Sizing up the Universe
Microwave mismatch proves our cosmos is a whopper.
18 May 2004
MARK PEPLOW

How big is the universe? It is one of the oldest questions in science, and the answer could be anything from "slightly bigger than the area of the universe that we can see" to "infinite".

Until now. Cosmologists scrutinizing patterns in the microwave radiation 'afterglow' of the big bang have taken a big chunk out of that uncertainty. They calculate that the universe cannot possibly be smaller than a hefty 78 billion light years across.

That rules out earlier suggestions that the universe could be a relatively small shape wrapped around itself. A recent suggestion that the cosmos could be shaped like a soccer ball1, for example, would have meant that the universe was just 60 billion light years across.

"There is not much room left for the small universe hypothesis," says Neil Cornish, a physicist from Montana State University, Bozeman, who led the study, due to be published in Physical Review Letters2,3.

Edge of space

If the universe were relatively small, it would not necessarily be that obvious because it would not have to have an edge. Space could be wrapped in on itself, like a video game where characters disappearing off one side of the screen instantly reappear on the other.

If that were the case, light from a distant object would be able to reach us along more than one path, just as one could travel from the North Pole to the South Pole along any number of different straight paths around our planet's curved surface. So we should be able to see light from the same object arriving from apparently different directions.

"In principle, it would not be ridiculous to see light from the Earth that has wrapped around the Universe, so we could see the Earth as it was when, say, life formed 4 billion years ago," says Cornish.

To test whether light was being wrapped around in this way, Cornish and his team analysed data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), which detects microwave radiation from just 379,000 years after the universe began.

If light from the same object was arriving from different directions, the researchers calculated that this should produce circular patterns of hot and cold spots in the radiation.

"But we did not find any statistically significant circle matches," says Cornish. He concludes that the universe must be larger than 78 billion light years across, much larger than the 28 billion light years or so that we can see with our telescopes.

Cornish believes that further observations by WMAP may push that minimum size limit up to about 90 billion light years. The probe lies 1.5 million kilometres from Earth, where it can detect temperature differences of just 20 millionths of a degree in the microwave background radiation.

References
Luminet, J.-P. et al. Nature, 425, 593 - 595, doi:10.1038/nature01944 (2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Preprint, http://arxiv.org/abs/astro-ph/0310233 (2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Phys. Rev. Lett., in press, (2004).


© Nature News Service / Macmillan Magazines Ltd 2004

From Natu
http://www.nature.com/nsu/040517/040517-3.html

Comment:
This must also push the age of the universe up substantially, and also introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far enough into space, I would also see far enough back in time to see the universe when it was very small. In principle, I should be able to see the matter (even if only the hydrogen and helium gas) from which the solar system, or at least the Milky Way, was formed.

As the shortest path through space AND time is via the light that strikes my instrument, how did the Earth outrun the light by such a margin that it took 45 billion years to reach my lens (if the universe is 90 billion light years across, then the light that strikes my 'lens' has been on its way for 45 billion years.)

But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;
B) radiation which has travelled from the furthest distance/earliest period in our universes' history;
C) light which is at least 35 billion years old (for a 70 billion light year universe) or 45 billion years (for a 90 billion light years universe).

So what happens to the 12~15 billion year estimate for the age of the universe?

--
Posted by
Robert Karl Stonjek.

Robert Karl Stonjek wrote:
Sizing up the Universe
Microwave mismatch proves our cosmos is a whopper.
18 May 2004
MARK PEPLOW
How big is the universe? It is one of the oldest questions in science,
and the answer could be anything from "slightly bigger than the area of
the universe that we can see" to "infinite".

Until now. Cosmologists scrutinizing patterns in the microwave radiation
'afterglow' of the big bang have taken a big chunk out of that
uncertainty. They calculate that the universe cannot possibly be smaller
than a hefty 78 billion light years across.

