# If spacetime is curved, how would anyone know? If anyone could tell, would that really be spacetime curving?

Analogy: how do we know that the surface of the Earth is curved? Well, we could e.g. draw a triangle on the surface of the Earth, and check the sum of the corner angles. If the Earth was flat, you'd always find that the sum of these angles was 180°, so it would be impossible to e.g. create a triangle with two 90° corners. However, since the Earth is curved, this is indeed possible; you could e.g. draw a triangle where one edge follows the equator, and the two others follow meridians from the equator to the north pole.

The same concept would apply to spacetime: simple geometric relationships such as e.g. the sum of corner angles in a triangle would be different in flat spacetime from curved spacetime, and these relationships should be possible to measure to figure out the curvature of spacetime itself.

For the two observers you describe, it's of course true that if the observers moved about in space they would see each other moving about in space. It's also true that if they remained 'floating' in a space that was itself 'moving', they would also see each other moving about in space. That is to say, upon the passage of a large gravitational wave between them, each observer would 'feel' nothing, providing tidal forces can be neglected, but they would see the other observer moving around.

So what if these two observers were each holding the end of a pole? As the gravitational wave passes through the pole, they would each feel it pushing and pulling on them. As you suggest, indeed one or both would lose grip of the pole if this cosmic event was violent enough. To give a more 'down-to-earth' analogy (pun to become apparent), if you placed two observers a very large distance from the earth with a very long pole connecting them, then as they fell towards the earth in the radial direction, their trajectories would tend towards one another, and each would feel the pole actively pushing them outwards. The situation here is quite analogous.