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Foundations of Physics

, 36:1070 | Cite as

A Model for Spacetime: The Role of Interpretation in Some Grothendieck Topoi

  • Jerzy Król
Article

We analyse the proposition that the spacetime structure is modified at short distances or at high energies due to weakening of classical logic. The logic assigned to the regions of spacetime is intuitionistic logic of some topoi. Several cases of special topoi are considered. The quantum mechanical effects can be generated by such semi-classical spacetimes. The issues of: background independence and general relativity covariance, field theoretic renormalization of divergent expressions, the existence and definition of path integral measures, are briefly discussed in the proposal. The connection with some problems in foundations of mathematics and differential topology are also discussed.

Keywords

topos theory spacetime structure intuitionism functional measures quantum mechanics 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of SilesiaKatowicePoland

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