That rules out earlier suggestions that the universe could be a
relatively small shape wrapped around itself. A recent suggestion that
the cosmos could be shaped like a soccer ball1, for example, would have
meant that the universe was just 60 billion light years across.

"There is not much room left for the small universe hypothesis," says
Neil Cornish, a physicist from Montana State University, Bozeman, who
led the study, due to be published in Physical Review Letters2,3.

Edge of space

If the universe were relatively small, it would not necessarily be that
obvious because it would not have to have an edge. Space could be
wrapped in on itself, like a video game where characters disappearing
off one side of the screen instantly reappear on the other.

If that were the case, light from a distant object would be able to
reach us along more than one path, just as one could travel from the
North Pole to the South Pole along any number of different straight
paths around our planet's curved surface. So we should be able to see
light from the same object arriving from apparently different directions.

"In principle, it would not be ridiculous to see light from the Earth
that has wrapped around the Universe, so we could see the Earth as it
was when, say, life formed 4 billion years ago," says Cornish.

To test whether light was being wrapped around in this way, Cornish and
his team analysed data from NASA's Wilkinson Microwave Anisotropy Probe
(WMAP), which detects microwave radiation from just 379,000 years after
the universe began.

If light from the same object was arriving from different directions,
the researchers calculated that this should produce circular patterns of
hot and cold spots in the radiation.

"But we did not find any statistically significant circle matches," says
Cornish. He concludes that the universe must be larger than 78 billion
light years across, much larger than the 28 billion light years or so
that we can see with our telescopes.

Cornish believes that further observations by WMAP may push that minimum
size limit up to about 90 billion light years. The probe lies 1.5
million kilometres from Earth, where it can detect temperature
differences of just 20 millionths of a degree in the microwave
background radiation.

References
Luminet, J.-P. et al. Nature, 425, 593 - 595, doi:10.1038/nature01944
(2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Preprint,
http://arxiv.org/abs/astro-ph/0310233 (2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Phys. Rev.
Lett., in press, (2004).


© Nature News Service / Macmillan Magazines Ltd 2004

From Natu
http://www.nature.com/nsu/040517/040517-3.html

Comment:
This must also push the age of the universe up substantially,

No. Why on earth do you think so?


and also
introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far
enough into space, I would also see far enough back in time to see the
universe when it was very small.

If the universe is infinite, saying that it was "very small" at one time
doesn't make much sense.


In principle, I should be able to see
the matter (even if only the hydrogen and helium gas) from which the
solar system, or at least the Milky Way, was formed.

Yes. Would be possible, *if* the universe is closed and *if* it had
the right curvature. But apparently, this isn't the case.



As the shortest path through space AND time is via the light that
strikes my instrument, how did the Earth outrun the light by such a
margin that it took 45 billion years to reach my lens (if the universe
is 90 billion light years across, then the light that strikes my 'lens'
has been on its way for 45 billion years.)

The earth didn't outrun anything. It was simply carried on by the
expanding space.


But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;

No. It detect light from material which was already far away from us
when the light was emitted.


B) radiation which has travelled from the furthest distance/earliest
period in our universes' history;

Yes.


C) light which is at least 35 billion years old (for a 70 billion light
year universe) or 45 billion years (for a 90 billion light years universe).

No, light which is about 13.7 billion years old, regardless of the size
of the universe.



So what happens to the 12~15 billion year estimate for the age of the
universe?

Nothing.


Bye,
Bjoern

On Wed, 19 May 2004 01:47:16 GMT, "Robert Karl Stonjek"
wrote:

Sizing up the Universe
Microwave mismatch proves our cosmos is a whopper.
18 May 2004
MARK PEPLOW

How big is the universe? It is one of the oldest questions in science, and the answer could be anything from "slightly bigger than the area of the universe that we can see" to "infinite".

Until now. Cosmologists scrutinizing patterns in the microwave radiation 'afterglow' of the big bang have taken a big chunk out of that uncertainty. They calculate that the universe cannot possibly be smaller than a hefty 78 billion light years across.

