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marcus

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## Main Question or Discussion Point

**Asselmeyer-Maluga and Rosé: Geometrization of Quantum Mechanics**

this paper was mentioned by selfAdjoint in another thread.

people there seemed to think it should be studied/discussed

so maybe this paper should have its own thread, besides

being included in our list of new QG/matter ideas

http://arxiv.org/abs/gr-qc/0511089

**Differential Structures - the Geometrization of Quantum Mechanics**

Torsten Asselmeyer-Maluga, Helge Rosé

13 pages, 2 figures

"The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor understanding of the geometrical character of quantum mechanics. In Einstein's theory gravitation is expressed by geometry of space-time, and the solutions of the field equation are invariant w.r.t. a certain equivalence class of reference frames. This class can be characterized by the differential structure of space-time. We will show that matter is the transition between reference frames that belong to different differential structures, that the set of transitions of the differential structure is given by a Temperley-Lieb algebra which is extensible to a C*-algebra comprising the field operator algebra of quantum mechanics and that the state space of quantum mechanics is the linear space of the differential structures. Furthermore we are able to explain the appearance of the complex numbers in quantum theory. The strong relation to Loop Quantum Gravity is discussed in conclusion."

my comment: this looks interesting. I would not have caught it. selfAdjoint flagged it.

https://www.physicsforums.com/showthread.php?p=834906#post834906

in post #7 of the Garrett Lisi thread.

what is impressing me most is that right now seems to be a time of new ideas. a lot of new ideas are appearing that connect different mathematical pictures of spacetime, all having to do with Quantum Gravity

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