AsselmeyerMaluga 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/grqc/0511089 Differential Structures  the Geometrization of Quantum Mechanics Torsten AsselmeyerMaluga, Helge Rosé 13 pages, 2 figures "The usual quantization of a classical spacetime field does not touch the nongeometrical 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 spacetime, 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 spacetime. 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 TemperleyLieb 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. http://www.physicsforums.com/showthr...906#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 
initial reaction
Thanks selfAdjoint and Marcus
Well I guess you know what I'm going to say! All roads lead... The references to Krol on page 2 are interesting. A recent and related paper by Krol is Model Theory and the AdS/CFT correspondence http://arxiv.org/PS_cache/hepth/pdf/0506/0506003.pdf Quote from the abstract: ...though explicit calculations refer to the would be noncompact smooth 4invariants based on the intuitionistic logic. I think it is just great that Rose' and AM have spelled this out carefully. :smile: 
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Helge is here! Hi!

Remember
Quantum general relativity and the classification of smooth manifolds Hendryk Pfeiffer http://arxiv.org/abs/grqc/0404088 Might be useful. 
these two people are at what I think is a semiprivate contract Research and Development organization. the byline says Fraunhofer Gesellschaft
http://www.fraunhofer.de/fhg/EN/company/index.jsp http://fraunhofersociety.biography.ms/ the byline says FIRST FhG, Berlin. FIRST must be an acronym for some department at Fraunhofer Yes, FIRST means FRAUNHOFER INSTITUTE COMPTERARCHITECTURE SOFTWARE TECHNOLOGY we would say FICST, but for them a computer is a "Rechner" (because it Reckons stuff) and so they say FIRST. I was wondering. http://www.first.fraunhofer.de/ Maybe it is like being at an IBM Lab. the FhG centersthere are many all over Europedo CONTRACT research for both private companies and governments, they say they are the biggest organization for APPLIED research in Europe Anyway these two young people Helge Rosé and Torsten AM must likely be BEGINNING researchers, because i dont find many previous papers by them, only I think one by Torsten. [EDIT: with Kea's help I found more papers by Torsten, he is more senior, has been working in this field 10 years, coauthored with Brans, is writing a book] Well I didnt know about the Fraunhofer Institutes. You learn something new everyday. I guess we all know about the famous Fraunhofer who was born in 1787 and invented spectroscopywhat much of atomic physics and astronomy is based on. http://www.biography.ms/Joseph_von_Fraunhofer.html It says he was orphaned at age 11, in 1798, so he had to go to work in a workshop, which however collapsed in 1801. Therefore as a young 14year old Fraunhofer was buried in the remains of a badly constructed Munich lensgrinding factory. This however worked to his advantage, since he was rescued by the Prince of Bavaria who later became Maximilian Joseph the King of Bavaria. This prince was leading the crew digging people out, and he later helped Fraunhofer get time and books to study physics. 
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yeah, I saw Helge was online here at PF, so that was what prompted me to start this thread. but it was sA who twigged the paper here are snapshots of the two guys who wrote the paper, Torsten and Helge http://mmm.first.fraunhofer.de/de/team/ 
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http://www.arxiv.org/find/grp_physic...4d475087264912 :smile: and also, one of the references in the paper Generation of Source Terms in General Relativity by differential structures T. Asselmeyer 14 pages http://www.arxiv.org/abs/grqc/9610009 
Are these differential structure related to topologial quantum field theories? Quantum Mechanics is derived from Quantum field theory where we have creation and anhiliation operators for particles. The double slit experiment tell us that there must be something global that influences the path of particles, such that a single particle going through one of the slits seems to take into account whether the other slit is covered or not. But before you can have a particle trajectory you must have particles. Virtual particles seem to pop into and out of existence as part of the zero point energy. They can be made real particles if one of the pair is captured by a horizon. So it seems we are looking for some global mechanism for particle creation in the first place. And the same global topological concerns that give rise to virtual particles to begin with should incorporate some dynamics to account for trajectories of real particles to end with. So I consider what topological entities might give rise to particles. I think in terms of an index theorm or some AdS/CFT effect going on.
