What's the difference between a two sphere and a three sphere?

[Baggio]

Just a couple of questions:

1. If we imagine space to be curved over a sphere is it possible to travel in one direction and eventually end up where you started, assuming that the sphere it self is not expanding.

2. What's the difference between a two sphere and a three sphere? I find it hard to grasp the idea of a three sphere, because if there is now a radial or z coordinate then it's not really a sphere is it?

Thanks

Raj

 

[jcsd]

Just a couple of questions:

1. If we imagine space to be curved over a sphere is it possible to travel in one direction and eventually end up where you started, assuming that the sphere it self is not expanding.

If you're thinking about something analogus to an explorer circumnavigating the globe, then yes certaily.

2. What's the difference between a two sphere and a three sphere? I find it hard to grasp the idea of a three sphere, because if there is now a radial or z coordinate then it's not really a sphere is it?

Thanks

-The main difference between a 2-sphere and a 3-sphere is their number of diemsnions (this is obvious I suppose).

-The idea of a 3-sphere is hard to grasp, the best way is by analogy to a 2-sphere.

-'the radila coordinate is something that is only really a coordiante when you embed the 3-sphere into a higher dimensional space, in the context of the space of the three sphere itself (assuming enough structure is defined) the 'radius' of the sphere is just a parameter that differentiates it from other simlair spaces.