Is space flat?

Wow, so many new folk. Hi purplecorndog! 3d? Yes, but we don't like to separate it from time, which gives us 4d.Flat? Well, it depends. Over small distances it is, to a very good approximation, flat. However, as you look on larger length scales you realise (using incredibly sensitve instrumentation) that around the earth, it is not totally flat. On sufficiently large scales the curvature can be quitepronounced, such as the whole universe being possibly curved into a (hyper)sphere, or around a black hole where things appear to curve the wrong way because the curvature is so extreme. The pit is space. This is a very common misconception with depictions of space(time). The pit shows that space is being stretched and distorted (by some mass such as a planet, star, black hole, etc) Yes, in quite a close sense, space(time) is a fabric.

Outside mathematics, it is a common misconception that a "higher dimension" is required for curvature. This is not true. Often a higher dimension is required for us to visualise curvature, e.g. a sphere (such as the surface of a snooker ball) is 2-dimensional, yet for us to appreciate that curavture we require a 3 dimensions in which to view it. The sphere itself requires no such higher dimension. Flat here refers to space and not space-time. We say spatially flat to be unambiguous. Space-time on the other hand is very curved.

Hi, welcome to EvC Yes No. 'things' as we think of them are actually ripples and bumps in the fabric. There is only the fabric. Those concepts don't have much meaning It just is. Everything that we think of is an aspect of the fabric. The fabric is existence. By stretching, we simply mean there is a concept of distance associated with pairs of points on the fabric, and distances can grow (or shrink) Thus the fabric doesn't tear nor stretch into something. See above What we think of as gravity is an effect of this stretching. We can see it in astronomical observations. But for us to strecth space-time would require manipulating immense energies - something for the far future.

No 'maybe' about it A physical object does not preclude space, it just occludes it - i.e. the object hides the background space.You have to understand that a 'physical object' is just a concentration of excitations of the underlying matter and force quantum fields. These fields overlap the space-time field perfectly - it is not a case of either/or. All the fields exist everywhere.