That rules out earlier suggestions that the universe could be a relatively small shape wrapped around itself. A recent suggestion that the cosmos could be shaped like a soccer ball1, for example, would have meant that the universe was just 60 billion light years across.

"There is not much room left for the small universe hypothesis," says Neil Cornish, a physicist from Montana State University, Bozeman, who led the study, due to be published in Physical Review Letters2,3.

Edge of space

If the universe were relatively small, it would not necessarily be that obvious because it would not have to have an edge. Space could be wrapped in on itself, like a video game where characters disappearing off one side of the screen instantly reappear on the other.

If that were the case, light from a distant object would be able to reach us along more than one path, just as one could travel from the North Pole to the South Pole along any number of different straight paths around our planet's curved surface. So we should be able to see light from the same object arriving from apparently different directions.

"In principle, it would not be ridiculous to see light from the Earth that has wrapped around the Universe, so we could see the Earth as it was when, say, life formed 4 billion years ago," says Cornish.

To test whether light was being wrapped around in this way, Cornish and his team analysed data from NASA's Wilkinson Microwave Anisotropy Probe (WMAP), which detects microwave radiation from just 379,000 years after the universe began.

If light from the same object was arriving from different directions, the researchers calculated that this should produce circular patterns of hot and cold spots in the radiation.

"But we did not find any statistically significant circle matches," says Cornish. He concludes that the universe must be larger than 78 billion light years across, much larger than the 28 billion light years or so that we can see with our telescopes.

Cornish believes that further observations by WMAP may push that minimum size limit up to about 90 billion light years. The probe lies 1.5 million kilometres from Earth, where it can detect temperature differences of just 20 millionths of a degree in the microwave background radiation.

References
Luminet, J.-P. et al. Nature, 425, 593 - 595, doi:10.1038/nature01944 (2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Preprint, http://arxiv.org/abs/astro-ph/0310233 (2004). |Article|
Cornish, N. J., Spergel, D. N., Starkman, D. N. & Komatsu, E. Phys. Rev. Lett., in press, (2004).


© Nature News Service / Macmillan Magazines Ltd 2004

From Natu
http://www.nature.com/nsu/040517/040517-3.html

Comment:
This must also push the age of the universe up substantially, and also introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far enough into space, I would also see far enough back in time to see the universe when it was very small. In principle, I should be able to see the matter (even if only the hydrogen and helium gas) from which the solar system, or at least the Milky Way, was formed.

As the shortest path through space AND time is via the light that strikes my instrument, how did the Earth outrun the light by such a margin that it took 45 billion years to reach my lens (if the universe is 90 billion light years across, then the light that strikes my 'lens' has been on its way for 45 billion years.)

But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;
B) radiation which has travelled from the furthest distance/earliest period in our universes' history;
C) light which is at least 35 billion years old (for a 70 billion light year universe) or 45 billion years (for a 90 billion light years universe).

So what happens to the 12~15 billion year estimate for the age of the universe?


12.4 billion x 2 pi = 78 billion around the sphere.

They said "across". The radius would be 12.4 billion years! Does that
make sense?

Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).

Comment:
This must also push the age of the universe up substantially, and also
introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far enough
into space, I would also see far enough back in time to see the universe
when it was very small. In principle, I should be able to see the matter
(even if only the hydrogen and helium gas) from which the solar system, or
at least the Milky Way, was formed.

As the shortest path through space AND time is via the light that strikes
my instrument, how did the Earth outrun the light by such a margin that it
took 45 billion years to reach my lens (if the universe is 90 billion light
years across, then the light that strikes my 'lens' has been on its way for
45 billion years.)

But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;
B) radiation which has travelled from the furthest distance/earliest
period in our universes' history;
C) light which is at least 35 billion years old (for a 70 billion light
year universe) or 45 billion years (for a 90 billion light years universe).

So what happens to the 12~15 billion year estimate for the age of the
universe?


12.4 billion x 2 pi = 78 billion around the sphere.

