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redskies
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Given the curvature of space-time, are all lines through space also loops? If so, are the loops always circular? If the loops are not always circular, what determines the shape of the loops?
cristo said:I'm really not sure what you're asking here. If all worldlines (lines in spacetime) were "loops" then this would mean that one's life would end at the same point in spacetime as it began, which is clearly not true. There are models of GR with so called closed timelike curves, but these are not physical solutions.
George Jones said:I think redskies is asking about loops in space, not spacetime, i.e., do there exist worldliines that begin and end at the same spatial comoving coordinates?
redskies, the answer is maybe. The situation depends on the spatial curvature of the universe, and we haven't measured spatial curvature with enough accuracy to give a definitive answer. Space might like the surface of the Earth (with one more dimension added), or it might be like like an infinite, unending (possible curved) blackboard. In the first case the answer is yes, while in the second its no.
Our measurements indicate that the spatial curvature of universe is near the borderline of these cases, and either case is consistent with the errors involved in the measurements.
This is correct.redskies said:Is it correct that curvature would not be constant throughout the universe because at a local level it would be affected by massive objects?
Right. Cosmological models are built taking into consideration average curvature at large scales, more than 100 Mpc. When you average the matter density over different regions greater than 100 Mpc you will find that there are nearly no deviations between these average values. Thus, at this scale the distribution of matter density is homogeneous. This determines a constant spatial curvature.redskies said:If so, when you speak of measuring spatial curvature, are you speaking of a measurement analogous to temperature in that it is an average of curvatures throughout the universe (in temperature's case an average of kinetic energies)?
hellfire said:This is correct.redskies said:Is it correct that curvature would not be constant throughout the universe because at a local level it would be affected by massive objects?
Chronos said:We know the universe is closer to dead flat than we can accurately measure. The more intriguing question is why? There is not nearly enough visible matter to explain why it appears to be so flat, hence the dark matter hypothesis [among other reasons supporting the DM hypothesis].
Chronos said:We know the universe is closer to dead flat than we can accurately measure. The more intriguing question is why? There is not nearly enough visible matter to explain why it appears to be so flat, hence the dark matter hypothesis [among other reasons supporting the DM hypothesis].
A line is a straight path that extends in both directions infinitely, while a loop is a closed shape that connects back to its starting point.
No, a line and a loop are two distinct geometric concepts and cannot be the same.
No, this statement holds true in all cases. A line and a loop have different defining characteristics and cannot be interchangeable.
Yes, a loop can intersect itself multiple times, creating multiple points of intersection.
A line has no endpoints and extends infinitely in both directions, while a loop has a defined starting and ending point and is a closed shape. You can also use the rule that a line cannot intersect itself, while a loop can intersect itself multiple times.