
Originally Posted by
Awesomeville
Does anyone have any cool universe theories?
Consider a space-time manifold of the following form :
wherein

is the step Heavyside function, and the exponents of
e are functions of
r and
t.
This can be considered a rather peculiar type of closed universe - if, starting from some arbitrary point, you travel around such a manifold once, you will arrive at the same spot again, at the same time you started out on, but with your orientation
reversed, i.e. your left hand has become your right, and vice versa. Only if you travel around the manifold a
second time will you be returned to the same spot, and the same time, with your orientation restored to normal. You can keep going round and round into all eternity, and at each odd numbered trip you become your own mirror imagine, only to be restored at each even numbered trip. This space-time is multiply connected, and contains stable closed time-like curves. Furthermore, electric polarity can no longer consistently be defined - a closer analysis reveals that positive and negative charges are exactly equivalent, and which one is which depends only on where they are located. This is an example of a
non-orientable space-time, in this instance with the global topology of a Klein bottle, something I personally have substantial interest in.
Cool, isn't it
