# Can we tell that we're in a flat space time? Or just in reference to other objects?

If you are sitting in space, far from any planet or large gravitational object, can you be sure that you're in a flat spacetime? Is it possible that some very distant object is heavily warping spacetime, but because it's so far away, it's acting uniformly on the area around you, so there is no way to detect that you are in warped spacetime?

Put another way, how do you know how warped spacetime is around you? Can you only measure it based on how other objects gravitational are accelerating towards you?

Put yet another way, is the curvature of spacetime absolute with some points in space having 0 spacetime curvature, or is the curvature relative to other areas?

If you are sitting in space, far from any planet or large gravitational object, can you be sure that you're in a flat spacetime? Is it possible that some very distant object is heavily warping spacetime, but because it's so far away, it's acting uniformly on the area around you, so there is no way to detect that you are in warped spacetime.

Your question, no offence, is too vague to be answered in specific terms. If you take a small enough space, it can be locally flat, but the nearer you are to a given mass, the smaller you will need to make that space in order for it to stay flat. It depends on the mass and how far you are away from it.

I appreciate doetoe's comment regarding my answer as it improves my wording:

Local flatness in the sense used by physicists doesn't say anything about flatness: it holds for any metric (flat or not). In fact (intrinsic) curvature is an absolute quantity, and it is defined at every point. Your second remark is a good one: a way to detect curvature at your location would be to look at triangles, but a single one is not enough if curvature is not constant.

Measuring Curvature.

Put another way, how do you know how warped spacetime is around you? Can you only measure it based on how other objects gravitational are accelerating towards you?

You can draw a triangle, and if the total number of internal degrees is greater than 180, then you are in K = +1 positive curvature space, if it is less than 180, you are in K = -1 negative curvature space.

Put yet another way, is the curvature of spacetime absolute with some points in space having 0 spacetime curvature, or is the curvature relative to other areas?

There are no absolutes, it all depends on the scale you use to measure.

• Thanks, I know this was a bit of a jumble of a question, but your answers all more or less got to what I was asking. Nov 29, 2016 at 16:31
• Thanks, I think if it wasn't for the idealizations of a small enough space being flat, half the material in GR texts would be gone. BTW, be ruthless with accepting another better answer later. Or you if see d/v from people with more experience.
– user108787
Nov 29, 2016 at 16:36
• No offence either ;) but I think your answer is a bit imprecise as well. Local flatness in the sense used by physicists doesn't say anything about flatness: it holds for any metric (flat or not). In fact (intrinsic) curvature is an absolute quantity, and it is defined at every point. Your second remark is a good one: a way to detect curvature at your location would be to look at triangles, but a single one is not enough if curvature is not constant. Dec 3, 2016 at 19:00
• @doetoe thanks for that, comments have a habit of disappearing so I will put yours in the answer above. That's the disadvantage of self study....nobody else to give another (better) pov or improve wording. This site has sorted me out on a lot of my assumptions, (as well as a thicker skin with some of the comments :)
– user108787
Dec 3, 2016 at 21:50

Not an expert, but if think we are comfortable with 3d space. It is easier to visualize flat space time. Please correct my notion if at all possible and not a violation of the rules. I am just here to learn