Geometry of schroedinger equation and riemannian geometry as a fiber bundle

[DoYouKnow]

Hi,

Has anyone read any of penrose's new book? From the parts I've read, it makes me curious if the geometry of the universe can be derived from the fact that at each point we make a measurement, the entire riemannian universe is visible from that point. This seems to me like it's a fiber bundle, since fiber bundles measure like a circle of intervals, for example, which would be a cylinder without top and bottom. If you can visualize this, it's like a bunch of intervals arranged in a circle. Has anyone explored this connection further? It seems that there might be a way to derive some type of quantum cosmology relationship from this. Keep in mind I haven't read the whole books, but Penrose's "The road to reality" and Weeks' "The Shape of Space" are good.

Good luck in your quest for the ultimate theory.

DoYouKnow

[Guille]

Hi and welcome to toequest. If your username is intended as question, then I must ask you what do you think it is to 'know', does it mean to have the truth in our thoughts? In that case, no, I don't know, and no one does, for it is impossible to have the 'truth' as it is aprt of nature, not of our minds. Anyway, I don't want to get off topic.

I haven't read any of Penrose's books, but I do know about riemann's and gauss' geometries. An important thing we should note about Riemman's geometry is that is only valid for the subatomic (or atomic, I can't remember) level. Our bodies don't work by that geometry, in fact our bodies are too complex for present day maths+physics.

[DoYouKnow]

Do you know?

[DoYouKnow]

I think that I was a little confused before. I seemed to imply that the schroedinger equation had a type of geometry in the sense of a riemannian geometry, while it doesn't really. I"ll have to read more to find out about this.

[Guille]

I think that I was a little confused before. I seemed to imply that the schroedinger equation had a type of geometry in the sense of a riemannian geometry, while it doesn't really. I"ll have to read more to find out about this.

But there IS a riemannian geometry, just as the gaussian geometry. That I do know, yes.

[Mohan.C]

Hi guille can you briefly tell me what this reumennian geomrtry is?

[Guille]

Hi guille can you briefly tell me what this reumennian geomrtry is?

This article is great explaining: http://en.wikipedia.org/wiki/Riemannian_geometry
If you want a description, just read the paragraph at the top. But if you want to understand hwo it works, go through it all, it's short enough and not hard.

[becomingagodo]

it would be impossible to describe any quantum pheonoma using riemann geometry because if you read chapter in road to reality measurement paradox it tell you that the two world are incompatable and the guage bundle and fibre cannot be renormlisied and would lead to a mess of infinte.
although if you read on near the end where it talks about hawking theory it talks about his theory of imaginary time that woud meet the goal of being a quantum theory with riemann geometry but this time is taken to be imaginary and it has the luck of not blowing up infinte in your face.