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Jan 2, 1996, 3:00:00 AM1/2/96

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This is a question that has bothered me for years --

The farther out we look all around us at the universe, at the

deepest penetration our telescopes allow, the closer we come to the

origin point of the Big Bang. This is easy to grasp, since, at least

according to currently accepted theories due to Hubble, we are looking

not only at distant space but distant time.

Now, according to General Relativity, the universe has no center

in space (the famous balloon analogy). But the expanding universe theory

seems to imply that it does have an *origin* in time and the farther out

we look all around us, the farther back in time we go toward that origin

point.

This seems to lead to some fantastic paradoxes, e.g. the center of

the universe is located at the periphery (which would imply that our

universe is "inside-out"). I know that Hawking has argued that there was

no actual beginning point in time. Perhaps some extrapolation from that

argument would save us here.

The farther out we look all around us at the universe, at the

deepest penetration our telescopes allow, the closer we come to the

origin point of the Big Bang. This is easy to grasp, since, at least

according to currently accepted theories due to Hubble, we are looking

not only at distant space but distant time.

Now, according to General Relativity, the universe has no center

in space (the famous balloon analogy). But the expanding universe theory

seems to imply that it does have an *origin* in time and the farther out

we look all around us, the farther back in time we go toward that origin

point.

This seems to lead to some fantastic paradoxes, e.g. the center of

the universe is located at the periphery (which would imply that our

universe is "inside-out"). I know that Hawking has argued that there was

no actual beginning point in time. Perhaps some extrapolation from that

argument would save us here.

Jan 4, 1996, 3:00:00 AM1/4/96

to

By the way do you know where in our Universe is the center of

the space (I mean the mass center of all galaxies).?

---

Best Regards,

Hannu Poropudas.

"It's Not What You Know That Matters

... It's Knowing What You Don't."

Jan 4, 1996, 3:00:00 AM1/4/96

to

In article <4chedk$i...@geraldo.cc.utexas.edu>,

Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:

>

>: By the way do you know where in our Universe is the center of

>masses of the continents in the surface of the Earth.

Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:

>

>: By the way do you know where in our Universe is the center of

>: the space (I mean the mass center of all galaxies).?

>

>Probably it is indefined. It is like asking about a center of >

>masses of the continents in the surface of the Earth.

That's right. As far as we can tell, the Universe is roughly

homogeneous on large scales. There doesn't seem to be any special

point that you'd want to call "the center." The analogy with the

surface of the Earth is a good one. Let me expand on it just a little

bit, in case anyone missed the point.

The Universe may be spatially finite and yet have no boundary. This

initially may sound impossible, but it's not. The surface of sphere

is a two-dimensional surface that has finite area and yet has no

boundary, and one can imagine analogous three-dimensional "surfaces"

(although such objects are hard to visualize).

If the Universe is of this form, then we can get some intuition about

what's going on by considering the analogy with the spherical

surface. It's crucial to remember that in this analogy the entire

three-dimensional volume of space is being compared to the

two-dimensional surface of the sphere. It may help to imagine a

species of little two-dimensional creatures crawling around on the

surface of the sphere. Since they live in only two dimensions, they

have no idea that their world is actually "curved" into "the third

dimension." As far as they're concerned, that two-dimensional surface

is all there is.

Now, these creatures could do experiments and discover that their

world is shaped like a sphere. They might find this result surprising

at first, but they'd get used to it eventually, and they'd realize

that although their world has finite area, it has no boundary. Nor

does it have a center, at least not one that they can point to. There

is no point on the surface of the sphere that you'd call the center:

all points on the surface look exactly the same. Similarly, if our

three-dimensional Universe is curved like a sphere, it could be finite

and yet have no center.

On the other hand, our Universe might be infinite. We have no way to

tell. If it's infinite, it still might not have a center. It might

just stretch on forever, with each point looking more or less like

every other point.

In fact, if you take our observations of the distribution of stuff in

the Universe, and extrapolate them in the simplest possible way, you

find that these two possibilities (curved like a sphere or extending

forever homogeneously) are the two simplest, most natural hypotheses.

That doesn't necessarily mean that either is right, of course. The

big problem is that we can only see a finite amount of the Universe:

since the Universe is only about 15 billion years old, we can't see

anything further away than about 15 billion light-years. That

distance is known as our "horizon." The Universe seems to be pretty

much homogeneous throughout the volume enclosed by our horizon, so

it's natural to guess that maybe things continue that way outside of

the horizon, but since we can't see out there, that's just a guess.

>You can try to define it as (1/M) SUM r_i m_i, where M is

>the total mass of the universe, m_i is the mass of the i-th

>particle of the universe, r_i is a position vector of that

>particle, and the sum goes throght all the particles in the

>universe (perhaps about 10^80, I am ignoring quantum efects).

>But in a curved space there is no such a thing as "position

>vector". If you substitute it by, say, the lenght of the

>geodesic from some "fix" point taken as origin, the result

>is going to depend on the point chosen.

Absolutely right. But things are even worse than that, because that

number 10^80 is the number of particles in the *observable* Universe

(i.e., within our horizon), not the number in the whole Universe. The

observable Universe is a sphere centered on us, since it's the set of

all points close enough to us for us to see them. So even if you

could get around the problems of spatial curvature, you wouldn't get

reliable results by computing the center of mass of all of the

observable particles. If you did compute such a thing, you'd find

that the center of the Universe was right here (or pretty close to

it), simply because you've artificially restricted your attention to a

sphere centered on us, instead of considering the whole Universe.

An alien in a distant galaxy could perform the same computation

using his own observable Universe, and he'd find that *he*

was at the center instead.

-Ted

Jan 4, 1996, 3:00:00 AM1/4/96

to

Hannu Poropudas (hannu.P...@ericsson.fi) wrote:

: By the way do you know where in our Universe is the center of

: the space (I mean the mass center of all galaxies).?

Probably it is indefined. It is like asking about a center of

masses of the continents in the surface of the Earth.

