Quantum gravity from descriptive set theory

摘要: Abstract We start from Hilbert’s criticism of the axioms classical geometry and possibility abandoning Archimedean axiom. Subsequently we proceed to physical a fundamental limitation on smallest length connected certain singular points in spacetime below which measurements become meaningless, Finally arrive at conclusion that maximising Hawking–Bekenstein informational content makes existence transfinite for “spacetime” not only plausible but probably inevitable. The main part paper is then concerned with proposal mathematical description transfinite, non-Archimedean using descriptive set theory. Nevertheless, despite all abstract mathematics, remain quite close similar lines investigation initiated by physicists like A. Wheeler, D. Finkelstein G. ‘tHooft. In particular introduce logarithmic gauge transformation linking gravity electro weak via version entropy. That way may claim have accomplished an important step towards general theory quantum e(∞) complexity finding α G =(2) ew −1 ≅(1.7)(10) 38 where dimensionless Newton constant, ≃128 fine structure constant scale.