Re: Constraints on spatial flatness.

[Chalky]

On Dec 30, 11:20Â*pm, carlip-nos...@physics.ucdavis.edu wrote:
> Chalky <chalkys...@bleachboys.co.uk> wrote:
>
> [...]
>
> > I was merely enquiring whether that spatial curvature (or lack of it)
> > also applies close to, for example, the surface of the Sun, or the
> > event horizon of a black hole.
>
> The spatial curvature people refer to when they say "the universe is
> nearly spatially flat" is the average curvature, averaged on the same
> scale that one can say "the universe is nearly sptially homogeneous." Â*

I have given this point some further thought since submitting my first
response, and your statement appears to imply that there are smaller
regions of positively curved space, and regions of negatively curved
space which happen to average out to close to zero, on the large
scale.

If that was the intended implication, I would like to ask.....Where
are they?

Lets start at home with the solar system, since we all know where we
stand here. I can easily understand spacetime curvature caused by the
Sun, in the sense that, after a year of time, the Earth returns to
pretty much where it started, in space (assuming Heliocentric
coordinates). I can also understand that spacetime curvature is
stronger closer to the Sun, since Mercury returns to the same point in
space more quickly. However, this does not alter the fact that space,
per se, still looks remarkably flat to me, from where I am standing,
and I doubt that this would change substantially if I moved to
Mercury. Hence my question. Where are these curved regions of space
supposed to be located?

[Phillip Helbig---remove CLOTHES to reply]

In article <mt2.1-9338-1230861325@silver>, Chalky
<chalkyspam@bleachboys.co.uk> writes:

> I have given this point some further thought since submitting my first
> response, and your statement appears to imply that there are smaller
> regions of positively curved space, and regions of negatively curved
> space which happen to average out to close to zero, on the large
> scale.

OK.

> If that was the intended implication, I would like to ask.....Where
> are they?
>
> Lets start at home with the solar system, since we all know where we
> stand here. I can easily understand spacetime curvature caused by the
> Sun, in the sense that, after a year of time, the Earth returns to
> pretty much where it started, in space (assuming Heliocentric
> coordinates). I can also understand that spacetime curvature is
> stronger closer to the Sun, since Mercury returns to the same point in
> space more quickly. However, this does not alter the fact that space,
> per se, still looks remarkably flat to me, from where I am standing,
> and I doubt that this would change substantially if I moved to
> Mercury.

The average density of the universe is about one atom of hydrogen per
cubic meter. If you were in intergalactic space, you would probably say
"that still looks remarkably empty to me". However, your personal
feelings, or more generally the appraisal of the situation by beings
whose senses evolved for quite different purposes, are irrelevant here.

> Hence my question. Where are these curved regions of space
> supposed to be located?

You mentioned it above: locally near masses and there is a negative
"global" curvature such that on average space is flat (with the various
qualifications and caveats which have been mentioned in other posts in
this thread).

[Chalky]

On Jan 2, 11:50Â*am, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
remove CLOTHES to reply) wrote:
> In article <mt2.1-9338-1230861325@silver>, Chalky
>
> <chalkys...@bleachboys.co.uk> writes:
> > I have given this point some further thought since submitting my first
> > response, and your statement appears to imply that there are smaller
> > regions of positively curved space, and regions of negatively curved
> > space which happen to average out to close to zero, on the large
> > scale.
>
> OK.
>
> > If that was the intended implication, I would like to ask.....Where
> > are they?
>
> > Lets start at home with the solar system, since we all know where we
> > stand here. I can easily understand spacetime curvature caused by the
> > Sun, in the sense that, after a year of time, the Earth returns to
> > pretty much where it started, in space (assuming Heliocentric
> > coordinates). I can also understand that Â*spacetime curvature is
> > stronger closer to the Sun, since Mercury returns to the same point in
> > space more quickly. However, this does not alter the fact that space,
> > per se, still looks remarkably flat to me, from where I am standing,
> > and I doubt that this would change substantially if I moved to
> > Mercury.
>
> The average density of the universe is about one atom of hydrogen per
> cubic meter. Â*If you were in intergalactic space, you would probably say
> "that still looks remarkably empty to me". Â*However, your personal
> feelings, or more generally the appraisal of the situation by beings
> whose senses evolved for quite different purposes, are irrelevant here.
>
> > Hence my question. Where are these curved regions of space
> > supposed to be located?
>
> You mentioned it above: locally near masses and there is a negative
> "global" curvature such that on average space is flat (with the various
> qualifications and caveats which have been mentioned in other posts in
> this thread).

I am sure you are absolutely correct. (When I ask questions here, it
is to clarify things I have become unsure of, or forgotten [or never
knew], not to wield some kind of philosophical axe).

However, the new side issue which intrigues me right now, is this:

To what extent can we say that the effects of spatial curvature [as
opposed to spacetime curvature] correspond to the effects of Newtonian
gravity.....or would such a suggestion be completely bonkers?