You can try to define it as (1/M) SUM r_i m_i, where M is

the total mass of the universe, m_i is the mass of the i-th

particle of the universe, r_i is a position vector of that

particle, and the sum goes throght all the particles in the

universe (perhaps about 10^80, I am ignoring quantum efects).

But in a curved space there is no such a thing as "position

vector". If you substitute it by, say, the lenght of the

geodesic from some "fix" point taken as origin, the result

is going to depend on the point chosen.

Miguel A. Lerma

Jan 4, 1996, 3:00:00 AM1/4/96

to

In article <4cbi01$r...@titania.pps.pgh.pa.us>,

everything you say up to the last paragraph is more-or-less

correct (in my humble opinion!). the `fantastic paradoxes'

i think you are noticing are:

- spacetime is curved. if the universe is smaller at earlier times

then it must have a smaller volume. so volume is not increasing

as we go further and further away (back in time). one effect of

this is that the angular size of galaxies stops getting smaller

as they get further away(!). the details depend on which model

of the universe you use, but if you want more info check out

`the angular diameter distance relation' in astronomy textbooks.

- even at the big bang, for a flat or open universe, the spatial

extent of the universe is infinite. this gives me a headache if

i think about it for too long, but you might consider it

`paradoxical'....

don't forget that as we approach the moment of the big-bang

the physics becomes less and less well known as the energies get

higher and higher. the `big bang' is only a model and it becomes

more and more uncertain as we approach the initial moment

(incidentally, if anyone out there knows, to what extent are

singularity theorems immune to changing physics?)

andrew

--

work phone/fax: 0131 668 8356, office: 0131 668 8357

institute for astronomy, royal observatory, blackford hill, edinburgh

http://www.roe.ac.uk/ajcwww

Jan 4, 1996, 3:00:00 AM1/4/96

to

In article <4ch3lc$d...@scotsman.ed.ac.uk>,

Andrew Cooke <A.C...@roe.ac.uk> wrote:

> - spacetime is curved. if the universe is smaller at earlier times

> then it must have a smaller volume. so volume is not increasing

Andrew Cooke <A.C...@roe.ac.uk> wrote:

> - spacetime is curved. if the universe is smaller at earlier times

> then it must have a smaller volume. so volume is not increasing

...as fast as you would expect...

> as we go further and further away (back in time). one effect of

> this is that the angular size of galaxies stops getting smaller

> as they get further away(!).

andrew

(just thought i better correct that!)

Jan 4, 1996, 3:00:00 AM1/4/96

to

'gra...@oberon.pps.pgh.pa.us (Victor Grauer)' wrote:

>This is a question that has bothered me for years --

Perhaps you will let me clear some things up then? >This is a question that has bothered me for years --

> The farther out we look all around us at the universe, at the

>deepest penetration our telescopes allow, the closer we come to the

>origin point of the Big Bang. This is easy to grasp, since, at least

>according to currently accepted theories due to Hubble, we are looking

>not only at distant space but distant time.

at distant time" just follows from the finite speed of light.

> Now, according to General Relativity, the universe has no center

>in space (the famous balloon analogy).

matter. What you describe may be a feature of a particular *solution* to

the field equations, but so far as I know is not a necessary feature of

all solutions.

>But the expanding universe theory

>seems to imply that it does have an *origin* in time and the farther out

>we look all around us, the farther back in time we go toward that origin

>point.

> This seems to lead to some fantastic paradoxes, e.g. the center of

>the universe is located at the periphery (which would imply that our

>universe is "inside-out").

out in all directions, we are really be looking at the same distant region

of space. We cannot look far enough out to see times right after the Big

Bang, so we cannot see all the way around the balloon to a point, but

merely see the perimeter of some "hidden region" (spooky).

Now, even assuming a universe with this topology, the distant region we

see in all directions is by no means special... it's more like our

antipode on the balloon. We happen to see it an earlier epoch, but it's

not "closer" to the "center". Heck, you just got through telling us that

the universe has no center :-) The Big Bang "happened" "everywhere" at

once, and the residual radiation that is supposed to be its signature is

permeating space.

In a nutshell, your "center is at the periphery" paradox mixes time and

space. Even relativity preserves *some* distinction. You can forget about

the balloon and see the situation clearly in a one-dimensional "rubber

band" universe, with signals of finite speed propagating around the band.

The Big Bang is the extrapolated time when the infinitesimal band first

popped into being. :-)

Suggestions for further handwaving:

Since we can't see 'round and 'round our universe, does this mean the

expansion was at some time faster than light? Or that now distant regions

of space have never communicated since the dawn of time? Strange. Then

again, everything in cosmology is strange. All cosmologies are

inconceivable, and yet one simply *is*.

Disclaimer:

This reply has started in certainty and ended in speculation. An

increasing density of "so far as I know" is to be assumed to the extent

necessary to vacate false assertions. :-)

>...Hawking has argued that there was

>no actual beginning point in time. Perhaps some extrapolation from that

>argument would save us here.

Save us from what? >argument would save us here.

--

Ed Green

egr...@nyc.pipeline.com

Jan 5, 1996, 3:00:00 AM1/5/96

to

In article <4cj3u2$m...@pipe10.nyc.pipeline.com>,

Edward Green <egr...@nyc.pipeline.com> wrote:

>'t...@physics2.berkeley.edu (Emory F. Bunn)' wrote:

>

>>The

>>big problem is that we can only see a finite amount of the Universe:

>>since the Universe is only about 15 billion years old, we can't see

>>anything further away than about 15 billion light-years.

>

>Then I misspoke. So we can see features that were formed right after the

>big bang.

Edward Green <egr...@nyc.pipeline.com> wrote:

>'t...@physics2.berkeley.edu (Emory F. Bunn)' wrote:

>

>>The

>>big problem is that we can only see a finite amount of the Universe:

>>since the Universe is only about 15 billion years old, we can't see

>>anything further away than about 15 billion light-years.

