Noncommutative gravity, a `no strings attached' quantum-classical duality, and the cosmological constant puzzle

TL;DR

This paper proposes a noncommutative geometric reformulation of quantum mechanics that reveals a duality between heavy and light particles, offering insights into the small but nonzero cosmological constant.

Contribution

It introduces a novel duality in noncommutative gravity linking quantum and classical regimes, addressing the cosmological constant puzzle.

Findings

Duality relates heavy and light particles with inverse masses.

Explains the small nonzero value of the cosmological constant.

Provides a geometric framework for quantum mechanics without classical spacetime.

Abstract

There ought to exist a reformulation of quantum mechanics which does not refer to an external classical spacetime manifold. Such a reformulation can be achieved using the language of noncommutative differential geometry. A consequence which follows is that the `weakly quantum, strongly gravitational' dynamics of a relativistic particle whose mass is much greater than Planck mass is dual to the `strongly quantum, weakly gravitational' dynamics of another particle whose mass is much less than Planck mass. The masses of the two particles are inversely related to each other, and the product of their masses is equal to the square of Planck mass. This duality explains the observed value of the cosmological constant, and also why this value is nonzero but extremely small in Planck units.