Emergence of Spacetime from Fluctuations

TL;DR

This paper introduces a basis-independent Euclidean path integral for gravity and matter, providing a framework for understanding how spacetime can emerge from pre-geometric regimes influenced by matter content and energy scale.

Contribution

It presents a novel basis-independent formulation of the gravitational path integral that describes both pre-geometric and emergent spacetime regimes, linking spacetime properties to matter composition.

Findings

Path integral is basis-independent, applicable to pre-geometric regimes.

Spacetime properties depend on fermionic and bosonic matter balance.

Effective spacetime dimension varies with energy scale.

Abstract

We use a result of Hawking and Gilkey to define a Euclidean path integral of gravity and matter which has the special property of being independent of the choice of basis in the space of fields. This property allows the path integral to describe also physical regimes that do not admit position bases. These physical regimes are pre-geometric in the sense that they do not admit a mathematical representation of the physical degrees of freedom in terms of fields that live on a spacetime. In regimes in which a spacetime representation does emerge, the geometric properties of the emergent spacetime, such as its dimension and volume, depend on the balance of fermionic pressure and bosonic and gravitational pull. That balance depends, at any given energy scale, on the number of bosonic and fermionic species that contribute, which in turn depends on their masses. This yields an explicit mechanism by which the effective spacetime dimension can depend on the energy scale.