a distinction
you need to grasp to understand this.

There
may "appear" to have been some form of BB, but appearances can be
deceptive!
Can you perhaps give me link to Super Nova information which is
claimed to be heavy support for BB?

http://www.arxiv.org/abs/astro-ph/0104382

I first mentioned the paper as evidence against Tired Light.
I expect to have to explain some of it so I suggest you
download it so we can discuss it over some time. I use PDF
format since I don't like the postscript viewers I have
tried. I have PDF format set as my default. Let me know if
you trouble setting it up.

best regards
George

Jim Greenfield replied to George Dishman:

Suppose you marked every third square with a letter on your
first sheet. That becomes every fourth square on the second
sheet. Now suppose we align B like this:

A B C D E F
A B C D E F

No. My letters spread as A B C D E F
(exagerated, but in yor spread, B is travelling the same speed
as F, which is not red shift observed)

In George's diagram, B did not move. It's "speed" is zero.
F moved 4 places to the right. It's "speed" is 4.

Here is the same demonstration of expansion that George is
using, and the same as I urged you to do with a rubber band
or elastic -- just a slightly different presentation.

Start with a line of letters on your monitor screen:

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&

Now expand the line uniformly and examine it at a series of
points in time:

Time
----
0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&
1 A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-a-b-c
2 A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--
3 A---B---C---D---E---F---G---H---I---J---K---L---M---N---O
4 A----B----C----D----E----F----G----H----I----J----K----L-
5 A-----B-----C-----D-----E-----F-----G-----H-----I-----J--
6 A------B------C------D------E------F------G------H------I
7 A-------B-------C-------D-------E-------F-------G-------H
8 A--------B--------C--------D--------E--------F--------G--

Letters which start out close together, such as B and C, move
apart slowly. B and C move apart 1 position per time increment.
Letters which start out far apart, such as B and F, move apart
rapidly. B and F move apart 4 positions per time increment.

At any point in time, the letters are distributed uniformly all
along the line, nomatter how long the line is, or even if it is
endless.

Do you agree with all of this?

-- Jeff, in Minneapolis

..

(Jeff Root) wrote in message . com...
Jim Greenfield replied to George Dishman:

Suppose you marked every third square with a letter on your
first sheet. That becomes every fourth square on the second
sheet. Now suppose we align B like this:

A B C D E F
A B C D E F

No. My letters spread as A B C D E F
(exagerated, but in yor spread, B is travelling the same speed
as F, which is not red shift observed)

In George's diagram, B did not move. It's "speed" is zero.
F moved 4 places to the right. It's "speed" is 4.

Here is the same demonstration of expansion that George is
using, and the same as I urged you to do with a rubber band
or elastic -- just a slightly different presentation.

Start with a line of letters on your monitor screen:

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&

Now expand the line uniformly and examine it at a series of
points in time:

Time
----
0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&
1 A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-a-b-c
2 A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--
3 A---B---C---D---E---F---G---H---I---J---K---L---M---N---O
4 A----B----C----D----E----F----G----H----I----J----K----L-
5 A-----B-----C-----D-----E-----F-----G-----H-----I-----J--
6 A------B------C------D------E------F------G------H------I
7 A-------B-------C-------D-------E-------F-------G-------H
8 A--------B--------C--------D--------E--------F--------G--

Letters which start out close together, such as B and C, move
apart slowly. B and C move apart 1 position per time increment.
Letters which start out far apart, such as B and F, move apart
rapidly. B and F move apart 4 positions per time increment.

At any point in time, the letters are distributed uniformly all
along the line, nomatter how long the line is, or even if it is
endless.

Do you agree with all of this?

Yes?, but see below- endless lines expanding? uh uh

-- Jeff, in Minneapolis

You have gone to some trouble here, and I appreciate your input, but
in order to not repeat myself, I will try to reply to George in detail
(but of course, still feel free)

Tie your rubber band to my nose. Start to stretch it, and if I could
maintain a view of the whole, your diagram (and Georges) stacks up.
But I can only see F (end of band) as it was BEFORE stretching. At
that time it was travelling at 3000km/sec (distant red shift). You are
taking the view that I can still see ALL OF the band at once, now.
Jim G
(I will amend my ABC spread next post)

Jim Greenfield wrote:

(Jeff Root) wrote in message . com...
Jim Greenfield replied to George Dishman:


[snip]


Yes?, but see below- endless lines expanding? uh uh

Yes. It just means that the distance between any two points on the line
increases. It makes no sense to say that the lenght of the line changes
because of this - the line had no defined length before, and it had to
defined length afterwards, because "infinite" is not a number.



