Phillip Helbig---remove CLOTHES to reply
Jan2-09, 06:00 AM
In article
<80fedc48-32f6-4681-8a00-46dbd8c0c0c8@s9g2000prg.googlegroups.com>,
Chalky <chalkyspam@bleachboys.co.uk> writes:
> > Local concentrations of matter will have local effects.
>
> Is that a yes or a no?
Yes. Whatever the average global value of spatial curvature, there are
local deviations caused by local concentrations of matter. This is
basic to the concept of GR. Except near black holes etc, they are
small.
> Let us try to keep this simple. I understood a 3% curvature margin of
> error to mean + - 3% deviation from Euclidean spatial geometry on the
> scale of the universe. Is that correct?
[[Mod. note -- I have changed a garbled character in the next line
to "+/-", which I am fairly confident is what was intended. -- jt]]
lambda + Omega = 1 +/- 3% is a statement most people familiar with the
observations would be comfortable with. Translating that to a deviation
from Euclidean spatial geometry is not straightforward. Think of the
radius of curvature R = c/H_0(Omega+lambda-1)^{0.5}. For a flat
universe, it is infinite. For a spatially curved universe, it has some
value.
> > Whether the angles of a triangle the size of the universe add up to 180
> > degrees is the interesting question.
>
> > Flat space is a good approximation.
>
> You seem to imply there is something more accurate.
Flat space is a good approximation on scales small enough relative to
the radius of curvature mentioned above.
> (Please, please don't fob me off with 2 dimensional analogies drawn on
> a 3D sphere. [Just because I said I never really came to terms with
> the geometrical interpretation of the GR axioms, that does not
> necessarily mean I am an idiot])
Actually, this might be what you want. Add up the angles of a triangle
and figure out the percentual deviation from the flat case. The larger
the triangle, the greater the percentual deviation (for the non-flat
case). So, the answer to your question depends on the scale.
<80fedc48-32f6-4681-8a00-46dbd8c0c0c8@s9g2000prg.googlegroups.com>,
Chalky <chalkyspam@bleachboys.co.uk> writes:
> > Local concentrations of matter will have local effects.
>
> Is that a yes or a no?
Yes. Whatever the average global value of spatial curvature, there are
local deviations caused by local concentrations of matter. This is
basic to the concept of GR. Except near black holes etc, they are
small.
> Let us try to keep this simple. I understood a 3% curvature margin of
> error to mean + - 3% deviation from Euclidean spatial geometry on the
> scale of the universe. Is that correct?
[[Mod. note -- I have changed a garbled character in the next line
to "+/-", which I am fairly confident is what was intended. -- jt]]
lambda + Omega = 1 +/- 3% is a statement most people familiar with the
observations would be comfortable with. Translating that to a deviation
from Euclidean spatial geometry is not straightforward. Think of the
radius of curvature R = c/H_0(Omega+lambda-1)^{0.5}. For a flat
universe, it is infinite. For a spatially curved universe, it has some
value.
> > Whether the angles of a triangle the size of the universe add up to 180
> > degrees is the interesting question.
>
> > Flat space is a good approximation.
>
> You seem to imply there is something more accurate.
Flat space is a good approximation on scales small enough relative to
the radius of curvature mentioned above.
> (Please, please don't fob me off with 2 dimensional analogies drawn on
> a 3D sphere. [Just because I said I never really came to terms with
> the geometrical interpretation of the GR axioms, that does not
> necessarily mean I am an idiot])
Actually, this might be what you want. Add up the angles of a triangle
and figure out the percentual deviation from the flat case. The larger
the triangle, the greater the percentual deviation (for the non-flat
case). So, the answer to your question depends on the scale.