Is the universe spatially infinite?

I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.

dkomo wrote:
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

Who said it is flat?

2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.

See answer to (1)

MorituriMax wrote:

dkomo wrote:
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

Who said it is flat?

Inflation theory.


2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.

See answer to (1)

dkomo wrote:

I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

Not necessarily.

2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.
The Big Bang Model is a broadly accepted theory for the
origin and evolution of our universe. It postulates that 12 to
14 billion years ago, the portion of the universe we can see
today was only a few millimeters across. It has since
expanded from this hot dense state into the vast and much
cooler cosmos we currently inhabit. We can see remnants of
this hot dense matter as the now very cold cosmic
microwave background radiation which still pervades the
universe and is visible to microwave detectors as a uniform
glow across the entire sky. About the early universe see:

Read Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm
http://www.astro.ucla.edu/~wright/cosmology_faq.html

WMAP: Foundations of the Big Bang theory
http://map.gsfc.nasa.gov/m_uni.html

WMAP: Tests of Big Bang Cosmology
http://map.gsfc.nasa.gov/m_uni/uni_101bbtest.html

Astronomy
http://edu-observatory.org/eo/mcc.html

dkomo wrote:
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?


Spacetime is *not* flat, at least not globally.

2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.


(1) is not true. Besides, a singularity exists in any past-directed null
cone in all standard models of cosmology.

dkomo wrote in message ...
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

No. Conceivably, the geometry of our universe could be that of a flat 3-torus.

http://www.geometrygames.org/ESoS/CosmologyNews.html

Eugene Shubert
http://www.everythingimportant.org

Perfectly Innocent wrote:

dkomo wrote in message ...
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

No. Conceivably, the geometry of our universe could be that of a flat 3-torus.


Spacetime flat on the cosmic scale and curved locally where there
is mass. The Sun is an excellent of a mass causing spacetime
curvature of our solar system.

The CMB data fits a model of a flat universe. See below.

13.7 billion years +/- 0.2 Gyr (WMAP data of the CMB) which is good
agreement with the oldest stars, the Hubble expansion rate as determined
independently by cephied variables and Type Ia supernovae data.

MAP Data Released!
Ref: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

11 Feb 2003 - The results from the first year of observing by the
Wilkinson Microwave Anisotropy Probe were announced today at a Space
Science Update in the auditorium of NASA HQ. Important results
include:

o The satellite has been renamed in honor of the late David T.
Wilkinson of Princeton University, a key member of the project from
its conception.

o The polarization of the microwave background anisotropy coming
from scattering by electrons 200 million years after the Big Bang
has been detected. This is evidence for an early generation of
stars existing 4 to 5 times earlier than any object yet observed.

o The WMAP data agree with previous work showing the Universe is
flat and in an accelerating expansion.

o The WMAP data give the most precise values for the density of
ordinary [baryonic] matter made of protons and neutrons and for the
dark matter: 0.4 and 2.5 yoctograms per cubic meter. These
correspond to omega_b = 0.0224 +/- 0.0009 and omega_m = 0.135 +/-
0.009.

o The WMAP data give the most precise value for the age of the
Universe: 13.7 +/- 0.2 Gyr. The Hubble constant is Ho = 71 +/- 4
km/sec/Mpc, and the vacuum energy density corresponds to lambda =
0.73 +/- 0.04. 13 papers by the science team and the maps and
power spectra are available by clicking on http://cmbdata.gsfc.nasa.gov

See: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

Suggestion: Spend some time with Cosmology FAQs
http://www.astro.ucla.edu/~wright/cosmology_faq.html

And Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm

Observational and Experimental Evidence Bearing on General Relativity
http://math.ucr.edu/home/baez/RelWWW/tests.html

General Relativity Tutorial
John Baez
http://math.ucr.edu/home/baez/gr/gr.html

Relativity on the World Wide Web
http://math.ucr.edu/home/baez/relativity.html

General Relativity and Cosmology FAQs
http://math.ucr.edu/home/baez/physics/

Developments in General Relativity: Black Hole Singularity and Beyond
http://arxiv.org/abs/gr-qc/0304052

Improved Test of General Relativity with Radio Doppler Data from the Cassini Spacecraft
http://arxiv.org/abs/gr-qc/0308010

What is the experimental basis of Special Relativity?
http://math.ucr.edu/home/baez/physic...xperiments.htm

Sam Wormley wrote:

Perfectly Innocent wrote:

dkomo wrote in message ...
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

No. Conceivably, the geometry of our universe could be that of a flat 3-torus.