-- Jeff, in Minneapolis

You have gone to some trouble here, and I appreciate your input, but
in order to not repeat myself, I will try to reply to George in detail
(but of course, still feel free)

Tie your rubber band to my nose. Start to stretch it, and if I could
maintain a view of the whole, your diagram (and Georges) stacks up.
But I can only see F (end of band) as it was BEFORE stretching. At
that time it was travelling at 3000km/sec (distant red shift). You are
taking the view that I can still see ALL OF the band at once, now.

A
s George already mentioned: homogenity doesn't refer what we see
directly. It refers to what *is* out there - and this can be determined
from our observations.


BTW, did you miss my last three posts, too?


Bye,
Bjoern

"Jim Greenfield" wrote in message
om...
(Jeff Root) wrote in message
. com...
Jim Greenfield replied to George Dishman:

Suppose you marked every third square with a letter on your
first sheet. That becomes every fourth square on the second
sheet. Now suppose we align B like this:

A B C D E F
A B C D E F

No. My letters spread as A B C D E F
(exagerated, but in yor spread, B is travelling the same speed
as F, which is not red shift observed)

In George's diagram, B did not move. It's "speed" is zero.
F moved 4 places to the right. It's "speed" is 4.

Here is the same demonstration of expansion that George is
using, and the same as I urged you to do with a rubber band
or elastic -- just a slightly different presentation.

Start with a line of letters on your monitor screen:

ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&

Now expand the line uniformly and examine it at a series of
points in time:

Time
----
0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz@#$%&
1 A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-a-b-c
2 A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--
3 A---B---C---D---E---F---G---H---I---J---K---L---M---N---O
4 A----B----C----D----E----F----G----H----I----J----K----L-
5 A-----B-----C-----D-----E-----F-----G-----H-----I-----J--
6 A------B------C------D------E------F------G------H------I
7 A-------B-------C-------D-------E-------F-------G-------H
8 A--------B--------C--------D--------E--------F--------G--

Letters which start out close together, such as B and C, move
apart slowly. B and C move apart 1 position per time increment.
Letters which start out far apart, such as B and F, move apart
rapidly. B and F move apart 4 positions per time increment.

At any point in time, the letters are distributed uniformly all
along the line, nomatter how long the line is, or even if it is
endless.

Do you agree with all of this?

Yes?, but see below- endless lines expanding? uh uh

-- Jeff, in Minneapolis

You have gone to some trouble here, and I appreciate your input, but

So do I Jeff, I thought _I_ would have to draw that, thanks!

in order to not repeat myself, I will try to reply to George in detail
(but of course, still feel free)

Tie your rubber band to my nose. Start to stretch it, and if I could
maintain a view of the whole, your diagram (and Georges) stacks up.
But I can only see F (end of band) as it was BEFORE stretching. At
that time it was travelling at 3000km/sec (distant red shift). You are
taking the view that I can still see ALL OF the band at once, now.


Jeff's diagram is a stacked set of maps, each at a given time with
the earliest, '0', at the top and now, 9, at the bottom and since
9 maps represent 13.7 billion years, they are about 1.5 billion
years apart so let's consider what we would see in this model. The
asterisks assume we are at 'A' are supposed to be scaled so that
they get further away by about 1.5 billion light years per map
(this is based on the conformal map from Ned Wright's pages):

Time
----
0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz...
1 A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-*-R-S-T-U-V-W-X-Y-Z-a-b-c
2 A--B--C--D--E--F--G--H--I--J*-K--L--M--N--O--P--Q--R--S--
3 A---B---C---D---E---F---*---H---I---J---K---L---M---N---O
4 A----B----C----D----*----F----G----H----I----J----K----L-
5 A-----B-----C---*-D-----E-----F-----G-----H-----I-----J--
6 A------B----*-C------D------E------F------G------H------I
7 A-------*-------C-------D-------E-------F-------G-------H
8 A---*----B--------C--------D--------E--------F--------G--
9 A---------B---------C---------D---------E---------F------