>

>big bang.

just after the `big bang' everything was so hot that photons were

continually scattering off particles (mainly electrons).

as things expanded and cooled this became less important, and

the effective change was actually quite sudden - so we can see

back to a certain point, but then no further because it is

`misty' due to all the scattering.

this `misty' early universe is what people are looking at when

they look at fluctuations in the microwave background. since

the universe was still expanding very rapidly at that time it

is at a very high redshift (about 1000 if i remember correctly).

that's why people were so interested in the fluctuations - they

were the very beginnings of the structures that are now galaxies.

and they are only just big enough (if they hadn't been seen people

would have had big problems because it would have been too smooth

to form the universe we have today).

andrew

Jan 5, 1996, 3:00:00 AM1/5/96

to

In <4cif07$f...@lmfpub.lmf.ericsson.se> Hannu.P...@ericsson.fi (Hannu Poropudas) writes:

>Earth have a center, but it is outside of Earth's surface.

Correct! The center of Earth's surface is not on the surface.

And the same is true of the universe: the center of the universe

is not in the universe. It lies outside the universe, 15 billion

or so years in the past. The center is not "near the center of

Virgo Super Cluster" or anywhere else accessible to us.

Jan 5, 1996, 3:00:00 AM1/5/96

to

I think the question might be better stated as: Where would be the center

of the universe in 3-dimensional space? To answer this would require

knowledge of the actual 'shape' of the universe in that space, and I

don't believe anyone actually agrees on that.

of the universe in 3-dimensional space? To answer this would require

knowledge of the actual 'shape' of the universe in that space, and I

don't believe anyone actually agrees on that.

--

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Paul J. Kossick Standing on a hill in my mountain of dreams

kos...@crl.com Telling myself it's not as hard, hard, hard as it seems

*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*

Jan 5, 1996, 3:00:00 AM1/5/96

to

In article <4chedk$i...@geraldo.cc.utexas.edu>

which is dated 4 Jan 1996 20:47:48 GMT

mle...@arthur.ma.utexas.edu (Miguel Lerma) wrote:

>Hannu Poropudas (hannu.P...@ericsson.fi) wrote:

>

>: By the way do you know where in our Universe is the center of

>: the space (I mean the mass center of all galaxies).?

>

>Probably it is indefined. It is like asking about a center of

>masses of the continents in the surface of the Earth.

>

Earth have a center, but it is outside of Earth's surface.

Perhaps center of the space (center of all galaxies) is

outside of visible Universe, perhaps in the side of

contracting part of it (please take a look of README-articles

in my directory mentioned below).?

Perhaps it could be somewhere near center of Virgo Super Cluster.

Perhaps in invisible center of M87.?

>You can try to define it as (1/M) SUM r_i m_i, where M is

>the total mass of the universe, m_i is the mass of the i-th

>particle of the universe, r_i is a position vector of that

>particle, and the sum goes throght all the particles in the

>universe (perhaps about 10^80, I am ignoring quantum efects).

>But in a curved space there is no such a thing as "position

>vector". If you substitute it by, say, the lenght of the

>geodesic from some "fix" point taken as origin, the result

>is going to depend on the point chosen.

>

>

>Miguel A. Lerma

Sure there is no such a thing as "position vector" in a curved

space. You have to generalize vector concept to be as "directed

geodesic line" in a curved space. You have to define also how

to add, subtract and multiply by scalar these "directed geodesic

lines". For example on two dimensional sphere surface you can

define multiplication and division of these "directed geodesic

lines". One problem remain and that is how to define these

four operations for these objects which starts from different

points on the sphere. Also this "algebra" has two characteristic

features, namely non-associativity and non-distributivity.

Please take a look at my trial in WWW.FUNET.FI (or FTP.FUNET.FI)

and directory pub/doc/misc/HannuPoropudas article is PostScript

file called surface_algebras.Z.

Jan 5, 1996, 3:00:00 AM1/5/96

to

On 4 Jan 1996, Hannu Poropudas wrote:

>

> By the way do you know where in our Universe is the center of

> the space (I mean the mass center of all galaxies).?

>

>

> ---

>

>

> Best Regards,

>

> Hannu Poropudas.

In the beginning, the Universe issued from a single point, and was

composed of a at least 11 dimensions. Then the universe became unstable,

and all but 3 of the dimensions collapsed, releasing tremendous energies,

and causing the center of the universe to actualy detach and become a

free wandering anomolie. The Center of the Universe has been wandering

around ever since, and has been sought after by the various civilizations

and species of the galaxy since the dawn of life. It is said that

whomsoever possesses the true center of the universe possesses infinite

power to reshape reality and bend others to his will...

Dave

ps--if any hollywood types wish to use the above for the

plot of a movie or something, dont forget my check...

Jan 5, 1996, 3:00:00 AM1/5/96

to

Hannu Poropudas (Hannu.P...@ericsson.fi) wrote:

[...]

: Earth have a center, but it is outside of Earth's surface.

[...]

: Earth have a center, but it is outside of Earth's surface.

I guess the closest to this idea is what Richard A. Schumacher says

in his post: the center is 15 million years in the past (Big Bang).

But I think this assumes that only the 3-space is curved, and that

the whole 4-dimensional manifold made up with the whole past, present

and future history of the universe is Euclidean. It is still possible

that the universe is even more complicated than that. I think Hawking

suggested that the whole 4-dimensional manifold is curved, and that

the Big Bang and the Big Cruch are just points like any other

else except for the fact that in a certain system of cordinates

all coordinates except one (i.e.: the three spacial coordinates

but not time) converge there (something similar to what happens

in the surface of the Earth with meridians and paralels). If that

is so, then the "center" of the universe can be conceived only

with help of a fith dimension, so than the universe is a 4-sphere

inmersed in a 5-dimencional Euclidean space.

Miguel A Lerma

Jan 5, 1996, 3:00:00 AM1/5/96

to

In article <4cjt0c$4...@crl2.crl.com>, Paul J. Kossick <kos...@crl.com> wrote:

>I think the question might be better stated as: Where would be the center

>of the universe in 3-dimensional space? To answer this would require

>knowledge of the actual 'shape' of the universe in that space, and I

>don't believe anyone actually agrees on that.

