Quantum Spacetime: Echoes of basho
Fedele Lizzi
TL;DR
The paper addresses the challenge of unifying quantum mechanics with gravity by arguing that spacetime cannot be accurately described by classical points at the quantum scale. It proposes noncommutative geometry and Nishida's bashō as a guiding relational framework, illustrating how measurements and observers shape spacetime geometry through operator algebras and traces rather than pointwise coordinates. A central contribution is the demonstration that precise localization is operationally undefinable below the Planck scale, necessitating a shift from point-based to algebraic/relational descriptions using density operators. The work provides a philosophical and mathematical foundation for quantum gravity approaches and informs how observational inferences should be interpreted at Planckian scales.
Abstract
I will discuss how the concept of basho, introduced by Nishida Kitaro nearly a century ago, can give an interesting insight to understand the concept of a point in modern quantum gravity. A quantum spacetime, necessary for the quantization of gravity, requires a whole rethinking of geometry, starting from the primitive concepts, like that of a point. I argue that the local vision of what becomes of classical points in quantum gravity, and in particular in noncommutative geometry, shows several similarities with Nishida's basho.