How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

Mike

On Sat, 26 Apr 2008 03:24:38 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

http://map.gsfc.nasa.gov/universe/uni_shape.html
"Recent measurements (c. 2001) by a number of ground-based and
balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and
DASI, have shown that the brightest spots are about 1 degree across.
Thus the universe was known to be flat to within about 15% accuracy
prior to the WMAP results. WMAP has confirmed this result with very
high accuracy and precision. We now know that the universe is flat
with only a 2% margin of error."

For a contrarian point of view  for the non-specialist, try:http://xyz.lanl.gov/abs/0704.3374
Geometry and Topology in Relativistic Cosmology
by Jean-Pierre Luminet

"a fair portion of the academic community believes the WMAP data has
ruled out multiply-connected models. However, at least the
second part of the claim is wrong." and "The new release of WMAP data
(Spergel et al., 2006), integrating two additional years of
observation with reduced uncertainty, strengthened the evidence for an
abnormally low quadrupole and other features which do not match with
the infinite flat space model (this explains the unexpected delay in
the delivery of this second release, originally announced for February
2004)."

(If multiply-connected, the universe might not only be finite but only
80% of the volume of the observable universe  (namely the volume of
the last scattering surface). 43 Gpc!

The book: The Poincare Conjecture by Donal o'Sheahttp://tinyurl.com/yvg2v6
is a useful account of the history of the mathematics of the possibly
hyperspherical  shape of the universe.

John

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

http://map.gsfc.nasa.gov/universe/uni_shape.html

On Sat, 26 Apr 2008 06:21:33 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:

On Apr 26, 8:40 am, John Bailey <john_bai...@rochester.rr.com> wrote:
On Sat, 26 Apr 2008 03:24:38 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:
For a contrarian point of view  for the non-specialist, try:http://xyz.lanl.gov/abs/0704.3374
Geometry and Topology in Relativistic Cosmology
by Jean-Pierre Luminet

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

Mike

On Apr 26, 8:40 am, John Bailey <john_bai...@rochester.rr.com> wrote:
On Sat, 26 Apr 2008 03:24:38 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:

For a contrarian point of view  for the non-specialist, try:http://xyz.lanl.gov/abs/0704.3374
Geometry and Topology in Relativistic Cosmology
by Jean-Pierre Luminet

Interesting paper. I have heard some reasons as to why the
dodecahedron hypothesis has failed but I do not recall them.

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

Mike

On Apr 26, 2:24 am, Mike <elea...@yahoo.gr> wrote:

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

In other words, does the evidence lean towards an infinite or finite
universe and in what sense and scales? For example, one possibility is
infinite space with finite mass distribution. Another is infinite
universe in dimensions but infinite mass, etc. Anyone?

Mike

The closed universe curve is 4 dimensional hypersphere.

Mitch Raemsch

On Sat, 26 Apr 2008 06:21:33 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:

On Apr 26, 8:40 am, John Bailey <john_bai...@rochester.rr.com> wrote:
On Sat, 26 Apr 2008 03:24:38 -0700 (PDT), Mike <elea...@yahoo.gr
wrote:
For a contrarian point of view for the non-specialist,
try:http://xyz.lanl.gov/abs/0704.3374
Geometry and Topology in Relativistic Cosmology
by Jean-Pierre Luminet

How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

Mike wrote:
How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

At present, the best measurements on a cosmological scale show that the
universe is spatially flat to within a few percent. And no evidence is
seen for multiple images of a single object or region.

The implications directly affect answers to your question. If a) the FRW
manifolds of General Relativity are a good model of the universe at
cosmological distances, and b) the universe is EXACTLY spatially flat,
then it cannot be spatially compact. However if there is a small
positive spatial curvature, then it could be compact (with a small
negative spatial curvature it still cannot be spatially compact).

So the measurements and GR are consistent with the universe being
spatially infinite. But they cannot rule out the universe being
spatially closed with a scale beyond our cosmological horizon (~14 giga
lightyears).

If GR is not a good model of the universe at cosmological scales, then
we don't know much until a better model can be formulated. While there
are phenomena that bring the validity of GR into question, none have
been established to the point of being generally accepted as a
refutation of GR.


Tom Roberts

You wrote:

" ...cosmological horizon ( ~14 giga lightyears ). ".

At this point in cosmological time ( i.e. comoving time )
the comoving distance to the cosmological horizon
is 45 giga lightyears away because, since the birth of

the Cosmic Microwave Background ( a blackbody ) 13.7 giga years ago,
our visible Universe has cooled and thinned by " z == 1,088 "
to 2.725 kelvin ( from 2,965 kelvin ).

P.S.
I see people who hate General Relativity and Einstein because,
in their twisted daydreams, Einstein is yet another Jewish bogeyman.

But I don't see these people proposing a better way to model,
say, the tiny 4-D gravitational field of a billiard ball.
As I've recently stated..

We can't imagine nature as she truly is.

We can't imagine ( nor measure precisely )
the tiny 4-D gravitational field of, say, a billiard ball.
Worse.. the field is invisible, infinite in extent, and unblockable.

For example, we could toss the IPK ( International Prototype Kilogram )
into the trash if we could measure its gravitational field
precisely ( and consistently ).

The NIST in Colorado is hoping to do just that by
using a high-precision absolute gravimeter ( accelerometer )
and an ultra-precise weighing ( using a Watt balance, in a vacuum ).

Einstein said:
" I see a pattern,
but my imagination cannot picture the maker of that pattern.
I see a clock, but I cannot envision the clockmaker.

The human mind is unable to conceive of the four dimensions,

so how can it conceive of a God,
before whom a thousand years and a thousand dimensions are as one ? ".
-- " The Expanded Quotable Einstein ",
Princeton University Press, 2000 Page 208

From Einstein's, " Ether and the Theory of Relativity " ( 1920 )
quoted at "http://TUHH.DE/rzt/rzt/it/Ether.html":

" But this ether may not be thought of as
endowed with the quality characteristic of ponderable media,
as consisting of parts which may be tracked through time.

The idea of motion may not be applied to it. ".

Petkov ( 2005 ) has this to say:
" This paper pursues two aims.

First, to show that the block universe view, regarding the universe as
a timelessly existing four-dimensional world,
is the only one that is consistent with special relativity.

Second, to argue that special relativity alone can resolve
the debate on whether the world is
three-dimensional or four-dimensional.

The argument advanced in the paper is that
if the world were three-dimensional

the kinematic consequences of special relativity and more importantly
the experiments confirming them would be impossible. ".

-- " Is There an Alternative to the Block Universe View ? "
http://Philsci-Archive.Pitt.EDU/archive/00002408/

Mike wrote:
How do the measurements (WMAP, etc.) fit with the notion of an
infinite or finite universe and in relation to GR?

At present, the best measurements on a cosmological scale show that the
universe is spatially flat to within a few percent. And no evidence is
seen for multiple images of a single object or region.

The implications directly affect answers to your question. If a) the FRW
manifolds of General Relativity are a good model of the universe at
cosmological distances, and b) the universe is EXACTLY spatially flat,
then it cannot be spatially compact.