Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity
If spacetime is a physical object, it is conceivable that it loses its integrity or is destroyed in some way as a continuum in an abrupt process initiated in spacetime itself. An example is a gravitational collapse leading to a spacetime singularity, as in the interior of a black hole. We find a con...
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2025-04-01
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| author | Jerzy Król Torsten Asselmeyer-Maluga |
| author_facet | Jerzy Król Torsten Asselmeyer-Maluga |
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| description | If spacetime is a physical object, it is conceivable that it loses its integrity or is destroyed in some way as a continuum in an abrupt process initiated in spacetime itself. An example is a gravitational collapse leading to a spacetime singularity, as in the interior of a black hole. We find a conservative extension of quantum mechanics by quantum set theory over the singular domain and show that it is reconcilable with the special extension of spacetime 4-diffeomorphisms by automorphisms of Boolean models of set theory. The extension of quantum mechanics supports the random sequences of the quantum mechanical outcomes that can negate Tsirelson’s conjecture, whereas the extension of 4-diffeomorphisms indicates the role of exotic smooth 4-spheres as gravitational instantons. This leads to the negation of the smooth 4-dimensional Poincaré conjecture before its final resolution by mathematicians. We also discuss the case where the Poincaré conjecture would remain true. |
| format | Article |
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| institution | OA Journals |
| issn | 2218-1997 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
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| spelling | doaj-art-ca553e3acde6409c8b4d39b14014617b2025-08-20T02:25:07ZengMDPI AGUniverse2218-19972025-04-0111412610.3390/universe11040126Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum GravityJerzy Król0Torsten Asselmeyer-Maluga1Cognitive Science and Mathematical Modeling, University of Information Technology and Management, ul. Sucharskiego 2, 35-225 Rzeszów, PolandGerman Aerospace Center (DLR), 10178 Berlin, GermanyIf spacetime is a physical object, it is conceivable that it loses its integrity or is destroyed in some way as a continuum in an abrupt process initiated in spacetime itself. An example is a gravitational collapse leading to a spacetime singularity, as in the interior of a black hole. We find a conservative extension of quantum mechanics by quantum set theory over the singular domain and show that it is reconcilable with the special extension of spacetime 4-diffeomorphisms by automorphisms of Boolean models of set theory. The extension of quantum mechanics supports the random sequences of the quantum mechanical outcomes that can negate Tsirelson’s conjecture, whereas the extension of 4-diffeomorphisms indicates the role of exotic smooth 4-spheres as gravitational instantons. This leads to the negation of the smooth 4-dimensional Poincaré conjecture before its final resolution by mathematicians. We also discuss the case where the Poincaré conjecture would remain true.https://www.mdpi.com/2218-1997/11/4/126Boolean models of ZFCquantum mechanicsquantum gravityphysics of exotic smooth 4-spheres |
| spellingShingle | Jerzy Król Torsten Asselmeyer-Maluga Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity Universe Boolean models of ZFC quantum mechanics quantum gravity physics of exotic smooth 4-spheres |
| title | Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity |
| title_full | Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity |
| title_fullStr | Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity |
| title_full_unstemmed | Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity |
| title_short | Negation of the Smooth Poincare Conjecture in Dimension 4 and Negation of the Tsirelson’s Conjecture Shed Light on Quantum Gravity |
| title_sort | negation of the smooth poincare conjecture in dimension 4 and negation of the tsirelson s conjecture shed light on quantum gravity |
| topic | Boolean models of ZFC quantum mechanics quantum gravity physics of exotic smooth 4-spheres |
| url | https://www.mdpi.com/2218-1997/11/4/126 |
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