Spacetime flat on the cosmic scale and curved locally where there
is mass. The Sun is an excellent of a mass causing spacetime
curvature of our solar system.

The CMB data fits a model of a flat universe. See below.


I was trying to get a verification of the following quotes:

"But if the universe is spatially infinite, there was already an
infinite spatial expanse at the moment of the big bang. At this
initial
moment, the energy density soared and an incomparably large
temperature
was reached, but these extreme conditions existed everywhere, not just
at one single point. In this setting, the big bang eruption took
place
everywhere on the infinite expanse. Comparing this to the
conventional
single-dot beginning, it is as though there were many big bangs, one
at
each point on the infinite spatial expanse."

Brian Greene, _The Fabric of the Cosmos_, p. 249

Why should we take this idea seriously? Because,

"We will see that there is mounting evidence that the overall shape of
space is not curved, and since there is no evidence as yet that space
has a video game shape [a 3-D torus], the flat, infinitely large
spatial
shape is the front-running contender for the large-scale structure of
spacetime."

Greene, p. 250

So what I got was a bunch of conflicting information in this thread.
Several people denied that spacetime is flat on a cosmic scale, even
though this is a key prediction of inflation theory and has been
verified by CMB measurements. And you claimed "that 12 to 14 billion
years ago, the portion of the universe we can see
today was only a few millimeters across", which is not correct if the
universe is spatially infinite.





13.7 billion years +/- 0.2 Gyr (WMAP data of the CMB) which is good
agreement with the oldest stars, the Hubble expansion rate as determined
independently by cephied variables and Type Ia supernovae data.

MAP Data Released!
Ref: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

11 Feb 2003 - The results from the first year of observing by the
Wilkinson Microwave Anisotropy Probe were announced today at a Space
Science Update in the auditorium of NASA HQ. Important results
include:

o The satellite has been renamed in honor of the late David T.
Wilkinson of Princeton University, a key member of the project from
its conception.

o The polarization of the microwave background anisotropy coming
from scattering by electrons 200 million years after the Big Bang
has been detected. This is evidence for an early generation of
stars existing 4 to 5 times earlier than any object yet observed.

o The WMAP data agree with previous work showing the Universe is
flat and in an accelerating expansion.

o The WMAP data give the most precise values for the density of
ordinary [baryonic] matter made of protons and neutrons and for the
dark matter: 0.4 and 2.5 yoctograms per cubic meter. These
correspond to omega_b = 0.0224 +/- 0.0009 and omega_m = 0.135 +/-
0.009.

o The WMAP data give the most precise value for the age of the
Universe: 13.7 +/- 0.2 Gyr. The Hubble constant is Ho = 71 +/- 4
km/sec/Mpc, and the vacuum energy density corresponds to lambda =
0.73 +/- 0.04. 13 papers by the science team and the maps and
power spectra are available by clicking on http://cmbdata.gsfc.nasa.gov

See: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

Suggestion: Spend some time with Cosmology FAQs
http://www.astro.ucla.edu/~wright/cosmology_faq.html

And Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm

Observational and Experimental Evidence Bearing on General Relativity
http://math.ucr.edu/home/baez/RelWWW/tests.html

General Relativity Tutorial
John Baez
http://math.ucr.edu/home/baez/gr/gr.html

Relativity on the World Wide Web
http://math.ucr.edu/home/baez/relativity.html

General Relativity and Cosmology FAQs
http://math.ucr.edu/home/baez/physics/

Developments in General Relativity: Black Hole Singularity and Beyond
http://arxiv.org/abs/gr-qc/0304052

Improved Test of General Relativity with Radio Doppler Data from the Cassini Spacecraft
http://arxiv.org/abs/gr-qc/0308010

What is the experimental basis of Special Relativity?
http://math.ucr.edu/home/baez/physic...xperiments.htm

[fixing the formatting of my last post]

Sam Wormley wrote:

Perfectly Innocent wrote:

dkomo wrote in message ...
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

No. Conceivably, the geometry of our universe could be that of a flat 3-torus.


Spacetime flat on the cosmic scale and curved locally where there
is mass. The Sun is an excellent of a mass causing spacetime
curvature of our solar system.

The CMB data fits a model of a flat universe. See below.


I was trying to get a verification of the following quotes:

"But if the universe is spatially infinite, there was already an
infinite spatial expanse at the moment of the big bang. At this
initial moment, the energy density soared and an incomparably large
temperature was reached, but these extreme conditions existed
everywhere, not just at one single point. In this setting, the big
bang eruption took place everywhere on the infinite expanse.
Comparing this to the conventional single-dot beginning, it is as
though there were many big bangs, one at each point on the infinite
spatial expanse."

