Quantum Gravity 99.8: Proton-Electron Algebra vs Entanglement Algebra
- From: "OsherD" <mdoctorow@xxxxxxxxxxx>
- Date: 4 Mar 2007 07:04:07 -0800
From Osher Doctorow
The idea that there can be "set algebras" with two types of sets,
finite or bounded sets A, B, C, ..., and infinite sets A', B', C',
etc. (where A' literally refers to the complement or part of the
Universe outside finite set A and nothing else), suggests the
possibility that such sets may actually be "represented" by circles or
preferably disks/discs (solid circles so to speak) or spheres or balls
(solid spheres so to speak) capable of:
1) expanding ("toward infinity") versus contracting ("toward a point
or line or line segment")
2) decreasing density (toward "overlap") versus increasing density
(toward "explosion")
Before continuing, it is remarkable to compare this with Saunders
MacLane's and Eliashberg's and later William Lawvere's "Category
Theory" which has the curious role with regard to sets of downplaying
sets by refusing to use the word "set" for things that are at least
generalized sets ("objects" in their terminology). On the contrary,
if I am correct in the first paragraph above, then what we need is the
opposite of Category Theory with regard to "objects" at least.
Low-density overlaps of sets (balls) or even parts of sets
(intersecting parts) could easily explain force-carrying bosons as
nothing but low-density intersections which later "disappear" when the
sets re-contract into separate sets, as well as explaining
entanglement as permanent intersections of two sets or parts of two
sets which then keeps expanding toward infinity.
Electron-electron repulsion and proton-proton repulsion as well as
electron-proton attraction could be explained as high-density
expansions-contractions of at least the following types:
3) Set A (electron for example) contracts, while set B (proton for
example) expands toward both set A and infinity.
4) Set A (electron for example) contracts while set B (electron for
example) also contracts, or set A expands toward infinity but not
toward set B while set B expands toward infinity but not toward set A.
In each case above, contraction is either automatically represented by
continuing to use the bounded set symbol A or by possibly
distinguishing A at different times by A_1, A_2, A_t1, A_t2, etc.;
while expansion is represented by replacing A by its "tending toward
infinity" dual A' .
Positive and negative electric charges seem to also easily fit into
this framework.
Osher Doctorow
.
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