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Abstract: According to D\-oring and Isham the spectral topos corresponds to any quantumsystem. The description of a system in the topos becomes similar to this givenby classical theory, up to multiplication of observables. Logic of the emergenttheory is rather intuitionistic than classical. Adding to the language the typeof self-adjoint operators and their products, which are interpreted by theon-stages daseinisations and their products, one gets commuting presheaves inthe topos. The interpretation agrees with on-stages daseinisations of squaresup to some automorphisms of the topos. The uncertainty principle does not holdfor such an interpretation. According to the recent proposition by the author,topoi can modify local smooth spacetime structure. A way how to add gravityinto the spectral topos of a system is presented. Assuming that a quantumsystem modifies the local spacetime structure and interacts with agravitational field via the spectral topos, the lowest energy modes of aquantum harmonic oscillator are gravitationally nullified. Moreover, a theoryof gravity and systems should be symmetric with respect to the 2-group ofautomorphisms of the category of topoi. Under the $\delta 0$-interpretation forthe hamiltonian of a quantum harmonic oscillator, its lowest modes havevanishing contributions to the cosmological constant. This is related with afundamental higher symmetry group of gravity. Without the$\delta 0$-interpretation, small non-zero value of the effective cosmologicalconstant can be approached.



Autor: Jerzy Król

Fuente: https://arxiv.org/







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