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help explain curvature of the universe
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t...@iol.ie
May 11, 2012, 4:32:43 AM5/11/12
to
if the universe is closed but unboounded, usually represented as the
surface of (an expanding) sphere,
with respect to what exactly , is it curved?
two concentric circles are not curved relative to each other
(circumferences are "paarallel" all the way round), but they are
curved with respect to a tangent line to one of them.
similarly the "two dimensional" surface of a sphere is curved with
respect to a plane.
but I can make no sense of how 3-d space can be curved "back" on
itself, the very definition of curvature requires something else
relative to which the curvature is measured.
or is it true to say "space-TIME" is curved, but 3-d space is not.?
that equally seems unintelligible to me.
surface of (an expanding) sphere,
with respect to what exactly , is it curved?
two concentric circles are not curved relative to each other
(circumferences are "paarallel" all the way round), but they are
curved with respect to a tangent line to one of them.
similarly the "two dimensional" surface of a sphere is curved with
respect to a plane.
but I can make no sense of how 3-d space can be curved "back" on
itself, the very definition of curvature requires something else
relative to which the curvature is measured.
or is it true to say "space-TIME" is curved, but 3-d space is not.?
that equally seems unintelligible to me.
dlzc
May 11, 2012, 10:10:17 AM5/11/12
to
Dear t...:
On Friday, May 11, 2012 1:32:43 AM UTC-7, t...@iol.ie wrote:
> if the universe is closed but unboounded, usually
> represented as the surface of (an expanding) sphere,
> with respect to what exactly , is it curved?
Forward or backward time.
Start moving towards some distant point at c or less (in forward time), without speed corrections, and you will end up shy of your target with each passing unit of time.
> two concentric circles are not curved relative to
> each other (circumferences are "paarallel" all the
> way round), but they are curved with respect to a
> tangent line to one of them. similarly the "two
> dimensional" surface of a sphere is curved with
> respect to a plane.
>
> but I can make no sense of how 3-d space can be
> curved "back" on itself, the very definition of
> curvature requires something else relative to
> which the curvature is measured.
The usual model is the surface of an idealized Earth, where an equator always goes east-west, but any unaccelerated path between the equator and the pole... orbits the equator.
> or is it true to say "space-TIME" is curved,
> but 3-d space is not.? that equally seems
> unintelligible to me.
They did a survey, space is verified globally flat. So the curvature with no significant mass concentrations, is only detectable along the time axis.
David A. Smith
On Friday, May 11, 2012 1:32:43 AM UTC-7, t...@iol.ie wrote:
> if the universe is closed but unboounded, usually
> represented as the surface of (an expanding) sphere,
> with respect to what exactly , is it curved?
Start moving towards some distant point at c or less (in forward time), without speed corrections, and you will end up shy of your target with each passing unit of time.
> two concentric circles are not curved relative to
> each other (circumferences are "paarallel" all the
> way round), but they are curved with respect to a
> tangent line to one of them. similarly the "two
> dimensional" surface of a sphere is curved with
> respect to a plane.
>
> but I can make no sense of how 3-d space can be
> curved "back" on itself, the very definition of
> curvature requires something else relative to
> which the curvature is measured.
> or is it true to say "space-TIME" is curved,
> but 3-d space is not.? that equally seems
> unintelligible to me.
David A. Smith
OG
May 14, 2012, 6:21:47 PM5/14/12
to
On 11/05/2012 09:32, t...@iol.ie wrote:
> if the universe is closed but unboounded, usually represented as the
> surface of (an expanding) sphere,
> with respect to what exactly , is it curved?
>
<snipped>
> if the universe is closed but unboounded, usually represented as the
> surface of (an expanding) sphere,
> with respect to what exactly , is it curved?
>
> but I can make no sense of how 3-d space can be curved "back" on
> itself, the very definition of curvature requires something else
> relative to which the curvature is measured.
>
Choose 3 points in space - use light to draw 3 straight lines between
> itself, the very definition of curvature requires something else
> relative to which the curvature is measured.
>
them, making a triangle.
Measure the 3 angles, if they add up to 180 degrees you have 'flat'
space. If they don't your space is curved.
Dr J R Stockton
May 15, 2012, 5:39:26 PM5/15/12
to
In sci.astro message <a1desk...@mid.individual.net>, Mon, 14 May 2012
23:21:47, OG <ow...@gwynnefamily.org.uk> posted:
False logic. If they do not, it is curved. But if they do, it might or
might not be.
--
(c) John Stockton, near London. *@merlyn.demon.co.uk/?.?.Stockton@physics.org
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, and links.
Correct <= 4-line sig. separator as above, a line precisely "-- " (RFC5536/7)
Do not Mail News to me. Before a reply, quote with ">" or "> " (RFC5536/7)
23:21:47, OG <ow...@gwynnefamily.org.uk> posted:
might not be.
--
(c) John Stockton, near London. *@merlyn.demon.co.uk/?.?.Stockton@physics.org
Web <http://www.merlyn.demon.co.uk/> - FAQish topics, acronyms, and links.
Correct <= 4-line sig. separator as above, a line precisely "-- " (RFC5536/7)
Do not Mail News to me. Before a reply, quote with ">" or "> " (RFC5536/7)
߃-- ¹¹
May 16, 2012, 12:10:41 AM5/16/12
to
"We must always remember that our ordinary physical laws, as they are
usually expressed, do not hold true when carried to an extent which
permits the error to be measured, because they do not follow a straight
line reaching to infinity, but a curve of finite radii.
In a timeless universe, this curve would be represented by a circle, but
since the laws operate through time as well as space, the curve is more
readily understood if depicted as a 'sine wave.'
The circle, being without beginning or end, symbolizes the infinite
nature of the Universe itself and the sine wave passing through it
symbolizes the curved but finite nature of the laws which operate within
the infinite whole.
The well known, ancient Chinese Yin -Yang Sine Wave Symbol, whose true
meaning has been blurred thru time, is but one earthly symbol that
represents the positive and negative aspects of the laws, that operate
within the infinite whole.
߃--¹¹
usually expressed, do not hold true when carried to an extent which
permits the error to be measured, because they do not follow a straight
line reaching to infinity, but a curve of finite radii.
In a timeless universe, this curve would be represented by a circle, but
since the laws operate through time as well as space, the curve is more
readily understood if depicted as a 'sine wave.'
The circle, being without beginning or end, symbolizes the infinite
nature of the Universe itself and the sine wave passing through it
symbolizes the curved but finite nature of the laws which operate within
the infinite whole.
The well known, ancient Chinese Yin -Yang Sine Wave Symbol, whose true
meaning has been blurred thru time, is but one earthly symbol that
represents the positive and negative aspects of the laws, that operate
within the infinite whole.
߃--¹¹
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