On a class of determinist models for emergent quantum mechanics

Wednesday, February 18, 2015
Ricardo Gallego Torrome
In this talk we discuss some models for emergent quantum mechanics in the line of 't Hooft's approach. After the geometric and dynamical setting is introduced, the construction of a phenomenological wave function and the Hilbert space structure is made from the fundamental elements of the models. Then we show how a geometric picture of quantum non-locality could be accommodated in these models. We will discuss a purely analytical-geometric mechanism for a spontaneous reduction of the quantum state and how this mechanism obligates to consider gravity as a classical and emergent interaction. Moreover, as a consequence of the same mechanism, the weak equivalence principle must be exact.
- R. Gallego Torromé, {Averaged Structures Associated to a Finsler structure}, {math.DG/0501058}; On the convex invariance in Finsler geometry, Symmetry: Culture and Science, Volume 23, Number 2, 133-140, 2012. - M. Gromov, {Riemannian structures for Riemannian and non-Riemannian spaces, Birkhäuser (1999). - G. 't Hooft, Determinism and Dissipation in Quantum gravity}, hep-th/0003005 - G. 't Hooft, How does God play dies?(Pre-) Determinism at the Planck Scale, hep-th/0104219 - G. 't Hooft, A mathematical theory for deterministic quantum mechanics, Conference Series, Volume 67, Issue 1, pp. 012015 (2007) - V. D. Milman and Gideon Schechtman, Asymptotic theory of Finite Dimensional normed spaces, Lecture notes in Mathematics 1200, Springer (2001). - R. Miron, D. Hrimiuc, H. Shimada and V. Sabau, The Geometry of Hamilton and Lagrange Spaces, Fundamental Theories in Physics 118, Kluwer (2001). - G. Randers, On an Asymmetrical Metric in the Four-Space of General Relativity, Phys. Rev. 59,195-199 (1941). - M. Talagrand, A new look at independence,Ann. Probab. Volume 24, Number 1, 1-34 (1996).