A * B C D E F G * Q | opaque

I've skipped the letters between G and Q because they get too
crowded. Can you see the what we observe is not homogenous, we
expect to see a higher density at greater distances, but this is
based on a model in which the maps are homogenous at any given
time. I think sometimes Jim, you think we mean that what we see
is homogenous when we are actually saying that the universe is
homogenous even if we can't see it. There is a process of
interpretation in between.

I'll say more on this in reply to Sean. (That's why I added a
ninth line BTW.)

George

"sean" wrote in message
om...

I dont find infinity hard to deal with although it is in a sense
impossible to visualiize an infinite volume. What I do is imagine a
finite universe and then just look beyond the edge.So its not
difficult. I realize it does open a pandoras box when discussing
infinity and I have been told recently that it drove a mathematician
called Cantor insane a century ago thinking about infinity. I am also
aware that some mathematicians can model different sizes of infinity
but also have been told by a reliable source that most of these
solutions are also not strictly correct or valid, in particular those
used by astronomers.

I didn't realise you were aware of that.

A few points I would like to make. First is the idea that different
sets of infinity can be larger or smaller. I definitely feel that
mathematicians are involved in a conceit and deceit here on this
point. Their logic is that beteween numbers 1-2 there are an infinite
amount of fractions or decimals ie 1.009785877 etc And between 1-3
there are twice as many and therefore there is a larger infinite
amount of fractions btween 1-3 than 1-2. But that doesnt work for me.

It's not correct. There are an infinite number of integers, let's
call that quantity A_0. You can also number all the even numbers
or odd numbers and so on so

A_0 + n = A_0

where n is any finite number

A_0 * n = A_0

A_0 ^ n = A_0

however

A_0 ^ A_0 is not the same as A_0

There are also an infinite number of
fractions and you can write every fraction like this:

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4 2/5
3/1 3/2 3/3 3/4 3/5
4/1 4/2 4/3 4/4 4/5
5/1 5/2 5/3 5/4 5/5
...

and then enumerate diagonally them starting

1/1,
2/1, 1/2,
1/3, 2/2, 3/1
4/1, 3/2, 2/3, 1/4

and so on, so you can produce a one-to-one correspondence
between the integers and the fractions so there are A_0 of
them too.

However, Cantor showed there are more decimals because
if, for example, you enumerate all the decimals from 0
using letters to represent digits as:

1 -- 0.a_1 a_2 a_3
2 -- 0.b_1 b_2 b_3
3 -- 0.c_1 c_2 c_3

then you can always construct a new one by picking a number
that differs in the first digit from the first, in the
second digit from the second and so on. Let's call the
number of decimals A_1. Cantor showed

A_0 ^ A_0 = A_1

but I don't know how.

You can only have a larger amount of something if the original amount
has a value. But inbetween 1-2 and 1-3 the amounts, being both
infinite, are NOT known and therefore you cannot prove that some sets
of infinity are larger than others as neither set has a specific
calculable value or amount. One can only speculate but thats not
rigorous enough. If I was to say to you prove to me that one infinite
set is larger than another you would be unable to supply two amounts
one larger than the other as definitive proof that two infinite sets
have different values or amounts.And as both sets are infinite you
cannot supply a specific amount to either set to compare against the
other.Therefore strictly speaking dfferent infinite sets cannot have
different sizes contrary to accepted belief.

They don't have a finite size in the normal sense but they
can differ as you can see. It's called cardinality and that's
about as far as my knowledge goes on the subject. It's from a
book I got as a child called "Mathematics and the Imagination"
by Kasner and Newman. I really had to shake the dust off that
one!

