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Vladimir Trifonov     Category and topos theory in physics; compatibility of general relativity and quantum mechanics; monocosm (axiomatic approach to quantum gravity)       

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      In the beginning...

God has been out there for eternity. In the beginning he was there alone. For an unimaginable number of millennia there's been nothing but him in the world. In fact, there was no world either. Since the eternity is infinitely long, God naturally got rather bored having done nothing for so long. That was probably why he eventually had a thought: if he is God and therefore omnipotent, he should not be just sitting, suffering from boredom - he should do something. No doubt, he could have done everything in a blink of an eye. For some reasons, however, he decided not to hurry. First he created heavens and earth. To reduce the possibility of a mistake, God needed light. It is clear, thus that in the preceding millennia he was forced to sit in total darkness. Fortunately, he was not at risk of hurting himself against something because there was nothing around … (La Bible Amusante

     Monocosm and observer-experient related papers

bulletOn the Origin of R-species, published in:
bullet Europhysics Letters 32 (8) (1995) 621-626, under the title A Linear Solution of the Four Dimensionality Problem (PDF). DOI: 10.1209/0295-5075/32/8/001. One of the earliest applications of topos theory in mathematical  physics. Discovery of a connection between the dimensionality and metric properties of unital algebras and internal logic of topoi they generate - if the internal logic of a topos is Boolean then the topos is generated by the quaternion algebra. The first technically  accurate description of natural Minkowski inner product on quaternions.
bulletNatural FLRW Metrics on the Lie Group of Nonzero Quaternions,  published in: 
bullet International  Journal of Theoretical Physics 46 (2) (2007) 251-257, under the title "Natural Geometry of Nonzero Quaternions", (PDF). DOI: 10.1007/s10773-006-9234-9. Discovery of a non-flat relativistic structure on nonzero quaternions - together with the natural Lorentzian metric they form a solution of the Einstein equations (closed FLRW geometry).
bulletGeometric modification of quaternionic quantum mechanics, published in:
bulletIJTP 47 (2) (2008) 492-510, under the title "GR-friendly description of quantum systems",  (PDF).   DOI: 10.1007/s10773-007-9474-3. A generalization of quantum mechanics that incorporates the kinematics of general relativity, and converts some of the axioms of GR into true theorems. It is shown that the dynamics of the theory is represented by a relativistic generalization of Schrödinger evolution and is equivalent to a superposition of three dependent Hamiltonian flows (hyper-Hamiltonian flow).

The above papers are copyrighted, and downloads are permitted for personal study only. For any other use please contact the author and/or corresponding publisher.

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