Talk:Curved space

Two dimensional paths on two dimensional surfaces of three dimensional solids
I am confused. The fact that: "an object constrained to lie on the surface of a sphere only has two dimensions that it can move in", seems to be either a tautology (ie a straight line on the surface of a sphere describes an arc and an arc is a path described in two dimensions), or it considers the surface of the sphere as a local inertial frame. However, neither seems to impact on the fact that a sphere not only looks three dimensional but is three dimensional.

Movements of objects constrained to lie on the non-curved surfaces of any three dimensional object might be described in one or more dimensions while for a curved surface such a path cannot be described in less than two dimensions apart from with respect to it being a local inertial frame.

It seems to me that a line drawn on the surface of a sphere will always curve relatively to both dimensions at a steady rate whereas for angular solids the path will only become two dimensional when it crosses an edge.

Could this be clarified in the article in some way?

--LookingGlass (talk) 14:27, 28 November 2012 (UTC)


 * It's true that any neighborhood on a curved surface is a three-dimensional object (as seen from outside), but an infinitesimal neighborhood is effectively flat, whence the "tautology". —Tamfang (talk) 22:36, 26 January 2013 (UTC)

Assessment comment
Substituted at 01:57, 5 May 2016 (UTC)

Surface of a sphere
Of course, a sphere is a 3D object. It does not just LOOK like that, it is reality! Why do you, writer of this article, want to confuse people??? Stay with your surface, that's what you want to talk about, don't you? Yeah, it's 2D. By the way, in the next section you talk about spaces and I don't read anything about the relationship between a surface and a space. Be more clear, man! Not everyone has the same knowledge as you. THIS IS WIKIPEDIA, NOT SOME KIND OF UNIVERSITY.

— Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 13:12, 27 October 2019 (UTC)

Earth on the trampoline like fabric is misleading example to explain curvature in spacetime
On the internet, perfectly misleading example showing Earth on the trampoline like fabric, has been depicted at many places to explain warp of spacetime. It is not correct example. For a sphere on trampoline like fabric it needs Earth's gravity to create that shape. Please refrain explanation using this example. Because it implies that cause of curvature in spacetime (gravity) is another gravity!

Reference:

https://physics.stackexchange.com/questions/3009/how-exactly-does-curved-space-time-describe-the-force-of-gravity

https://physics.stackexchange.com/questions/102910/why-would-spacetime-curvature-cause-gravity

https://physics.stackexchange.com/questions/222390/how-does-curved-space-explain-gravitational-attraction

Moreover, the image of the Earth on curved 2D surface, seems has been removed by NASA too. Need to remove that misleading image from Wikipedia. Atuldpatil (talk) 15:06, 15 March 2024 (UTC)