Emergent Gravity of Fractons: Mach's Principle Revisited

TL;DR

This paper explores how fractons, particles with restricted mobility in certain quantum phases, can exhibit emergent gravitational behavior, including an effective attraction and Mach's principle, within a tensor gauge field framework.

Contribution

It introduces a model linking fractons to emergent gravity, reformulates fracton interactions as geometric geodesics, and demonstrates how inertia arises from large-scale fracton distributions.

Findings

Fractons exhibit an emergent attractive interaction resembling gravity.

A geometric, geodesic-like formulation of fracton interactions is developed.

Inertia of fractons arises from the distribution of other fractons, illustrating Mach's principle.

Abstract

Recent work has established the existence of stable quantum phases of matter described by symmetric tensor gauge fields, which naturally couple to particles of restricted mobility, such as fractons. We focus on a minimal toy model of a rank 2 tensor gauge field, consisting of fractons coupled to an emergent graviton (massless spin-2 excitation). We show how to reconcile the immobility of fractons with the expected gravitational behavior of the model. First, we reformulate the fracton phenomenon in terms of an emergent center of mass quantum number, and we show how an effective attraction arises from the principles of locality and conservation of center of mass. This interaction between fractons is always attractive and can be recast in geometric language, with a geodesic-like formulation, thereby satisfying the expected properties of a gravitational force. This force will generically be short-ranged, but we discuss how the power-law behavior of Newtonian gravity can arise under certain conditions. We then show that, while an isolated fracton is immobile, fractons are endowed with finite inertia by the presence of a large-scale distribution of other fractons, in a concrete manifestation of Mach's principle. Our formalism provides suggestive hints that matter plays a fundamental role, not only in perturbing, but in creating the background space in which it propagates.