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From: vincent64 on 21 Jun 2010 19:57
Assuming that the Universe is compact and expanding at a constant rate
in all directions, and using a model of the Universe that seems
reasonable:

1) Can we measure the minimum speed v at which a particle must move
(assuming it is moving in the same direction in a curved Universe), in
order to come back indefinitely to its initial position?

2) Depending on star sparsity, can such a particle never be captured
by the gravitational fields of nearby stars (that is, never enter into
an elliptic orbit around a nearby star or star cluster)? In other
words, could a particle be "on the loose" for ever if stars are sparse
enough?

Full discussion at
http://www.analyticbridge.com/group/mathandcomputerscienceproblems/forum/topics/a-question-for-physicists
From: Sam on 21 Jun 2010 20:04
On Jun 21, 6:57 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
wrote:
> Assuming that the Universe is compact and expanding at a constant rate
> in all directions, and using a model of the Universe that seems
> reasonable:
>
> 1) Can we measure the minimum speed v at which a particle must move
> (assuming it is moving in the same direction in a curved Universe), in
> order to come back indefinitely to its initial position?
>

There is no absolute reference frame.

No Center
http://www.astro.ucla.edu/~wright/nocenter.html
http://www.astro.ucla.edu/~wright/infpoint.html

Also see Ned Wright's Cosmology Tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm
http://www.astro.ucla.edu/~wright/cosmology_faq.html
http://www.astro.ucla.edu/~wright/CosmoCalc.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
From: vincent64 on 21 Jun 2010 20:42
On Jun 21, 5:04 pm, Sam <sworml...(a)gmail.com> wrote:
> On Jun 21, 6:57 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
> wrote:
>
> > Assuming that the Universe is compact and expanding at a constant rate
> > in all directions, and using a model of the Universe that seems
> > reasonable:
>
> > 1) Can we measure the minimum speed v at which a particle must move
> > (assuming it is moving in the same direction in a curved Universe), in
> > order to come back indefinitely to its initial position?
>
>   There is no absolute reference frame.
>
>   No Center
>    http://www.astro.ucla.edu/~wright/nocenter.html
>    http://www.astro.ucla.edu/~wright/infpoint.html
>
>   Also see Ned Wright's Cosmology Tutorial
>    http://www.astro.ucla.edu/~wright/cosmolog.htm
>    http://www.astro.ucla.edu/~wright/cosmology_faq.html
>    http://www.astro.ucla.edu/~wright/CosmoCalc.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

How can you have no center and either expand or collapse: if you have
no center, then from where are you expanding - from which reference
point? You can expand and have no center if you are not compact
(meaning e.g. that the average distance between 2 closest neighboring
stars is increasing over time, on average), but if you believe that
the universe is not compact, then how do you explain the big bang? Was
the universe compact (finite) when the big bang happened, and
suddenly, one day the universe became infinite (non compact)?
From: Sam on 21 Jun 2010 22:51
On Jun 21, 7:42 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
wrote:
> On Jun 21, 5:04 pm, Sam <sworml...(a)gmail.com> wrote:
>
>
>
>
>
> > On Jun 21, 6:57 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
> > wrote:
>
> > > Assuming that the Universe is compact and expanding at a constant rate
> > > in all directions, and using a model of the Universe that seems
> > > reasonable:
>
> > > 1) Can we measure the minimum speed v at which a particle must move
> > > (assuming it is moving in the same direction in a curved Universe), in
> > > order to come back indefinitely to its initial position?
>
> >   There is no absolute reference frame.
>
> >   No Center
> >    http://www.astro.ucla.edu/~wright/nocenter.html
> >    http://www.astro.ucla.edu/~wright/infpoint.html
>
> >   Also see Ned Wright's Cosmology Tutorial
> >    http://www.astro.ucla.edu/~wright/cosmolog.htm
> >    http://www.astro.ucla.edu/~wright/cosmology_faq.html
> >    http://www.astro.ucla.edu/~wright/CosmoCalc.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
>
> How can you have no center and either expand or collapse: if you have
> no center, then from where are you expanding - from which reference
> point? You can expand and have no center if you are not compact
> (meaning e.g. that the average distance between 2 closest neighboring
> stars is increasing over time, on average), but if you believe that
> the universe is not compact, then how do you explain the big bang? Was
> the universe compact (finite) when the big bang happened, and
> suddenly, one day the universe became infinite (non compact)?

You seemed to have missed a very important point,
namely everywhere space is expanding. You should
Read the references I posted for you and bring yourself
up2date on what the observation are telling us.

Everywhere is the center. Read the references!

From: Igor on 22 Jun 2010 10:07
On Jun 21, 8:42 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
wrote:
> On Jun 21, 5:04 pm, Sam <sworml...(a)gmail.com> wrote:
>
>
>
>
>
> > On Jun 21, 6:57 pm, "vincen...(a)yahoo.com" <datashap...(a)gmail.com>
> > wrote:
>
> > > Assuming that the Universe is compact and expanding at a constant rate
> > > in all directions, and using a model of the Universe that seems
> > > reasonable:
>
> > > 1) Can we measure the minimum speed v at which a particle must move
> > > (assuming it is moving in the same direction in a curved Universe), in
> > > order to come back indefinitely to its initial position?
>
> >   There is no absolute reference frame.
>
> >   No Center
> >    http://www.astro.ucla.edu/~wright/nocenter.html
> >    http://www.astro.ucla.edu/~wright/infpoint.html
>
> >   Also see Ned Wright's Cosmology Tutorial
> >    http://www.astro.ucla.edu/~wright/cosmolog.htm
> >    http://www.astro.ucla.edu/~wright/cosmology_faq.html
> >    http://www.astro.ucla.edu/~wright/CosmoCalc.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
>
> How can you have no center and either expand or collapse: if you have
> no center, then from where are you expanding - from which reference
> point?

Any reference point. The surface of a sphere has no center, yet it
can expand. Points on the surface appear to move away from each other
and any point is as good as any other.


>You can expand and have no center if you are not compact
> (meaning e.g. that the average distance between 2 closest neighboring
> stars is increasing over time, on average), but if you believe that
> the universe is not compact, then how do you explain the big bang? Was
> the universe compact (finite) when the big bang happened, and
> suddenly, one day the universe became infinite (non compact)?

No one has recently suggested the universe is infinite. In fact,
Olbers showed it can't be infinite based on what we understand about
light in a very clever paradox. Modern cosmology, based on GR,
suggests that the universe is finite but unbounded (like the fore-
mentioned spherical surface).


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