>I think the question might be better stated as: Where would be the center

>of the universe in 3-dimensional space? To answer this would require

>knowledge of the actual 'shape' of the universe in that space, and I

>don't believe anyone actually agrees on that.

I'm not sure I understand what you mean here. Space, as far as we can

tell, looks like a three-dimensional manifold. It fills all of

three-dimensional space, more or less by definition, and so it doesn't

have a "shape in 3-dimensional space." It seems to me that one only

talks about the "shape" of something if the something is embedded in

some larger volume. For example, we might talk about the shape of a

spherical volume that's embedded in a larger three-dimensional space.

But since the Universe doesn't seem to be embedded in a larger

three-dimensional space, I don't know what meaning one would attach to

a phrase like "the shape of the Universe in three-dimensional space."

If you like, you can choose to imagine that the Universe is embedded

in some space of a larger number of dimensions. This is a useful

thing to do when trying to get some intuition about curved spacetime,

although we have no particular reason to believe that space really is

embedded in such a way. In this context, it would make sense to talk

about the shape of the Universe within this larger (four or more

dimensional) space.

-Ted

Jan 5, 1996, 3:00:00 AM1/5/96

to

>The

>big problem is that we can only see a finite amount of the Universe:

>since the Universe is only about 15 billion years old, we can't see

>anything further away than about 15 billion light-years.

>big problem is that we can only see a finite amount of the Universe:

>since the Universe is only about 15 billion years old, we can't see

>anything further away than about 15 billion light-years.

Then I misspoke. So we can see features that were formed right after the

big bang.

-- big bang.

Ed Green

egr...@nyc.pipeline.com

Jan 5, 1996, 3:00:00 AM1/5/96

to

In article <4cjj8k$7...@pipe11.nyc.pipeline.com>,

Edward Green <egr...@nyc.pipeline.com> wrote:

>'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

>> as things expanded and cooled this became less important, and

>> the effective change was actually quite sudden - so we can see

>> back to a certain point, but then no further because it is

>> `misty' due to all the scattering.

>The I assume this era was relatively brief by current models. A million

>years? A thousand? A nanosecond?

Edward Green <egr...@nyc.pipeline.com> wrote:

>'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

>> as things expanded and cooled this became less important, and

>> the effective change was actually quite sudden - so we can see

>> back to a certain point, but then no further because it is

>> `misty' due to all the scattering.

>years? A thousand? A nanosecond?

i can't remember. certainly not long compared to the age of

the universe. it would also depend on the details of the model

(density, inflation, etc).

i *should know* (and so should my office mate!) - i'll check it

when i'm next in the library.

>> this `misty' early universe is what people are looking at when

>> they look at fluctuations in the microwave background. since

>> the universe was still expanding very rapidly at that time it

>> is at a very high redshift (about 1000 if i remember correctly).

>

>I though I remembered the explanation that this radiation had "cooled".

>Now I suppose cooling can be distinguished form a straight red-shift by

>spectral signature. This is the "4K" background radition I take it.

>Comment?

yes, it was cooling and expanding and yes, it's the 4(3?)K

background - at a redshift of 1000 it would be at a temperature

of 4 x 10^12 K - a lot hotter!

when i say `redshift of 1000' i mean that if there was something

at that distance then, if we could observe a recognisable

spectrum, it would have a redshift of 1000 (ish). in practice

you are not going to able to do that because there wasn't any

significant line emission (the universe was in almost perfect

thermal equilibrium?). so all i am doing is giving the redshift

from a mathematical model, not an observed measurement. the

most distant things we *observe* (apart from the structure in

the microwave background) have a redshift of about 5.

for a `black body' (which is the spectrum of the background) you

can't measure a redshift - at different redshifts you just have

different temperature black bodies!

hope that makes sense,

Jan 5, 1996, 3:00:00 AM1/5/96

to

hannu.P...@ericsson.fi (Hannu Poropudas) writes:

-> By the way do you know where in our Universe is the center of

-> the space (I mean the mass center of all galaxies).?

This is an interesting question. I believe some of the hyperspace equations

show that if the universe is closed then there is no center, or alternative

every point can be viewed as the center. Of course to see this requires

viewing in more than 3 dimensions, but an analogy is to view the earth's 2

dimensions from 3 dimensions, and then it is obvious that no point on the

surface of the earth is the center, and that every point can also be viewed as

the center, since all other points on the surface are symetrically surrounding

it.

Marshall

-> By the way do you know where in our Universe is the center of

-> the space (I mean the mass center of all galaxies).?

This is an interesting question. I believe some of the hyperspace equations

show that if the universe is closed then there is no center, or alternative

every point can be viewed as the center. Of course to see this requires

viewing in more than 3 dimensions, but an analogy is to view the earth's 2

dimensions from 3 dimensions, and then it is obvious that no point on the

surface of the earth is the center, and that every point can also be viewed as

the center, since all other points on the surface are symetrically surrounding

it.

Marshall

Jan 5, 1996, 3:00:00 AM1/5/96

to

'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

> just after the `big bang' everything was so hot that photons

were

> continually scattering off particles (mainly electrons).

>

> just after the `big bang' everything was so hot that photons

were

> continually scattering off particles (mainly electrons).

>

> as things expanded and cooled this became less important, and

> the effective change was actually quite sudden - so we can see

> back to a certain point, but then no further because it is

> `misty' due to all the scattering.

The I assume this era was relatively brief by current models. A million

years? A thousand? A nanosecond?

> the effective change was actually quite sudden - so we can see

> back to a certain point, but then no further because it is

> `misty' due to all the scattering.

The I assume this era was relatively brief by current models. A million

years? A thousand? A nanosecond?

> this `misty' early universe is what people are looking at when

> they look at fluctuations in the microwave background. since

> the universe was still expanding very rapidly at that time it

> is at a very high redshift (about 1000 if i remember correctly).