They said "across". The radius would be 12.4 billion years! Does that
make sense?

Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).

RKS:
There may have been an error in the article, but the relevant passage reads:
""But we did not find any statistically significant circle matches," says
Cornish. He concludes that the universe must be larger than 78 billion light
years **across**, much larger than the 28 billion light years or so that we
can see with our telescopes."

We can see 28 billion light years, not in circumference (which would work
out to just 4.4 billion light years in any direction). The most distant
objects currently seen are at around 12 billion light years.

The Hubble deep field could see objects with redshift of 7 to 12,
corresponding with a galaxies that existed between 400 and 800 million years
after the BB. See the 'Hubble Site' at

http://hubblesite.org/newscenter/new.../2004/07/text/

The article I posted says that the universe must be around three times
bigger than the universe thus far seen via telescopes.

I don't think your "make it fit" math solves the problem.

Kind Regards,
Robert Karl Stonjek.

Comment:
This must also push the age of the universe up substantially,

No. Why on earth do you think so?


RKS:
It must take more time for the universe to evolve to a 78~90 billion light
year diameter than to 24 billion light year one.


and also
introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far
enough into space, I would also see far enough back in time to see the
universe when it was very small.

If the universe is infinite, saying that it was "very small" at one time
doesn't make much sense.

RKS:
It is my understanding that the BB theory assumes a finite universe that has
existed for a finite time (since the initial inflation stage). Thus, if I
can see far enough back in time, I can see a time when the universe was
smaller (assuming that it was smaller in the past). This isn't MY theory, I
am commenting on the BB.


In principle, I should be able to see
the matter (even if only the hydrogen and helium gas) from which the
solar system, or at least the Milky Way, was formed.

Yes. Would be possible, *if* the universe is closed and *if* it had
the right curvature. But apparently, this isn't the case.


But seeing back into the past, to a time when the universe was smaller, it
must be possible to see matter from every part of that smaller universe (so
long as it glowed).


As the shortest path through space AND time is via the light that
strikes my instrument, how did the Earth outrun the light by such a
margin that it took 45 billion years to reach my lens (if the universe
is 90 billion light years across, then the light that strikes my 'lens'
has been on its way for 45 billion years.)

The earth didn't outrun anything. It was simply carried on by the
expanding space.

RKS:
The none of the matter seen locally could also be seen at a distance. It is
not possible for us to see the early universe, for instance. Or is it?


But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;

No. It detect light from material which was already far away from us
when the light was emitted.


RKS:
If the CMBR comes from the after glow of the big bang, then you are saying
that the Earth was some 10 or 20 billion light years distant at that time?
That doesn't make any sense. The CMBR comes from a period between 300
million and 1 billion years after the big bang (later estimates put it
closer to 300 million). The universe could not have been much bigger than
600 million light years across at that time assuming that the expansion rate
was at around the speed of light.

Is that "far away"? Does it take light 15 billion years to traverse the
universe when it was just 300 million years old?

If what you say is true, then we can not see the early universe because we
were not far enough away from it at the time. This doesn't seem to make
much sense.


B) radiation which has travelled from the furthest distance/earliest
period in our universes' history;

Yes.


C) light which is at least 35 billion years old (for a 70 billion light
year universe) or 45 billion years (for a 90 billion light years
universe).

No, light which is about 13.7 billion years old, regardless of the size
of the universe.

RKS:
So you are saying that it is not possible to see light, or that there isn't
any light, that comes from a point now more than 13.7 billion light years
from us?



So what happens to the 12~15 billion year estimate for the age of the
universe?

Nothing.

RKS:
Your numbers don't add up, not even approximately. It seems like a lot of
wishful thinking to me.

--
Kind Regards,
Robert Karl Stonjek.

Robert Karl Stonjek wrote:
Comment:
This must also push the age of the universe up substantially,

No. Why on earth do you think so?