And regarding your argument about infinite space being able to expand
because there is always more space for it to expand into. I think
George that maybe your argument neglects to take into account that
your initial section of space that is expanding cannot expand into
other available parts of the universe simply because ALL other
available parts of the infinite universe are already taken in
infinitum by other spaces trying to expand.. Everywhere wants to
expand and if everywhere is already taken by space trying to expand
there is thus , in an infinite universe , no available *extra* empty
space into which any one space can expand to. Your logic is flawed
because your infinite universe is actually a finite universe within an
other empty *unoccuppied* infinite universe that isnt or cant expand
but supplies the neccesary space into which your finite universe can
expand to. Your paper experiment is a finite paper experiment. Your
sheets you use can only expand IF there is an edge to your paper or
groups of paper that beyond which have no paper. Just imagine if your
sheets of expanding paper were set into an infinity of expanding
sheets of paper.

That's they way to do it, I map an infinite space using an infinite
number of finite sheets. Now suppose each sheet is 10cm square and
the first sheet wants to expand to 12cm square but the centre is
pinned. It expands 1cm in each direction. The sheet to its right
also wants to expand to 12cm but it has to move over by 1cm as well
to make room for the first, so its centre has to move by 2cm and the
far edge will move away from the pin in the first sheet by 3cm. The
next sheet also wants to expand to 12cm square but its centre has
to move by 4cm to allow this to happen.

Now consider the centres. The first sheet is pinned - no motion. The
centre of the second sheet is 10cm from the pin and it moves 2cm. The
centre of the third sheet starts 20cm from the pin and it moves 4cm.
The essential equation here for the speed of each sheet is

v = d/5

where v is the speed and d is the initial distance from the pin. The
result is

* no gaps
* no overlaps
* each expands from 100 sq cm to 144 sq cm
* speed is proportional to distance

and finally if there were dots on the sheets, the density of the dots
would fall from n/100 dots per sq cm to n/144 dots per sq cm if the
average number of dots per sheet was n.

So no matter how far you go there are still always
sheets trying to expand. Where can they expand to ? The only place is
into other sheets . So in that case maybe some papers can expand but
that implies that others have to reduce to give up that extra space .
In your expanding paper universe only some sheets can expand at the
expense of others.And your original sheet cannot expand because there
is no space in the infinite universe where there is NO paper and
therefore no extra space , into which it can expand into.Your argument
assumes that somewhere in your universe an infinite amount of space
is available where there is no paper.And you admit this by saying
above... " there is always more space beyond.." What *more space* ..
empty space?

The space recently vacated by those galaxies beyond.

Eddingtons ballon analogy only works because his ballon is a finite
size and the only ballon in much larger airspace with no other
ballons. His balloon wouldnt expand if there was an infinity of
ballons in all directions trying to expand into ITS space.

The surface of the balloon represents space, it is not expanding
into space.

I would like to end on a slightly ddiffernt point . If lets say your
universe could expand it also follows that the speed at which two
points in an infinitely expanding universe are expanding would have to
always increase their relative speeds from each other or accelerate
away from each other.

No, that's not true. Jeff Root did a nice set of slices in a
reply to Jim and I'll pinch them here. I hope he doesn't mind.
BTW Jeff, I took the 'at' symbol out as it turns the line into
an email address in Outlook Express :-(

This is Jeff's original. It shows each letter moving away from A.
More distant letters are moving faster because the line slope
more steeply. The speed for each is constant because the letters
are in straight lines:

Time
----
0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz...
1 A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z-a-b-c
2 A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--
3 A---B---C---D---E---F---G---H---I---J---K---L---M---N---O
4 A----B----C----D----E----F----G----H----I----J----K----L-
5 A-----B-----C-----D-----E-----F-----G-----H-----I-----J--
6 A------B------C------D------E------F------G------H------I
7 A-------B-------C-------D-------E-------F-------G-------H
8 A--------B--------C--------D--------E--------F--------G--
9 A---------B---------C---------D---------E---------F------


Up to about a decade ago, it was assumed that gravity slowed
expansion so the pattern was expected to look like this:

0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz...
3 A----B----C----D----E----F----G----H----I----J----K----L-
6 A-------B-------C-------D-------E-------F-------G-------H
9 A---------B---------C---------D---------E---------F------

I've only done every third because ASCII doesn't have the
resolution, hence I needed a ninth row. Look at the curve
produced by the 'B' sequence. It starts by moving rapidly
but moves a smaller distance between each map.

