Quantum gravity may permit contextual deviations from the Fisher metric, inducing observer-dependent modifications to the Born rule.
Nambu quantum mechanics: A Nonlinear generalization of geometric quantum mechanics
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abstract
We propose a generalization of the standard geometric formulation of quantum mechanics, based on the classical Nambu dynamics of free Euler tops. This extended quantum mechanics has in lieu of the standard exponential time evolution, a nonlinear temporal evolution given by Jacobi elliptic functions. In the limit where latter's moduli parameters are set to zero, the usual geometric formulation of quantum mechanics, based on the Kahler structure of a complex projective Hilbert space, is recovered. We point out various novel features of this extended quantum mechanics, including its geometric aspects. Our approach sheds a new light on the problem of quantization of Nambu dynamics. Finally, we argue that the structure of this nonlinear quantum mechanics is natural from the point of view of string theory.
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Quantum spacetime with a non-commutative dual explains the fixed Born rule of quantum theory and leads to gravitized quantum mechanics featuring dynamical probabilities and higher-order interference.
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Information Metrics and Possible Limitations of Local Information Objectivity in Quantum Gravity
Quantum gravity may permit contextual deviations from the Fisher metric, inducing observer-dependent modifications to the Born rule.
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Quantum Spacetime, Quantum Gravity and Gravitized Quantum Theory
Quantum spacetime with a non-commutative dual explains the fixed Born rule of quantum theory and leads to gravitized quantum mechanics featuring dynamical probabilities and higher-order interference.