The authors argue that quantum gravity and general covariance force the information geometry of quantum theory to become dynamical, requiring a modified Born rule testable via triple-slit matter-wave interference.
Constraints on a Generalization of Geometric Quantum Mechanics from Neutrino and $B^0$-$\overline{B^0}$ Oscillations
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abstract
Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which the manifold over which the "phase" of an energy eigenstate time evolves is modified. This generalization affects oscillation and interference phenomena through the introduction of two deformation parameters that quantify the extent of deviation from canonical Quantum Mechanics. In this paper, we constrain these parameters utilizing atmospheric neutrino oscillation data, and $B^0$-$\overline{B^0}$ oscillation data from Belle. Surprisingly, the bound from atmospheric neutrinos is stronger than the bound from Belle. Various features of Nambu Quantum Mechanics are also discussed.
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Physical limits on information metrics and quantum gravity as gravitized quantum theory
The authors argue that quantum gravity and general covariance force the information geometry of quantum theory to become dynamical, requiring a modified Born rule testable via triple-slit matter-wave interference.