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Author Topic: Would travel backwards through a wormhole require duplication of your atoms?  (Read 6832 times)

Offline chiralSPO

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If you define parallel lines as straight lines that are always the same distance, then it is impossible to have parallel lines on the surface of a sphere.

But if you define parallel lines as in the attached diagram, then you can have parallel lines on a sphere, and they will necessarily intersect at two points.
« Last Edit: 14/06/2015 21:14:31 by chiralSPO »
 

Offline jeffreyH

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Lines of latitude at equal distances above and below the equator can be considered parallel. These are not geodesics as they do not trace the shortest path around a sphere. This shortest path between two points is traced out by a great circle. At the equator and for an infinitesimal distance two great circles can be considered parallel. Objects that attempt to follow lines of latitude will not describe an orbit and will require a force to maintain this trajectory. This is best illustrated by the principle of least action.

https://en.wikipedia.org/wiki/Principle_of_least_action
 

Offline chiralSPO

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parallel, yes. lines, no. As you point out, they are not geodesic.
 

Offline jeffreyH

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I should have made that point more explicitly. Thanks.
 

Offline Bill S

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Quote from: Chiral
parallel, yes. lines, no. As you point out, they are not geodesic.

Are you saying that only geodesics qualify as lines?
 

Offline chiralSPO

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My understanding is that in a curved space, a geodesic (shortest path between two points) is the best definition of a straight line. I am open to corrections if this is not the case...
 

Offline jeffreyH

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My understanding is that in a curved space, a geodesic (shortest path between two points) is the best definition of a straight line. I am open to corrections if this is not the case...

If you were to open out a sphere and flatten it then only geodesics would appear to be straight lines. The lines of latitude would appear as curves since they do not describe the shortest path.
 

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