Nonlinear modification of quantum mechanics

TL;DR

This paper proposes a novel quantum gauge theory called superrelativity, aiming to unify quantum mechanics and general relativity by constructing an affine connection from the Fubini-Study metric in quantum state space.

Contribution

It introduces a new gauge theory framework that potentially unifies quantum mechanics with general relativity through geometric constructions in quantum state space.

Findings

The theory differs from standard gauge theories by using derivatives of the Fubini-Study metric.

It aims to address foundational conflicts between quantum theory and relativity.

The approach suggests a geometric unification of fundamental physics.

Abstract

In order to prevent ``unavoidable'' break-down of the ``peaceful coexistence'' between foundations of quantum theory and relativity I propose a new type of a quantum gauge theory (superrelativity). This differs from ordinary gauge theories in the sense that the affine connection of this theory is constructed from first derivatives of the Fubini-Study metric tensor in the projective Hilbert space of the pure quantum states CP(N). That is we have not merely analogy with general relativity but this construction should presumably provide a unification of general relativity and quantum theory.