I though I remembered the explanation that this radiation had "cooled".

Now I suppose cooling can be distinguished form a straight red-shift by

spectral signature. This is the "4K" background radition I take it.

Comment?

> they look at fluctuations in the microwave background. since

> the universe was still expanding very rapidly at that time it

> is at a very high redshift (about 1000 if i remember correctly).

I though I remembered the explanation that this radiation had "cooled".

Now I suppose cooling can be distinguished form a straight red-shift by

spectral signature. This is the "4K" background radition I take it.

Comment?

> that's why people were so interested in the fluctuations - they

> were the very beginnings of the structures that are now galaxies.

> and they are only just big enough (if they hadn't been seen people

> would have had big problems because it would have been too smooth

> to form the universe we have today).

-- > were the very beginnings of the structures that are now galaxies.

> and they are only just big enough (if they hadn't been seen people

> would have had big problems because it would have been too smooth

> to form the universe we have today).

Ed Green

egr...@nyc.pipeline.com

Jan 5, 1996, 3:00:00 AM1/5/96

to

Edward Green (egr...@nyc.pipeline.com) wrote:

: 'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

:

: > just after the `big bang' everything was so hot that photons

: were

: > continually scattering off particles (mainly electrons).

: >

: > as things expanded and cooled this became less important, and

: > the effective change was actually quite sudden - so we can see

: > back to a certain point, but then no further because it is

: > `misty' due to all the scattering.

:

: The I assume this era was relatively brief by current models. A million

: years? A thousand? A nanosecond?

: 'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

:

: > just after the `big bang' everything was so hot that photons

: were

: > continually scattering off particles (mainly electrons).

: >

: > as things expanded and cooled this became less important, and

: > the effective change was actually quite sudden - so we can see

: > back to a certain point, but then no further because it is

: > `misty' due to all the scattering.

:

: The I assume this era was relatively brief by current models. A million

: years? A thousand? A nanosecond?

A few hundred thousand years. Pretty brief.

:

: > this `misty' early universe is what people are looking at when

: > they look at fluctuations in the microwave background. since

: > the universe was still expanding very rapidly at that time it

: > is at a very high redshift (about 1000 if i remember correctly).

:

: I though I remembered the explanation that this radiation had "cooled".

: Now I suppose cooling can be distinguished form a straight red-shift by

: spectral signature. This is the "4K" background radition I take it.

: Comment?

Yes. The temperature at recombination was some 3000 to 4000 K (it helps

to look things up; I almost told you the time at recombination was 3000

years, but that was the temperature I had remembered :-).

The cooling is different from a red shift. A red shift tells you a

relative velocity, while the temperature refers to a _random_ velocity

(in this case, momentum, since we're speaking of photons after

recombination).

BTW... recombination refers to the capturing of the free electrons in

the 'cosmic soup' by protons. Before this time, you had several species

of particle -- which mix is a function of the temperature and density --

all interacting via scattering. This keeps all the constituent

temperatures the same. So right before recombination everything had the

same temperature -- about 3000 K -- and right afterward, the radiation

bath and hydrogen bath still had the same temperature. But afterward

they evolved independently; the photon bath cools as the 'scale factor'

R expands (T is inversely proportional to R).

It is called "re"-combination because the physical process involved is

seen in the lab after you ionise a gas. A bit of historical baggage.

source:

J N Islam, An Introduction to Mathematical Cosmology (Cambridge, 1992)

--

Mach's gut!

Bruce Scott The deadliest bullshit is

Max-Planck-Institut fuer Plasmaphysik odorless and transparent

b...@ipp-garching.mpg.de -- W Gibson

Jan 6, 1996, 3:00:00 AM1/6/96

to

If, at the farthest reaches of space in all directions we see extremely

red shifted photons which are relics of a time very close to the time of

the big bang, then, to me, this clearly means that the center of the

universe is at the periphery.

red shifted photons which are relics of a time very close to the time of

the big bang, then, to me, this clearly means that the center of the

universe is at the periphery.

Jan 6, 1996, 3:00:00 AM1/6/96

to

Victor Grauer (gra...@oberon.pps.pgh.pa.us) wrote:

: If, at the farthest reaches of space in all directions we see extremely

: If, at the farthest reaches of space in all directions we see extremely

: red shifted photons which are relics of a time very close to the time of

: the big bang, then, to me, this clearly means that the center of the

: universe is at the periphery.

: the big bang, then, to me, this clearly means that the center of the

: universe is at the periphery.

Don't forget you are looking back in time. As someone else said, this

means the center of the universe is its beginning.

[At t=0 in the standard model, the curvature is infinite for all values

of the other three coordinates.]

Jan 6, 1996, 3:00:00 AM1/6/96

to

In article <4cm998$j...@titania.pps.pgh.pa.us>,

Victor Grauer <gra...@oberon.pps.pgh.pa.us> wrote:

>If, at the farthest reaches of space in all directions we see extremely

>red shifted photons which are relics of a time very close to the time of

>the big bang, then, to me, this clearly means that the center of the

>universe is at the periphery.

Victor Grauer <gra...@oberon.pps.pgh.pa.us> wrote:

>If, at the farthest reaches of space in all directions we see extremely

>red shifted photons which are relics of a time very close to the time of

>the big bang, then, to me, this clearly means that the center of the

>universe is at the periphery.

That conclusion doesn't follow. When we look at the farthest reaches

of space, we are looking far into the past, since light from those

points has taken a long time to reach us. In fact, the limit on the

furthest points we can see is set by the age of the Universe: we can't

see objects further than about 15 billion light-years, since light

from more distant objects hasn't had time to reach us.

So when we look at the furthest objects we can see, we're necessarily

going to be seeing them as they were when the Universe was very

young. That's why points near the edge of the observable Universe

look like they're "close to the big bang". They're not *spatially*

any closer to the center than we are. The light we see from those

points did originate from *times* close to the big bang, but that's

just because we happen to be looking at those points from very far

away; it's not anything special about that region of space.

