[mrob]

>It is that spacetime which is curved rather than just space.

This is the crucial point that many discussions overlook. The concept of "curvature of space" is obvious nonsense because curvature is measured with respect to space. For space itself to curve implies the existence of meta-space (and as many nested metaspaces as you like). But "spacetime" does not work like "space", and there actually is no metaspace. Talking about "space" curving or expanding is unnecessarily confusing.

[repsilat]

>> It is that spacetime which is curved rather than just space.

> This is the crucial point that many discussions overlook

I agree completely with this (and have said as much in the past --https://www.reddit.com/r/cosmology/comments/2zy19s/bowling_b...) but

> The concept of "curvature of space" is obvious nonsense

This is emphatically not correct. Space can be curved without being embedded in a higher "meta-space". You can have a 2D surface that is curved as if it were the surface of a sphere without it actually being on an actual 3D sphere -- it just has to "connect up" the right way and have "parallel" lines bend towards each other and so on. Ditto in more dimensions.

[danbruc]

The concept of "curvature of space" is obvious nonsense because curvature is measured with respect to space.

This is not really true. If you take a flat two dimensional space, a sheet of paper, this space has no intrinsic curvature. You surely now imagine this sheet of paper laying flat on a table in front of you embedded in our usual three dimensional space. Now pick it up and role it to form a cylinder. This gives extrinsic curvature to the space, curvature in the space the sheet is embedded in. But the sheet has still no intrinsic curvature, if you were a two dimensional creature living on the sheet you can not tell whether it is laying flat on the table or is rolled up to a cylinder, at least ignoring the fact that the cylinder connects two opposite edges of the space.

The surface of the earth on the other hand has intrinsic curvature, angles of triangles don't add up to 180 degrees for example. And this intrinsic curvature is a feature of the space not of the embedding into a higher dimensional space. It is not easy to visualize if possible at all, but spaces can have intrinsic curvature independent or even without an embedding, our three dimensional space can be curved without being embedded in a higher dimensional space and the same of course holds for space-time.

[mrob]

"Extrinsic curvature" is normally called just "curvature". "Intrinsic curvature" isn't normally called anything because it has minimal relevance to everyday life. If you talk about "curvature of space" the natural assumption is that you mean extrinsic curvature.

[danbruc]

But in general relativity extrinsic curvature is the irrelevant thing, it's all about intrinsic curvature. We don't think of space-time being embedded in a higher dimensional space but we still talk about curvature of space-time, its intrinsic curvature.

These demonstrations with balls rolling on a stretchable rubber sheet to visualize gravity are really misleading in this regard because they use a good deal of extrinsic curvature to make things work but in reality mass doesn't deform space-time into a fifth dimension or at least it doesn't necessarily do so.

[kgwgk]

Curvature is not "measured with respect to [an embedding] space". If you have a triangle and the sum of the angles is not 180 degrees that's a non-Euclidian (curved) space.

[mrob]

But that's not how the word "curved" is used in everyday life. Call it non-Euclidian if it's non-Euclidian. Redefining common words only leads to confusion.

[kgwgk]

Participating in a discussion about an article titled "the quantum source of space-time" to say that basic concepts are nonsense because some words do not have the same meaning as in everyday life also leads to confusion.

[aroberge]

Take a 50-kg object (110 pounds) and carry it in your arms for an hour on a flat road. You will have done no work against gravity. You may complain that this is not how the word "work" is used in everyday life - and that you will have done a lot of "work" against gravity (preventing the object from falling to the ground). However, if you wish to discuss Physics and Mathematics, using terms that have precise definitions in those fields, you cannot object on the basis that these words do not have the same meaning as non-Physicist and non-Mathematicians ascribe to them.

[andyjohnson0]

Why stop there? Field, black hole, wormhole, string, force, spin, colour, charm, strangeness. All of these terms and more are used by physicists and have very different meanings to those used in "everyday life".