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From: Androcles on 9 Aug 2010 18:52

<carlip-nospam(a)physics.ucdavis.edu> wrote in message
news:i3po53$7aq$1(a)speranza.aioe.org...

For example, in two dimensions, a cylinder is flat

===============================================
Bwahahahahahahahahahaha!!


From: srp on 12 Aug 2010 08:26
On 9 août, 16:24, carlip-nos...(a)physics.ucdavis.edu wrote:
> Sam Wormley <sworml...(a)gmail.com> wrote:
> > I gave a presentation yesterday to an audience that included
> > one of my retired physics professors. I had responded to a
> > question during the presentation saying that the universe could
> > be infinite, but that since we cannot observe it, we cannot say
> > for sure.
> > After the presentation, Barney Cook, said I was wrong, that
> > the the measured flatness of the universe means the universe
> > is infinite.
>
> This is not correct, for two reasons:
>
> 1.  We can't measure the spatial curvature of the Universe exactly
> -- there is no way to know whether it is zero or just  smaller than
> our current resolution.  (I don't know of any way to determine this
> even in principle.)  So, for instance, while a spatial three-sphere
> has positive curvature, a sphere with a large enough radius of
> curvature can have an arbitrarily small positive curvature.
>
> (Note that this doesn't work the other way.  We *could*, in principle,
> measure a positive or negative curvature accurately enough to exclude
> the possibility of flatness.)
>
> 2.  Even if the Universe is spatially flat, that would not imply an
> infinite size.  While infinite flat space is the simplest possibility,
> it is not unique.  For example, in two dimensions, a cylinder is flat
> (that is, the axioms of Euclidean geometry hold, which is essentially
> what we measure).  A torus can be given a flat metric; so can a Klein
> bottle.  This is equally true for the three-dimensional generalizations
> of these topologies.
>
> We might hope to observe whether the Universe has, for example, the
> topology of a torus.  If it does, we might be able to see "around" a
> circumference -- that is, the Universe might look identical in two
> opposite directions.  This is tricky, since the light travel time to a
> given object would be different in the two directions, so we would
> see it at two different ages, but there are interesting ideas about how
> to sort this out.  Again, though, while we could conceivably detect
> a torus topology, we could never disprove the possibility -- if the
> circumferences of the torus were large enough, light would not have
> had time to travel all the way around in the age of the Universe, so
> the topology would be essentially invisible.
>
> Steve Carlip

Thank you Steve for bringing a touch of reason from authority
on this site.

It truly saddens me to see so many half-truths thrown out here
without subsequent clarifications from knowledgeable people
with enough authority stick.

How many students and eager amateurs who never contribute
but read this stuff and adopt unclarified false ideas afterwards just
can't be assessed.

Just recently, a regular supposedly competent pillar of most of
these public sites, a teacher if I recall, flatly asserted that
relativistic mass was an outdated concept. This has been
asserted over and over by many here without anybody
caring to rectify if any of the regulars even understand the
fact.

I for one have no authority so I mostly just observe.

André Michaud
From: Raymond Yohros on 12 Aug 2010 13:22
On Aug 9, 3:24 pm, carlip-nos...(a)physics.ucdavis.edu wrote:
> Sam Wormley <sworml...(a)gmail.com> wrote:
> > I gave a presentation yesterday to an audience that included
> > one of my retired physics professors. I had responded to a
> > question during the presentation saying that the universe could
> > be infinite, but that since we cannot observe it, we cannot say
> > for sure.
> > After the presentation, Barney Cook, said I was wrong, that
> > the the measured flatness of the universe means the universe
> > is infinite.
>
> This is not correct, for two reasons:
>
> 1.  We can't measure the spatial curvature of the Universe exactly
> -- there is no way to know whether it is zero or just  smaller than
> our current resolution.  (I don't know of any way to determine this
> even in principle.)  So, for instance, while a spatial three-sphere
> has positive curvature, a sphere with a large enough radius of
> curvature can have an arbitrarily small positive curvature.
>
> (Note that this doesn't work the other way.  We *could*, in principle,
> measure a positive or negative curvature accurately enough to exclude
> the possibility of flatness.)
>
> 2.  Even if the Universe is spatially flat, that would not imply an
> infinite size.  While infinite flat space is the simplest possibility,
> it is not unique.  For example, in two dimensions, a cylinder is flat
> (that is, the axioms of Euclidean geometry hold, which is essentially
> what we measure).  A torus can be given a flat metric; so can a Klein
> bottle.  This is equally true for the three-dimensional generalizations
> of these topologies.
>
> We might hope to observe whether the Universe has, for example, the
> topology of a torus.  If it does, we might be able to see "around" a
> circumference -- that is, the Universe might look identical in two
> opposite directions.  This is tricky, since the light travel time to a
> given object would be different in the two directions, so we would
> see it at two different ages, but there are interesting ideas about how
> to sort this out.  Again, though, while we could conceivably detect
> a torus topology, we could never disprove the possibility -- if the
> circumferences of the torus were large enough, light would not have
> had time to travel all the way around in the age of the Universe, so
> the topology would be essentially invisible.
>
> Steve Carlip

to make an analogy of spacetime's curvature with a wave,
the maximum amplitude should be at the bb.

and flat when it reaches the equilibrium position at its
full extension. silent and huge with no visible stars.

of course neutrino currents will be so great that after an almost
eternal flat spacetime, the curvature will slowly but surely come
in reverse (going from equilibrium to a peek amplitude)

regards
r.y
From: eric gisse on 13 Aug 2010 06:26
srp wrote:
[...]

> Just recently, a regular supposedly competent pillar of most of
> these public sites, a teacher if I recall, flatly asserted that
> relativistic mass was an outdated concept.

That's because it is.

> This has been
> asserted over and over by many here without anybody
> caring to rectify if any of the regulars even understand the
> fact.
>
> I for one have no authority so I mostly just observe.
>
> Andr� Michaud

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