Here's another way to put it. At this very moment there could be a

race of creatures in a galaxy at the edge of our observable Universe.

If they look our way, they will see radiation that left our patch of

space shortly after the moment of the big bang. They might conclude

that our patch of space is "close to the big bang", just as we might

conclude the same thing from our observations of their patch of

space. But we'd both be wrong.

-Ted

Jan 6, 1996, 3:00:00 AM1/6/96

to

On Jan 05, 1996 17:26:27 in article <Re: Center of Universe?>,

'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

>

> for a `black body' (which is the spectrum of the background) you

> can't measure a redshift - at different redshifts you just have

> different temperature black bodies!

Yes, I see what you mean. A constant factor in the frequency cannot be

distinguished from an equivalent change in temperature. My thanks to Emory

Bunn also for mentioning this.

'b...@ipp-garching.mpg.de (Bruce Scott TOK )' was kind enough to look up

some numbers and also wrote:

>The cooling is different from a red shift. A red shift tells you a

>relative velocity, while the temperature refers to a _random_ velocity

>(in this case, momentum, since we're speaking of photons after

>recombination).

Conceptually different, no doubt. But practically, if we can't

distinguish red shift from cooling, is that trying to tell us something?

Or this only an incredible coincidence brought on by lack of mathematical

imagination on the part of the universe?

(Not a rhetorical question, but I don't necessarily expect an answer)

Now, to shift gears, I've been trying my hand as a pro-aether crank

recently :-) , and when

't...@physics2.berkeley.edu (Emory F. Bunn)' writes:

>All that matters is that

>the expansion of the Universe stretched the wavelengths of all of

>those photons by a factor of 1100.

why that just gives me verbal fodder!

From a cosmological point of view it's apparent we regard the idea that

space is a *stuff* and matter in energy are embedded in that *stuff* as the

mildest milque-toast; indeed, isn't that the meta-model of GR, which

Einstein is supposed to have regarded as evidence for an aether?

This successful 'reification' of space seems to stand in spendid isolation,

a problem we sometimes describe as requiring the "quantization of

gravity", but may equally well require the "general relativization of the

remaining forces" . (Let me put myself out on a limb; when this happens,

I think virtual particles will be seen as a calculational method only)

Someday I hope to tell you what I think a string is, but not too soon.

I just can't model it mathematically at the moment. :-( :-(

--

Ed Green

egr...@nyc.pipeline.com

'a...@reaxp01.roe.ac.uk (Andrew Cooke)' wrote:

>

> for a `black body' (which is the spectrum of the background) you

> can't measure a redshift - at different redshifts you just have

> different temperature black bodies!

distinguished from an equivalent change in temperature. My thanks to Emory

Bunn also for mentioning this.

'b...@ipp-garching.mpg.de (Bruce Scott TOK )' was kind enough to look up

some numbers and also wrote:

>The cooling is different from a red shift. A red shift tells you a

>relative velocity, while the temperature refers to a _random_ velocity

>(in this case, momentum, since we're speaking of photons after

>recombination).

distinguish red shift from cooling, is that trying to tell us something?

Or this only an incredible coincidence brought on by lack of mathematical

imagination on the part of the universe?

(Not a rhetorical question, but I don't necessarily expect an answer)

Now, to shift gears, I've been trying my hand as a pro-aether crank

recently :-) , and when

't...@physics2.berkeley.edu (Emory F. Bunn)' writes:

>All that matters is that

>the expansion of the Universe stretched the wavelengths of all of

>those photons by a factor of 1100.

why that just gives me verbal fodder!

From a cosmological point of view it's apparent we regard the idea that

space is a *stuff* and matter in energy are embedded in that *stuff* as the

mildest milque-toast; indeed, isn't that the meta-model of GR, which

Einstein is supposed to have regarded as evidence for an aether?

This successful 'reification' of space seems to stand in spendid isolation,

a problem we sometimes describe as requiring the "quantization of

gravity", but may equally well require the "general relativization of the

remaining forces" . (Let me put myself out on a limb; when this happens,

I think virtual particles will be seen as a calculational method only)

Someday I hope to tell you what I think a string is, but not too soon.

I just can't model it mathematically at the moment. :-( :-(

--

Ed Green

egr...@nyc.pipeline.com

Jan 6, 1996, 3:00:00 AM1/6/96

to

Emory F. Bunn (t...@physics2.berkeley.edu) wrote:

> In article <4ck30f$b...@geraldo.cc.utexas.edu>,

> Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

> >I guess the closest to this idea is what Richard A. Schumacher says

> >in his post: the center is 15 million years in the past (Big Bang).

> In article <4ck30f$b...@geraldo.cc.utexas.edu>,

> Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

> >I guess the closest to this idea is what Richard A. Schumacher says

> >in his post: the center is 15 million years in the past (Big Bang).

> You mean "billion" rather than "million." Specifically, I should

> point out for the benefit of non-U.S. readers that I mean a

> U.S. billion, 1000000000, not a U.K. billion, which is 1000 times

> bigger. (I think even Nature uses "billion" in the U.S. sense

> now, by the way.)

Right, I meant (US) "billion". Sorry.

> >But I think this assumes that only the 3-space is curved, and that

> >the whole 4-dimensional manifold made up with the whole past, present

> >and future history of the universe is Euclidean.

> I can't speak for Richard Shumacher, but I can tell you that this isn't

> how I interpreted what he wrote. Standard theories of cosmology

> are based on the theory of general relativity. In general relativity,

> spacetime is modeled as a four-dimensional manifold, but definitely

> not a Euclidean one. Spacetime has curvature in all of these models.

[...]

Your remarks are perfectly sound. I was just playing around with

"naive" models of the universe, just to see in what extent they

could provide some meaning to the original question. In particular,

the idea that places the "center" of the universe in the Big Bang

comes from a model in which the universe is like a balloon growing

from an initial point, and the radial coordinate would be the time.

