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1.) Minkowski space is illustrated in one of my books as a cone, with it's apex as the "origin", the side as the "light cone", the bend curvature inside the cone as the "hypoerbolic space" and a point inside the cone as "a point in spacetime". Please explain this to me.

2.) How does gravity make space non-Euclidean? Is it because gravity bends space, which causes non-Euclidean assumptions (e.g. angles in a triangle add up to 180 degrees, and parallel lines are possible) to be false?

3.) How effective is gravitational lensing in distorting our perception of the world? Would it be proper to assume that the 'actual' position of a still object on Earth deviates a fraction of a millimeter (or smaller) from our human perception due to this phenomenon?

4.) Why excactly don't the laws of Euclidean geometry hold in a uniformly rotating system? A text states that this occurs because space warps due to the contraction of the circumference. Why? Does this have anything to do with the centrifugal force? If so, doesn't the centrifugal force 'push away' objects from their original path and thus cause an expansion of the circumference?

5.) "Imagine a circle spinning in space. According to special relativity, the boundary of the disk contracted as it spun. There was a force acting on the circle at the boundary -- the centrifugal force -- and its action was analogous to that of a gravitational force. But the same contraction that affected the outer circle left the diameter unchanged. Thus...the ration of the circle to the diameter was no longer pi."

i. Once again, the centrifugal force is said to contract the boundary (like the gravitational force). I was under the impression that the centrifugal force pushes objects away from centripetal motion - -and it is actually centripetal force which pushes them towards the orbit's center. Also, why does the diameter remain unchanged?