Brian Greene, _The Fabric of the Cosmos_, p. 249

Why should we take this idea seriously? Because,

"We will see that there is mounting evidence that the overall shape of
space is not curved, and since there is no evidence as yet that space
has a video game shape [a 3-D torus], the flat, infinitely large
spatial shape is the front-running contender for the large-scale
structure of spacetime."

Greene, p. 250

So what I got was a bunch of conflicting information in this thread.
Several people denied that spacetime is flat on a cosmic scale, even
though this is a key prediction of inflation theory and has been
verified by CMB measurements. And you claimed "that 12 to 14 billion
years ago, the portion of the universe we can see today was only a few
millimeters across", which is not correct if the universe is spatially
infinite.





13.7 billion years +/- 0.2 Gyr (WMAP data of the CMB) which is good
agreement with the oldest stars, the Hubble expansion rate as determined
independently by cephied variables and Type Ia supernovae data.

MAP Data Released!
Ref: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

11 Feb 2003 - The results from the first year of observing by the
Wilkinson Microwave Anisotropy Probe were announced today at a Space
Science Update in the auditorium of NASA HQ. Important results
include:

o The satellite has been renamed in honor of the late David T.
Wilkinson of Princeton University, a key member of the project from
its conception.

o The polarization of the microwave background anisotropy coming
from scattering by electrons 200 million years after the Big Bang
has been detected. This is evidence for an early generation of
stars existing 4 to 5 times earlier than any object yet observed.

o The WMAP data agree with previous work showing the Universe is
flat and in an accelerating expansion.

o The WMAP data give the most precise values for the density of
ordinary [baryonic] matter made of protons and neutrons and for the
dark matter: 0.4 and 2.5 yoctograms per cubic meter. These
correspond to omega_b = 0.0224 +/- 0.0009 and omega_m = 0.135 +/-
0.009.

o The WMAP data give the most precise value for the age of the
Universe: 13.7 +/- 0.2 Gyr. The Hubble constant is Ho = 71 +/- 4
km/sec/Mpc, and the vacuum energy density corresponds to lambda =
0.73 +/- 0.04. 13 papers by the science team and the maps and
power spectra are available by clicking on http://cmbdata.gsfc.nasa.gov

See: http://www.astro.ucla.edu/~wright/cosmolog.htm#News

Suggestion: Spend some time with Cosmology FAQs
http://www.astro.ucla.edu/~wright/cosmology_faq.html

And Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm

Observational and Experimental Evidence Bearing on General Relativity
http://math.ucr.edu/home/baez/RelWWW/tests.html

General Relativity Tutorial
John Baez
http://math.ucr.edu/home/baez/gr/gr.html

Relativity on the World Wide Web
http://math.ucr.edu/home/baez/relativity.html

General Relativity and Cosmology FAQs
http://math.ucr.edu/home/baez/physics/

Developments in General Relativity: Black Hole Singularity and Beyond
http://arxiv.org/abs/gr-qc/0304052

Improved Test of General Relativity with Radio Doppler Data from the Cassini Spacecraft
http://arxiv.org/abs/gr-qc/0308010

What is the experimental basis of Special Relativity?
http://math.ucr.edu/home/baez/physic...xperiments.htm

* dkomo:
I need a definitive answer to two questions:

1. does the fact that space is flat imply that the universe is spatially
infinite?

Who knows whether it's flat or not. But assuming it's flat and finite then
it isn't a 3-sphere. It might then be torus, but that means there would be
absolute directions to be found ("someone": dream up the proper experiment!
(unless the CMB data is already that experiment)).


2. if (1) is true then does that imply that at the instant of the big
bang the universe was *still* spatially infinite, and that the
traditional idea that the universe was "collapsed" to a tiny point is
simply untrue.

No, because as you later quoted from Brian Greene, the case of an infinite
universe is simply an infinite number of cases of finite universe: if it
works for a finite universe, then it works for an infinite one because it
then works for each one of the infinitely many finite parts of that.

Personally I don't think it (the Big Bang) works for a finite universe, but
that opinion is on philosophical grounds, not hard physics. Also, the
philosophy is rather simple: that BB doesn't solve anything fundamental
while introducing extreme loads of unobservable baggage. IOW., Occam.

--
A: Because it messes up the order in which people normally read text.
Q: Why is it such a bad thing?
A: Top-posting.
Q: What is the most annoying thing on usenet and in e-mail?