Re: Eigenfunction Diffeomorphism

Posted by moorglade on November 13, 2002 at 20:55:00:

In Reply to: Eigenfunction Diffeomorphism posted by xjgraviton on November 11, 2002 at 01:54:19:

Very interesting, Iam about to delve into a book by Roger Penrose! I Have myself been aware of what you state here;Non-Euclidean geometry has great explanatory power, yet there must be a type of "dynamics" involved, possibly related to a type of configuration space or varying density gradients. Static geometry cannot be the whole, complete explanation.

Mathematician Roger Penrose demonstrated how many of the properties of three dimensional space can be created out of networks of spinors, the simplest possible "quantum mechanical objects". These spinors are used to define the two possible values of an electron's spin.

He then generalized the spinor into a mathematical quantity called a twistor. The mathematics of complex numbers is used, which makes twistors hard to visualize. Geometrically, the notion of a point becomes more complicated, and secondary, defined by a conjunction of many individual twistors. A daunting approach mathematically.

So it becomes interesting when you later state;OK, "A directed or 'oriented' line - a one dimensional 'manifold' - has
for its boundary the starting point and the terminal point, both zero dimensional." A closed circuit.

The starting point is "negative".

The end point is "positive".

-A + A = 0.

-A------0------A

The starting point is also the ending point.

--------->
<---------

"The zero dimensional boundary of a one dimensional boundary of a two dimensional region is zero".

A true statement.

"The one dimensional boundary of the two dimensional boundary of a three dimensional region is zero".

A true statement.

Space is three dimensional. A cube or tetrahedron is three dimensional.

Also symmetrical

Energy and momentum are conserved.

For this statement places space as 'ISOLATED', and therefore one cannot emmbed an energy to it.

Quantum 'waves' were discovered by Einstein long before anyone knew what he meant!..it is there in black and white so to speak!

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