Drawing links: Matter, Mass-energy, Space-time, and the Geometric Universe

[IDMclean]

Here's the challenge, and I am going to start it.

 

There is allot of threads here on Hypography regarding the nature of our Geometric universe. If this information was collected together into a more readable format where one can make sense of it, I believe a more complete understanding would arrise and a new layer of discussion could arrise.

 

Here are the main ones that I see.

A query about Blackholes

Science Breakthrough of the year

Relative Quantum Charge Dynamics

A simple Geometric Proof with Profound consequences by DoctorDick

Is 'time' a measurable variable?

Resolution of the Relativity/Quantum Mechanics Conflict

 

Geometrization Conjecture, Wikipedia

Poincare Conjecture, Wikipedia

 

I have a feeling that all of these are very much interrelated. I am interested in connecting the disperate threads of the forums together and discussing the consequences of their relationships.

[IDMclean]

Alright, After taking time to consider I would like to talk briefly about an interesting correlation.

 

DoctorDick poised a slight alteration to Einstein's:

[math]dS = icd\tau = \sqrt{(dx)^2 + (dy)^2 + (dz)^2 - (cdt)^2}[/math]

[math]dS = cdt = \sqrt{(dx)^2 + (dy)^2 + (dz)^2 + (cd\tau)^2}[/math]

If I am not mistaken this is major if considered in conjunction with the Poincare conjecture and Geometrization conjecture. As it would seem this lends itself to a 3-space closed manifold.

 

Furthermore it can be taken together with the mass conjecture that results (see Doctor Dick's paper above), in which mass is momentum propagating along the [math]\tau[/math] axis. What this results in, if I am not mistaken, and I am no math wiz but none the less what I visualize is a 4 dimensional object "submerged" in a three dimensional space. For moving mass this is a propagating disturbance on the hypersurface of the 3-space closed manifold. In which case mass is analogous to bump mapping on the hypersurface.

 

I realize that isn't an easy thing to visualize. So a word on hypersurfaces. A hypersurface is the "surface" of a n dimensional manifold. If you have a 3 dimensional space, a 2-space closed manifold like a sphere, then the surface of the sphere is the sphere's sub manifold and area. If you extend this to a 3-space, then the "surface" is 3 dimensional. the hypervolume is 4 dimensional.

 

I would suggest looking into such things independently, as I realize my short comings in mathematics, and so my limitations of expression.