RKS:
It must take more time for the universe to evolve to a 78~90 billion light
year diameter than to 24 billion light year one.

Only if we assume that it is finite.

And if it is: since we know the age of the universe from other
observations, this does simply imply that the *speed* of the expansion
was greater.


and also
introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far
enough into space, I would also see far enough back in time to see the
universe when it was very small.

If the universe is infinite, saying that it was "very small" at one time
doesn't make much sense.


RKS:
It is my understanding that the BB theory assumes a finite universe

Then your understanding is wrong.

According to the BBT, the universe can be open, flat or closed. If it is
open or flat, its volume is infinite. We can measure the geometry by a
parameter denoted by Omega. For Omega 1, it is closed, for Omega = 1,
it is flat, and for Omega 1, it is open. The measurements so far say
Omega = 0.99 +- 0.02. So we still don't know if it is open, flat or closed.


that has
existed for a finite time (since the initial inflation stage).

The "finite time" is correct. But this doesn't imply a finite size.


Thus, if I
can see far enough back in time, I can see a time when the universe was
smaller (assuming that it was smaller in the past). This isn't MY theory, I
am commenting on the BB.

Unfortunately, you seem to know not enough about the BBT.



In principle, I should be able to see
the matter (even if only the hydrogen and helium gas) from which the
solar system, or at least the Milky Way, was formed.

Yes. Would be possible, *if* the universe is closed and *if* it had
the right curvature. But apparently, this isn't the case.



But seeing back into the past, to a time when the universe was smaller, it
must be possible to see matter from every part of that smaller universe (so
long as it glowed).

No. Even if the universe is closed (and thus finite), by looking back in
time, we can't see everything in the universe. Try reading up on
"horizon". (not the event horizon of Black Holes!)



As the shortest path through space AND time is via the light that
strikes my instrument, how did the Earth outrun the light by such a
margin that it took 45 billion years to reach my lens (if the universe
is 90 billion light years across, then the light that strikes my 'lens'
has been on its way for 45 billion years.)

The earth didn't outrun anything. It was simply carried on by the
expanding space.


RKS:
The none of the matter seen locally could also be seen at a distance.

"none of the matter"? Huh?


It is
not possible for us to see the early universe, for instance. Or is it?

We can see back to a time about 380,000 years after the BB. Before that, the
universe consisted of a hot plasma in which the photons could not
propagate freely.


But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;

No. It detect light from material which was already far away from us
when the light was emitted.



RKS:
If the CMBR comes from the after glow of the big bang, then you are saying
that the Earth was some 10 or 20 billion light years distant at that time?

Distant from what??? The Big Bang didn't happen at one specific location
- it happened everywhere at once.


That doesn't make any sense. The CMBR comes from a period between 300
million and 1 billion years after the big bang (later estimates put it
closer to 300 million).

Wrong. 380,000 years.

300 million years was never in discussion, AFAIK.


The universe could not have been much bigger than
600 million light years across at that time assuming that the expansion rate
was at around the speed of light.

Saying that the expansion rate was "around the speed of light" makes no
sense. The expansion rate is measured in 1/seconds. How do you plan to
compare a number with that dimension with the speed of light?

Try reading this:
http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2
http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN
http://www.astro.ucla.edu/~wright/infpoint.html


Is that "far away"? Does it take light 15 billion years to traverse the
universe when it was just 300 million years old?

Depends on how fast the expansion was.


If what you say is true, then we can not see the early universe because we
were not far enough away from it at the time. This doesn't seem to make
much sense.

No, that is *not* what I was saying. Why on earth do you think so?




B) radiation which has travelled from the furthest distance/earliest
period in our universes' history;

Yes.



C) light which is at least 35 billion years old (for a 70 billion light
year universe) or 45 billion years (for a 90 billion light years
universe).

No, light which is about 13.7 billion years old, regardless of the size
of the universe.


RKS:
So you are saying that it is not possible to see light, or that there isn't
any light, that comes from a point now more than 13.7 billion light years
from us?