The center would correspond to t=0. Of course, if we want to

deal with "state of the art" models of the universe, we need to

look at relativistic cosmology.

By the way, I have always found intriguing the relation between

the local structure of the universe (as a differenciable manifold)

and its global topology. I think most of the time cosmologists make

implicit assumptions about how they are related. In particular they

estimate the size of the universe from its local curvature. However,

it seems to me that they are different problems. I can imagine, for

instance, manifolds of zero curvature and finite size, e.g. a plane

torus. Also I can conceive, say, infinite 2-manifolds with constant

positive curvature. A sofisticated but interesting example is the

following: let H be the the open upper half complex plane, Q the set of

rational numbers, H-hat = H union Q union {infinity}, j: H-hat -> P^1(C)

the j-invariant (P^1(C) is the Riemann sphere, j appears in the theory

of modular forms), and s: P^1(C) -> S^2 a stereographic projection. S^2

(2-sphere) is assumed to have its usual constant curvature differential

structure. Recall that j is invariant by the modular group, and that H-hat

can be partitioned into infinitely many fundamental domains. The interesting

thing is that the H-hat can be endowed with a contant positive curvature

differential structure via the map z -> s(j(z)), and each fundamental

domain maps bijectively to S^2. It is like having infinitely 2-spheres

glued together in a single 2-manifold.

In short, I do not think that the local structure of the universe

allows us to get conclusions about its global structure without

additional assumptions.

Miguel A. Lerma

Jan 6, 1996, 3:00:00 AM1/6/96

to

In article <4cmo6n$2...@geraldo.cc.utexas.edu>,

Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

Miguel Lerma <mle...@arthur.ma.utexas.edu> wrote:

>By the way, I have always found intriguing the relation between

>the local structure of the universe (as a differenciable manifold)

>and its global topology. I think most of the time cosmologists make

>implicit assumptions about how they are related. In particular they

>estimate the size of the universe from its local curvature. However,

>it seems to me that they are different problems. I can imagine, for

>instance, manifolds of zero curvature and finite size, e.g. a plane

>torus.

You're absolutely right. The "standard model" of cosmology

involves a couple of assumptions that people sometimes don't bother

to state explicitly:

1. The density is roughly uniform over very large scales

2. The Universe is simply connected.

There's pretty good evidence for 1, at least over the scales that we

can observe. On the other hand, if the Universe is much larger than

our horizon, it's quite plausible that the density might vary

dramatically over scales of, say, a trillion light-years, and we'd

never know it. So even if someone found an incredibly clever way to

measure the density within our horizon and thereby established that

space was negatively curved around here, that wouldn't prove that the

Universe was truly open, since openness is a global property that

depends on what things look like at arbitrarily large distances.

The second assumption (the one about topology) is the one you were

talking about. Cosmologists usually say that if the Universe has zero

or negative curvature, then it goes on forever. That conclusion

depends on assumption 2. For both flat and negatively curved models,

the only simply connected topology is the one that goes on forever,

but in both cases you can change the topology to get a compact space.

(In the flat case, the simplest way is to make space a 3-torus, as you

say. If there's uniform negative curvature then you have to go to

more complicated topologies.)

There is a relatively small literature of attempts to place

constraints on these alternative topologies. As far as I know, only

the flat toroidal case has been considered, since the open case is

much more complicated. As you'd expect, if the size of the torus is

much larger than our horizon, there's no way you can tell you're in a

torus rather than an infinite space. If the size is comparable to the

horizon or smaller, then there are observational tests you can

perform. If anyone is really interested, I can look up the limits

that have been placed on the torus size in these models. (I think the

length of the torus is constrained to be larger than something like

0.2 to 0.5 horizon sizes.)

>Also I can conceive, say, infinite 2-manifolds with constant

>positive curvature.

That's interesting. I didn't know that such things existed. I'm

afraid I didn't really understand your construction of such a thing on

first reading; I'll try to look at it more carefully later.

I have the impression that you can't make a noncompact 3-manifold with

constant positive curvature. Do you know if that's true or not? (I'm

a couple of miles from my book on Riemannian geometry at the moment;

I'll try to look it up later if I remember.) If that's true, then the

conventional wisdom that locally positive curvature implies a finite

Universe depends only on assumption 1 above, not on assumption 2.

(Note that we cosmologists think we're doing pretty well if our

conclusions depend on only *one* wholly unverifiable assumption! :-)

>In short, I do not think that the local structure of the universe

>allows us to get conclusions about its global structure without

>additional assumptions.

Agreed. For what it's worth, most working cosmologists know

this, although we're frequently to careless to say so.

-Ted

Jan 7, 1996, 3:00:00 AM1/7/96

to

Emory F. Bunn (t...@physics2.berkeley.edu) wrote:

[...]> >Also I can conceive, say, infinite 2-manifolds with constant

> >positive curvature.

> That's interesting. I didn't know that such things existed. I'm

> afraid I didn't really understand your construction of such a thing on

> first reading; I'll try to look at it more carefully later.

I mentioned that example because it is related to a problem I have

been studying recently, but there are simpler examples. However

one should be cautious, because that kind of surface is not

completely homogeneous, it contains some exceptional points

(perhaps I abused the language by calling it "manifold"). For instance,

consider the Riemann surface for f(z) = sqrt(z). It can be seen as two

Riemann spheres glued along the negative real axis. If you identify each

of those Riemann spheres with S^2 and look at its differential structure,

you see an object of constant positive curvature with the size of two

spheres of the same curvature. But it contains two branching points:

0 and infinity. Almost everywhere that manifold looks like a sphere,

but at z=0 (and at z=infinity) little circles surounding that point

have length close to 4*pi*r instead of 2*pi*r.

In my example, the surface can be seen as infinitely many

spheres glued in a certain way along the negative real axis

and the interval [0,1728]. At almost every point that manifold

looks like a piece of sphere, but the point 0 is exceptional.

