Hyperspherical Universe????
August 3, 2006
Is the Universe Hyperspherical?
Of course not!!!!
A Hypersphere is described by the equation below:
x^2+y^2+z^2+w^2 +t^2=R^2
The cross-section above cannot be obtained from this equation and that means that I don't really know what is the name (if it has a name) of the 5-Dimensional Object I consider the Universe to be....
Of course, one can write the Universe parametric equations as:
Fi * C=R; (notice that I made Fi as a Cosmological Time, to make things simple)...:)
X=R* ThetaX; ThetaX is the Cosmological Angle for X.
{x,Tau} and {x', Tau'} are related through Lorentz Transforms if you consider Tau as proper time.
{x,Tau} and {x', Tau'} are related through a simple Rotation Matrix you consider Tau as a direction in the Four-Dimensional Space. This might seem confusing, but that is how I thought about the problem...
One cannot not write a theory just because an Object has no Name...
I named it Hyperspherical... I am sure someone will eventually give it the appropriate name...
In fact, now that I thought a little more about the subject, the topology might be a HyperCilindrical...:) HyperToroidal...:) ... or something lame as HyperCircular...:)
I don't know... Should I call the expansion a Lightspeed Expanding HyperToroidal or Hypercircular Universe..
If that is the case, let me know your preferences, and I will recast it as a HyperToroidal Object...:)
That is why I sought a better name for the theory which would hide this small detail.... The topology of my Universe has no name...:)
Now the Cat is Out of The Bag and I don't mean the Schrodinger Cat...:)