This is like the sheets above expanding from 10cm to 12cm
in the first second, 12cm to 13cm is the next second and
from 13cm to 13.5cm in third second. The speed of each
distant sheet centre would be decelerating.

However, measurements suggest 'dark energy', whatever that
may turn out to be, is causing the expansion to accelerate.
Simple acceleration would look like this:

0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz...
3 A--B--C--D--E--F--G--H--I--J--K--L--M--N--O--P--Q--R--S--
6 A-----B-----C-----D-----E-----F-----G-----H-----I-----J--
9 A---------B---------C---------D---------E---------F------

Again note that 'B' moves two across between '0' and '3',
three from '3' to '6' and four from '6' to '9'. Although
the rate is changing, if every sheet in our map is behaving
the same way at the same time, there will still be no gaps
or overlaps.

Put them together and you get what the measurements tell us
seems to be actually happening:

0 ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwx yz...
1 A----B----C----D----E----F----G----H----I----J----K----L-
2 A-------B-------C-------D-------E-------F-------G-------H
3 A---------B---------C---------D---------E---------F------
4 A----------B----------C----------D----------F----------G-
5 A-----------B-----------C-----------D-----------E--------
6 A-------------B-------------C-------------D-------------E
7 A----------------B----------------C----------------D-----
8 A--------------------B--------------------C--------------
9 A-------------------------B-------------------------C----


And the farther away from each other those
points are the faster they have to move away from each other. Its odd
then that supposedly observations recently have been made that imply
that the universe expansion is accelerating. Because in your model of
an expanding BB universe it does seem that any two points would have
to accelerate away from each other to accomadate the expansion of your
universe. Interesting, but only if infinity could expand which I
dont beleive it can and only if those supernova observations correctly
imply that the universe is expanding.

It's a fascinating subject and we are here at a time when
modern telescopes are showing us more than we have ever
imagined. Making sense of it isn't simple, and I still expect
a few surprises. Still it's fun trying to keep up with it all :-)

best regards
George

Jim Greenfield replied to Jeff Root:

Do you agree with all of this?

Yes?, but see below- endless lines expanding? uh uh

You agree but you don't agree? Could you be more clear
than "uh uh"? :-)

If you still have a problem with an endless line of letters
expanding, tell us what that problem is.

Tie your rubber band to my nose. Start to stretch it, and if I
could maintain a view of the whole, your diagram (and Georges)
stacks up. But I can only see F (end of band) as it was BEFORE
stretching. At that time it was travelling at 3000km/sec (distant
red shift). You are taking the view that I can still see ALL OF
the band at once, now.

I was writing about a line of letters on your monitor screen,
or a rubber band. Neither of those is moving at 3000 km/s, and
red shift is not a factor in what I was describing and asking
whether you agreed.

What I described was expansion. What I was asking you was
whether you agree that:

1) The letters remain uniformly distributed along the length
of the line
2) The letters move apart from each other at different speeds
(the farther apart two letters are at a given point in time,
the faster they are moving apart)
3) There is no limit to the length of the line-- it could even
be endless.

As it happens, I don't believe that an infinite amount of
matter could be taking part in the expansion of the Universe.
It strikes me as being physically unlikely to the point of
absurdity. However, the amount of matter actually visible in
the Universe is already absurdly huge, and there is no logical,
mathematical, or geometric reason why it couldn't be infinite.
But all that is irrelevant to the ideas I described and the
questions I'm asking.

To answer the questions, you do not even need to know that
there is such a thing as light. This is pure kinematics--
and almost pure arithmetic.

-- Jeff, in Minneapolis

..

Bjoern Feuerbacher asked Jim Greenfield:

BTW, did you miss my last three posts, too?

In the thread "Popping The Big Bang"? Posted October 22?

-- Jeff, in Minneapolis

..

It's from a book I got as a child called "Mathematics and the
Imagination" by Kasner and Newman. I really had to shake the
dust off that one!

That title sounds familiar, though the authors do not. Could
you describe the book? I think it would be cool if I've read
it, too. I might have checked it out of the school library.

-- Jeff (wearing no at), in Minneapolis

..