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 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.