Why we can not see the curvature of the quantum state space?

TL;DR

This paper introduces superrelativity, a gauge quantum theory linking the geometry of quantum state space with gravity, aiming to unify general relativity and quantum mechanics by exploring the metric properties of the projective Hilbert space.

Contribution

It proposes a novel gauge quantum theory where the affine connection is derived from the Fubini-Study metric, potentially unifying gravity and quantum theory.

Findings

The affine connection is constructed from derivatives of the Fubini-Study metric.

The metric properties of the projective Hilbert space have physical significance.

The theory suggests a new geometric approach to quantum gravity.

Abstract

A new type of gauge quantum theory (superrelativity) has been proposed. This differs from ordinary gauge theories in sense that the affine connection of our theory is constructed from first derivatives of the Fubini-Study metric tensor. That is we have not merely analogy with general relativity but this construction should presumably provide a unification of general relativity and quantum theory. Here we shall discuss the physical meaning of metric properties of the projective Hilbert space and manifestation of its nontrivial physical character.