When I think of the first particles arising from the tiny, expanding universe, it seems that whatever the mechanism of virtual particle creation, it must some how proceed in a smooth way from a singularity. The first fluxuations would be in the size and location of the entire, tiny spacetime of the universe. There would not be room enough, yet for virtual particles, and the fluxuation would simply be in some degree of freedom in the boundary or overall size of the tiny universe. Perhaps this is the same mechanism that forces the universe to expand. Then as the universe becomes large enough, these fluxuations can include particles that pop in and out of existence as these overall topological entities change. 
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Helge said that Torsten was writing a book. Exotic Structures and Physics: Differential Topology and Spacetime Models I can make better sense of that now that I know he has been working in this general field for 10 years. 
Thats right, we think about the topic nearly 15 years. Torstens DS idea is younger (10 years). Since 2 years he could show that the DS should build a Hilbertspace. The TemperleyLiebalgebra structure of the changes is from this year.

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I hope you return here tomorrow. I will try to have some questions. I don't understand how a 3D submanif. can represent a particle but no use explaining now, I will give it another try tomorrow 
This (post #6) is correct. We are work at FIRST in Berlin. We have published papers about different topics (Evolutionary Algorithms, QuantumHalleffect, Quantum Computing, Computerstuff like simulation of complex systems ...) e.g. http://www.first.fhg.de/helge.rose/publications
or my homepage http://www.first.fhg.de/helge.rose We have not published our ideas to QG (except Torstens 1996 paper) until now because  well it is not an easy topic and very explosive. We would like to make the ideas save to form a whole picture. The last steps (TemperlyLiebalgebra of DS transitions) are appeared this year. This paper is only a first step  so to say the "kinematik" of the theory. We have ideas to the next steps  the dynamics, i.e. the field equation. Only this will complete the picture and hopefully get a new usefull theory. But we think the results from the 0506067paper are promissing. I think the interessting discussion here will be very fruitfull for this. 
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"In the introduction we have shown that there is a close relation between the transition of the DS and a singular connection with 3D supports. Such connections are expressed by singular 1forms with 3D supports." I am struggling at the very beginning of understanding this. I am familiar with connection being expressed by a 1form (with values in a somewhat arbitrarily chosen Lie algebra)unless I am confusing something, this is very usual. But there is a lot that is new here. I think of an earthquake and a "FAULTLINE" which is actually a fault surface going deep into the earth, and I try to imagine a 4D analog. So there is a 3D "FAULT" hypersurface. And somehow the change in DS is closely related to a connection (or a 1form) defined on this 3D "fault". This 3D thing is the SUPPORT of the 1form. It is a set. And when you make the algebra, you are using what looks like it might be ordinary set operations, like UNION and INTERSECTION of these support sets. It becomes very urgent for me to try to understand how the support set of the 1form can, in some way, characterize the earthquake that happens when you go from one DeeEss to another DeeEss. I am a slow learner, it may take days before my brain stops smoking and making sparks and begins to understand this idea of transition of DeeEss. 
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I will try to answer your post about 3dsupport next morning (at night of your time). 
This discussion started on another thread, but I thought it best to bring it over here:
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This does agree with the wikipedia entry: http://en.wikipedia.org/wiki/Differential_structure Is this what you're saying? Because I think it's either not true, there's some miscommunication, or I'm really messing up. (And it was a friend who pointed out to me this was a potential problem with your paper, I was just bumbling around confused.) The table you quote is only true for spheres. Except in n=4 the sphere is not known to have an infinite number of DS, though it might. As a counter example, I read in Brans latest paper that the number of DS is 1 for R^n when n>4. Could you help clear this up? Or maybe you need to fix your paper? I do really like the main idea. 
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