No, I did not say that. Why on earth do you think so?


So what happens to the 12~15 billion year estimate for the age of the
universe?

Nothing.


RKS:
Your numbers don't add up, not even approximately.

They do. Why on earth do you think otherwise?


It seems like a lot of wishful thinking to me.

It seems like you don't understand the BBT.

What have you read about it so far?


Bye,
Bjoern

John C. Polasek wrote:

[snip]


So what happens to the 12~15 billion year estimate for the age of the universe?



12.4 billion x 2 pi = 78 billion around the sphere.

Where did you get the number 12.4 billion from? And what sphere are you
talking about here?


They said "across". The radius would be 12.4 billion years!

The radius of what? The universe isn't a sphere.


Does that make sense?

No.


Bye,
Bjoern

Robert Karl Stonjek wrote:
Comment:
This must also push the age of the universe up substantially, and also

introduce another paradox:

If I could see, with some device (perhaps as yet undreamt of), far enough

into space, I would also see far enough back in time to see the universe
when it was very small. In principle, I should be able to see the matter
(even if only the hydrogen and helium gas) from which the solar system, or
at least the Milky Way, was formed.

As the shortest path through space AND time is via the light that strikes

my instrument, how did the Earth outrun the light by such a margin that it
took 45 billion years to reach my lens (if the universe is 90 billion light
years across, then the light that strikes my 'lens' has been on its way for
45 billion years.)

But isn't that what WMAP detects ie light coming from
A) the material which later forms the Milky Way, Solar System and Earth;
B) radiation which has travelled from the furthest distance/earliest

period in our universes' history;

C) light which is at least 35 billion years old (for a 70 billion light

year universe) or 45 billion years (for a 90 billion light years universe).

So what happens to the 12~15 billion year estimate for the age of the

universe?


12.4 billion x 2 pi = 78 billion around the sphere.

They said "across". The radius would be 12.4 billion years! Does that
make sense?

Mr. Dual Space
(If you have something to say, write an equation.
If you have nothing to say, write an essay).


RKS:
There may have been an error in the article, but the relevant passage reads:
""But we did not find any statistically significant circle matches," says
Cornish. He concludes that the universe must be larger than 78 billion light
years **across**, much larger than the 28 billion light years or so that we
can see with our telescopes."

We can see 28 billion light years, not in circumference (which would work
out to just 4.4 billion light years in any direction). The most distant
objects currently seen are at around 12 billion light years.

Wrong. It is often reported that way in popular science accounts - but
in reality, this means only that the light took 12 billion years to
reach us. The objects are much farther away from us now.
Try reading the section "Most Distant Object Record Smashed" at
http://www.astro.ucla.edu/~wright/cosmolog.htm#News, for example.


The Hubble deep field could see objects with redshift of 7 to 12,
corresponding with a galaxies that existed between 400 and 800 million years
after the BB. See the 'Hubble Site' at

http://hubblesite.org/newscenter/new.../2004/07/text/

Right.


The article I posted says that the universe must be around three times
bigger than the universe thus far seen via telescopes.

I don't think your "make it fit" math solves the problem.

Well, that's something I can agree with.


Bye,
Bjoern

"Robert Karl Stonjek" wrote

RKS:
It must take more time for the universe to evolve to a 78~90 billion light
year diameter than to 24 billion light year one.


This might be true if the Universe started out being a definite,
finite, small size and the relative velocities of its parts could not
exceed a given value. But neither of these premises is necessary.
First, the standard hypothesis is for a spatially *infinite* Universe,
which was infinite right from, or even before (given inflation), the
hot Big Bang era. The Universe expands only in the sense that a given
finite portion of the infinite space becomes larger over time. Second,
thanks to GR, space can expand at a rate such that the physical
distance between objects increases at a rate greater than c. (This is
possible if the objects are in widely-separated regions.)

