- #1
Hypercube
- 62
- 36
Hello everyone,
I don't normally come to Astro/Cosmo forums, but I stumbled upon a discussion between a mentor and a PF member here, which involved explanations on the geometry of the universe: difference between boundless vs unlimited, 2-torus vs 3-torus, why are tori boundless, etc. This got me curious about a few things, so I was wondering if someone could verify:
1. At present, do we know the shape of the universe?
2. Is the current assumption (or model) that the universe is flat, uniform and unlimited? We call that "3-plane"?
3. Speaking of these "exotic"-sounding shapes, like 3-torus and 3-sphere, can they also be a viable possibility?
4. If they are, that would suggest that they are so large that their curvature is practically undetectable? Hence, why we assume flat universe...?
5. In the discussion, someone mentioned Occam's razor; so, although we can keep coming up with differently closed surfaces of different shapes, can we say that the plane is the simplest one (and hence most probable)?
6. This is perhaps subjective, but does anyone else have a problem "accepting" the infinite universe with infinite mass, uniformly distributed? As an aspiring physicist I shouldn't go by what I "feel", but I cannot help that these infinities somehow go "against me" in some way. A 3-sphere would be boundless, but the mass would have to be finite, so I have no issues there...
7. Is Carroll An Introduction to Modern Astrophysics a good resource?
8. Do books on cosmology normally provide overview of GR? Or would you recommend to first read an introductory text on GR before I even dare open an astro/cosmology textbook?
Thank you.
My level: intermediate undergraduate, who has not taken any astro courses yet, and only conceptually knows what manifolds are. (This is probably wrong, but I think of it as some sort of generalisation of vector calculus.)
Edit: evidently, I can't count.
I don't normally come to Astro/Cosmo forums, but I stumbled upon a discussion between a mentor and a PF member here, which involved explanations on the geometry of the universe: difference between boundless vs unlimited, 2-torus vs 3-torus, why are tori boundless, etc. This got me curious about a few things, so I was wondering if someone could verify:
1. At present, do we know the shape of the universe?
2. Is the current assumption (or model) that the universe is flat, uniform and unlimited? We call that "3-plane"?
3. Speaking of these "exotic"-sounding shapes, like 3-torus and 3-sphere, can they also be a viable possibility?
4. If they are, that would suggest that they are so large that their curvature is practically undetectable? Hence, why we assume flat universe...?
5. In the discussion, someone mentioned Occam's razor; so, although we can keep coming up with differently closed surfaces of different shapes, can we say that the plane is the simplest one (and hence most probable)?
6. This is perhaps subjective, but does anyone else have a problem "accepting" the infinite universe with infinite mass, uniformly distributed? As an aspiring physicist I shouldn't go by what I "feel", but I cannot help that these infinities somehow go "against me" in some way. A 3-sphere would be boundless, but the mass would have to be finite, so I have no issues there...
7. Is Carroll An Introduction to Modern Astrophysics a good resource?
8. Do books on cosmology normally provide overview of GR? Or would you recommend to first read an introductory text on GR before I even dare open an astro/cosmology textbook?
Thank you.
My level: intermediate undergraduate, who has not taken any astro courses yet, and only conceptually knows what manifolds are. (This is probably wrong, but I think of it as some sort of generalisation of vector calculus.)
Edit: evidently, I can't count.