cianfa72's latest activity

The notion of traveling along a straight line at constant velocity has different meaning depending on the "physics framework" used. The...

a) It is Klein bottle, not klien. It is constructed as a quotient space ##\{[0,1]\times [0,1]\}/\sim ## where ##(0,y)\sim (1,y)## and...

I was trying to visualize ##\mathbb S^2 \times R## as a "block" extending across all 3D euclidean space with a spherical hole inside it...

Try thinking of ##\mathbb S^3## in terms of the space obtained by gluing the spherical boundary of two 3-balls in 3D space. This space...

It's worth noting that dividing the distance I measure you to travel by the time I measure you to take is a quantity called velocity...

True but not relevant. What matters is the (intrinsic) ##\mathbb S^3## topology. In this topology (homeomorphic to two 3-balls glued...

No, being pairwise linked (as in the image with keyrings in wikipedia link) is invariant under stereographic projection. Happy 2026 !

By Whitney embedding theorem, n=6 as Euclidean space is enough to embed ##S^2 \times R## in. I'm not sure whether there is an embedding...

Yes, this is the same for parallel straight lines in Euclidean space. The minimum distance between parallels A and B depends on our...

I think you're actually assuming a stationary spacetime where the spacelike slices adapted to the time symmetry are the same (whormholes...

Yes, that's correct; the hourglass visualization represents 2-spheres by circles, so it's taking out one angular (or rotational)...

So, do you mean that the whormhole throat would be visibile/look as a 2D spherical surface in a spacelike slice of the underlying...

BTW, the fibers ##S^1## of the Hopf fibration are supposed to be what R. Penrose calls Clifford parallels in his book "The Road to Reality".

As shown by this animation, the fibers of the Hopf fibration of the 3-sphere are circles (click on a point on the sphere to visualize...

This is probably true for textbook problems, where simple systems are meant to be solved by hand. But this assessment might change in...