Equation alert:

ds^2 = c^2 dt^2 - a^2(t) (dx^2 + dy^2 + dz^2)

ds^2 is the physical interval between two events in spacetime
separated by dt, dx, etc., a is the scale factor. If a(t) increases
then space is expanding. This can occur whether or not the space
parameterised by x,y,z is finite. If da/dt is very large, the distance
between two objects, each of which has a fixed x,y,z, value, can
increase at a rate greater than c: ds/dt = - da/dt * (delta x) for two
objects at x and x + delta x resp.

The latest results only show that if the space is finite it has to be
larger than 78 b ly across. Schematically, the maximum value of delta
x is 78 b ly at the present day.

RKS:
It is my understanding that the BB theory assumes a finite universe that has
existed for a finite time (since the initial inflation stage).

No, the Universe can be spatially infinite, or can be enormously
larger than the region currently observed.

if I can see far enough back in time, I can see a time when the universe was
smaller (assuming that it was smaller in the past).

Smaller, but still possibly much much larger than anything we can
observe.

But seeing back into the past, to a time when the universe was smaller, it
must be possible to see matter from every part of that smaller universe (so
long as it glowed).

No, we can see only those parts of the "smaller" Universe that lie on
our past light cone. In general we can't see our own butts, because
they don't satisfy the equation delta x = c delta t.

RKS:
The none of the matter seen locally could also be seen at a distance. It is
not possible for us to see the early universe, for instance. Or is it?

It's not possible for us to see the Galaxy as it was 14 b y ago,
because it is much closer than 14 b ly. We don't have light signals
that travel through time but stay in the same place! If we want to see
objects from 14 b y ago, we have to look at things that 14 b ly away
from us.

No. It detect light from material which was already far away from us
when the light was emitted.


RKS:
If the CMBR comes from the after glow of the big bang, then you are saying
that the Earth was some 10 or 20 billion light years distant at that time?
That doesn't make any sense. The CMBR comes from a period between 300
million and 1 billion years after the big bang (later estimates put it
closer to 300 million). The universe could not have been much bigger than
600 million light years across at that time assuming that the expansion rate
was at around the speed of light.

See my first comment. The Big Bang does not imply that the total
absolute size of the Universe was small at any point, only that its
size relative to today was much smaller.

RKS:
So you are saying that it is not possible to see light, or that there isn't
any light, that comes from a point now more than 13.7 billion light years
from us?


If it came from farther away, it would have to go faster than light to
get to us!

Robert Karl Stonjek wrote:
This must also push the age of the universe up substantially, and also
introduce another paradox:
If I could see, with some device (perhaps as yet undreamt of), far enough
into space, I would also see far enough back in time to see the universe
when it was very small. In principle, I should be able to see the matter
(even if only the hydrogen and helium gas) from which the solar system, or
at least the Milky Way, was formed.

There is no limit on the speed with which the universe expands.
Moreover, there is no constraint that it be spatially finite, even
though there was a big bang.

Please note that the limit of 78 billion lightyears is on the total size
of the universe, not on the visible universe. The size of the visible
universe is indeed limited to the cosmological time since the big bang,
for the simple reason that we use light to observe with. But when we say
"this quasar is 10 billion lightyears away", we are really saying that
the light from the quasar traveled 10 billion lightyears wrt
cosmological coordinates. Right now, in cosmological time, it is much
further away than that (and is probably no longer anything at all like
what we observe, because it has been evolving for 10 billion years since
it generated the image we observe).


As the shortest path through space AND time is via the light that strikes
my instrument, how did the Earth outrun the light by such a margin that it
took 45 billion years to reach my lens (if the universe is 90 billion light
years across, then the light that strikes my 'lens' has been on its way for
45 billion years.)

It doesn't work that way. See above. You are assuming that your common
notions about Euclidean space apply to cosmology; they don't. Nor can
you use notions about SR. It is essential to use GR, and apply a
reasonable model to the cosmos. What cosmologists consider to be a
"reasonable" model is evolving quite rapidly today....


Tom Roberts