If you are close to z=0 in one of the spheres and go around it

in a small circle, you will go through six diferent spheres

making an arc of 180 degrees in each one, so you need to turn

180*6 = 1080 degrees arround that point to return to the

starting point. At the point z=1728, a path arround it goes

through two different spheres 360 degrees each, 720 in total.

At z=infinity the circles go through infinitely many spheres

and have infite length.

> I have the impression that you can't make a noncompact 3-manifold with

> constant positive curvature. Do you know if that's true or not? (I'm

[...]

I guess that can also be done in a similar way as above, but if

exceptional branching points are not allowed, you might be right.

Miguel A. Lerma

Jan 7, 1996, 3:00:00 AM1/7/96

to

mle...@arthur.ma.utexas.edu (Miguel Lerma) writes:

>By the way, I have always found intriguing the relation between

>the local structure of the universe (as a differenciable manifold)

>and its global topology. I think most of the time cosmologists make

>implicit assumptions about how they are related. In particular they

>estimate the size of the universe from its local curvature. However,

>it seems to me that they are different problems. I can imagine, for

>instance, manifolds of zero curvature and finite size, e.g. a plane

>torus.

Interestingly, universes with torus-like geometry (that is, periodic

in one or more spatial dimensions, often called "small universes")

can be ruled out by observations. The spatial periodicity introduces

a long-wavelength cutoff and this distorts the spectrum of the cosmic

microwave background radiation. I believe the limits from observations

are actually good enough now to rule out these small-universe models.

>Also I can conceive, say, infinite 2-manifolds with constant

>positive curvature. A sofisticated but interesting example ... [deleted]

>In short, I do not think that the local structure of the universe

>allows us to get conclusions about its global structure without

>additional assumptions.

Well, quite probably, but the limits on alternative (non-Friedmann)

universes may be quite strict. If one can cook up a model which

fits all the observations and makes no predictions differently from

a Friedmann model, that is of theoretical interest but may not be

of any practical interest to astronomers, especially observers.

Them's the breaks.

--

NO STEP

Jan 7, 1996, 3:00:00 AM1/7/96

to

In article <4cnqv0$4...@electron.rutgers.edu>,

Ben Weiner <bwe...@electron.rutgers.edu> wrote:

> Outside the horizon, the universe could do just

>about anything it wants and we'd have no way of knowing. There could

>be a domain wall sweeping everything into oblivion heading for us at

>the speed of light, ready to come through the horizon tomorrow, and we

>wouldn't know - nor should we care much. It wouldn't get here for

>approximately a bazillion years anyway.

Ben Weiner <bwe...@electron.rutgers.edu> wrote:

> Outside the horizon, the universe could do just

>about anything it wants and we'd have no way of knowing. There could

>be a domain wall sweeping everything into oblivion heading for us at

>the speed of light, ready to come through the horizon tomorrow, and we

>wouldn't know - nor should we care much. It wouldn't get here for

>approximately a bazillion years anyway.

??? If it's heading directly for us at the speed of light, we wouldn't

know about it until it was already here.

--

Robert Israel isr...@math.ubc.ca

Department of Mathematics (604) 822-3629

University of British Columbia fax 822-6074

Vancouver, BC, Canada V6T 1Y4

Jan 7, 1996, 3:00:00 AM1/7/96

to

I wrote:

>Interestingly, universes with torus-like geometry (that is, periodic

>in one or more spatial dimensions, often called "small universes")

>can be ruled out by observations. The spatial periodicity introduces

>a long-wavelength cutoff and this distorts the spectrum of the cosmic

>microwave background radiation. I believe the limits from observations

>are actually good enough now to rule out these small-universe models.

That is, to rule out models in which the periodicity is significantly

smaller than the horizon size (the size of the observable universe),

as Ted Bunn said. Outside the horizon, the universe could do just

about anything it wants and we'd have no way of knowing. There could

be a domain wall sweeping everything into oblivion heading for us at

the speed of light, ready to come through the horizon tomorrow, and we

wouldn't know - nor should we care much. It wouldn't get here for

approximately a bazillion years anyway.

This is what I alluded to when I said that nonstandard topologies

may be theoretically amusing but not of much practical interest.

I believe de Oliveira-Costa & Smoot (1995, Ap.J. 448, 477 - "Constraints

on the Topology of the Universe from the 2 Year COBE Data") discusses

the present limits. Oh, I found another abstract:

Stevens, Scott & Silk, 1993, Phys Rev Lett 71, 20 -

"Microwave background anisotropy in a toroidal universe."

Abstract: Large-scale cosmic microwave background temperature

fluctuations are calculated for a universe with the topology of a

3-torus. In such a universe only perturbations which are harmonics of

the fundamental mode are permitted. By comparison with data from the

Cosmic Background Explorer satellite, we find that the minimum

(comoving) scale of a cubic toroidal universe is 2400/h Mpc for an n =

1 inflationary model. This is approximately an order of magnitude

greater than previous limits and 80 percent of the horizon scale,

implying that a topologically 'small' universe is no longer an

interesting cosmological model.

--

"If current World Wide Web usage trends continue, as with prior Internet growth,

we project that the US economy will collapse on June 10, 1998, as the rate of

white collar workers going pointy-clicky pointy-clicky all day goes asymptotic."

--- President's Council of Economic Advisors report, 12/1/95 (classified)

Jan 7, 1996, 3:00:00 AM1/7/96

to

'egr...@nyc.pipeline.com (Edward Green)' wrote:

>Now, to shift gears, I've been trying my hand as a pro-aether crank

What, no replies! Oh, I can see you shaking your heads sadly... >Now, to shift gears, I've been trying my hand as a pro-aether crank

100 times: I will *not* write aether. I will *not* write aether...

I'd still like to know if the red-shift/temperature-shift equivalence in

black-body spectrums is some incredible cosmic coincidence, or the source

of deep insight. Does anybody have an opinion on that?

--

Ed Green

egr...@nyc.pipeline.com

Jan 7, 1996, 3:00:00 AM1/7/96