On the Microscopical Structure of the Classical Spacetime

TL;DR

This paper proposes viewing classical spacetime as a complex system composed of fundamental microscopical entities, emphasizing the importance of a macroscopic limit before quantization, with implications for black hole spacetimes.

Contribution

It introduces the idea that spacetime should be seen as a collection of microscopical entities, requiring a macroscopic limit prior to quantization, challenging traditional approaches in quantum gravity.

Findings

Classical spacetime viewed as a complex system of fundamental entities

Quantization requires a prior macroscopic limit of spacetime

Discussion of implications for black hole spacetimes

Abstract

Our purpose here is to introduce the idea of viewing the spacetime as a macroscopic complex system which, consequently, cannot be directly quantized. It should be thought of as a collection of more fundamental "microscopical" entities (atoms of geometry), much like a solid system, in which an atomic (classical) structure must be first recognized in order to ensure a correct and meaningful quantization procedure. In other words, we claim that the classical limit from a quantum theory of gravity could not give a four dimensional Einstein spacetime directly, but requiring {\it a further} macroscopical limit. This is analogous to a material medium, whose complete description does not come from any quantized field. We also discuss a possible realization of this hypothesis for black hole spacetimes.