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A new paper by Helge Rose and Torsten A-M was recently added to the bibliography and sparked comment. This thread is in case there is any further related comment or discussion.
The authors had an interesting conjecture, right at the very end of the paper, on page 15:
==sample excerpt==
"At the end we want to give another interpretation of the Casson handle. Connes [37] showed that by means of the non-commutative geometry the action of the standard model can be reproduced. His model is based on the space M×F where the additional space F is ad hoc and has no relation to the spacetime M.
In our model the space F could be interpreted as an expression of the Casson handle and so of the smoothness of spacetime establishing a deep relation between quantum matter and space."
==endquote==
One of us, Jfy4, commented as follows.
This is actually a very broad topic. I guess nearly everybody is aware of the work of Sundance Bilson-Thompson and 4 or 5 others along entirely different lines----still it's getting matter out of spatial geometry/topology features, in that case it was braids and knots in networks.
For instance, several papers by Yidun Wan:
http://arxiv.org/find/hep-th/1/au:+Wan_Y/0/1/0/all/0/1
marcus said:Torsten and Helge have discussed their idea some with us here at PF Beyond. It is a radical and high-risk idea.
http://arxiv.org/abs/1006.2230
On the geometrization of matter by exotic smoothness
Torsten Asselmeyer-Maluga, Helge Rose
17 pages
(Submitted on 11 Jun 2010)
"Clifford's hypothesis is investigated: A particle is made up of nothing but a distinct type of a space manifold, differing from the surrounding manifold of empty space. It is shown that this distinct space manifold representing matter differs from the surrounding vacuum by the exotic smoothness of its spacetime. The smoothness structure of spacetime can be described by a tree-like subset -- the Casson handle -- consisting of immersed discs and connecting tubes between them. The Weierstrass representation shows that the immersed discs are represented by spinors fulfilling the Dirac equation and leading to a mass-less Dirac term in the Einstein-Hilbert action. The connecting tubes between the discs realize an action term of a gauge field. Both terms are purly geometrical and characterized by the mean curvature of the components of the Casson handle. This gives a good support to Clifford's conjecture that matter is nothing more but an exotic kind of space."
The authors had an interesting conjecture, right at the very end of the paper, on page 15:
==sample excerpt==
"At the end we want to give another interpretation of the Casson handle. Connes [37] showed that by means of the non-commutative geometry the action of the standard model can be reproduced. His model is based on the space M×F where the additional space F is ad hoc and has no relation to the spacetime M.
In our model the space F could be interpreted as an expression of the Casson handle and so of the smoothness of spacetime establishing a deep relation between quantum matter and space."
==endquote==
One of us, Jfy4, commented as follows.
jfy4 said:Ahh! recently I have been considering to myself whether it would be possible to construct matter from space using a transformation of sorts. in fact it was 2 days ago that this idea hit me, and then yesterday I come to PF only to find a Paper on that very idea, and a long history of interest in the possibility forming matter out of geometry. My intuition told me that using a discrete set of space-time quanta, one could assemble a wave in much the same way a discrete transform takes quanta inputs and out-puts a continuous wave. A very alluring idea.
This is actually a very broad topic. I guess nearly everybody is aware of the work of Sundance Bilson-Thompson and 4 or 5 others along entirely different lines----still it's getting matter out of spatial geometry/topology features, in that case it was braids and knots in networks.
For instance, several papers by Yidun Wan:
http://arxiv.org/find/hep-th/1/au:+Wan_Y/0/1/0/all/0/1
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