Need Help Understanding Misner Space Terminology

[Quantum Copy]

Hello! I'm having trouble understanding some of the terminology used to describe Misner (or Milne) Space. Some of the words that are troubling me are "Orbifold" (is this related at all to the cylindrical structure of the Misner universe?), "translation symmetry" (does this refer to the idea that the opposite "walls" of this space-time are identified with each other, so that if you enter one wall you emerge from the opposite one?), "axisymmetric Bianchi I universe" and "Klein bottle topology". I'm trying to understand more about Misner space, because I find it to be such a fascinating model, but I need some help with the terminology. Thanks so much!

 

[tiny-tim]

Welcome to PF!

Hi Quantum Copy! Welcome to PF!

Some of the words that are troubling me are "Orbifold" (is this related at all to the cylindrical structure of the Misner universe?), "translation symmetry" (does this refer to the idea that the opposite "walls" of this space-time are identified with each other, so that if you enter one wall you emerge from the opposite one?), "axisymmetric Bianchi I universe" and "Klein bottle topology". I'm trying to understand more about Misner space, because I find it to be such a fascinating model, but I need some help with the terminology. Thanks so much!

"Orbifold" and "Bianchi I universe" … dunno.

"translation symmetry" … no, it just means it looks the same everywhere … see http://en.wikipedia.org/wiki/Translational_symmetry

"Klein bottle topology" … look at the "Construction" section of http://en.wikipedia.org/wiki/Klein_bottle

 

[Entropia]

Hello! I understand your confusion with the terminology used to describe Misner Space. Let me try to explain it in simpler terms.

Firstly, an orbifold is a type of space that is similar to a manifold, but with some points or regions being identified with each other. In the case of Misner Space, the cylindrical structure is indeed related to the orbifold structure, as the two "walls" of the cylinder are identified with each other.

Translation symmetry refers to the idea that the laws of physics remain the same regardless of where you are in the space. In Misner Space, this means that the laws of physics are the same on both walls of the cylinder, as they are identified with each other.

The term "axisymmetric" means that the space has a rotational symmetry around a central axis. In the case of the Bianchi I universe, this means that the universe has a cylindrical shape and is rotating around its central axis.

Lastly, the Klein bottle topology refers to the shape of the space, which is similar to a Möbius strip. This means that the space has only one side and no boundary.

I hope this helps to clarify some of the terminology used in describing Misner Space. It is indeed a fascinating model that has been studied extensively in theoretical physics. If you have any further questions, please don't hesitate to ask. Best of luck in your understanding of Misner Space!