On the depth of quantum space

Abstract

We focus on the question: "Is space fundamentally discrete or continuous?" in the context of current quantum gravity research. In particular, we paint a scenario based on the idea that 'quantum space' is a sort of peculiar condensed matter system, and on the speculation that its microscopic dynamics is described by a 'group field theory' formalism. We suggest that, from this perspective, on the one hand the question has no absolute meaning, so no answer, but also that, on the other hand, the reason why this is the case is the 'quantum space' is much richer and more interesting than we may have assumed. We also speculate on further physical implications of the suggested scenario.

18 pages, 4 figures; amended version of a non-technical essay submitted for the third FQXi Essay Contest: "Is Reality digital or analog?"

References in corpus (11)

• Group field theory with non-commutative metric variables
• Quantum field theory, gravity and cosmology in a fractal universe
• Group field theory renormalization - the 3d case: power counting of divergences
• Bosonic Colored Group Field Theory
• Bounding bubbles: the vertex representation of 3d Group Field Theory and the suppression of pseudo-manifolds
• Gravitational dynamics in Bose Einstein condensates
• Towards classical geometrodynamics from Group Field Theory hydrodynamics
• Discrete to continuum transition in multifractal spacetimes
• Background independent condensed matter models for quantum gravity
• Doubly-Special Relativity: Facts, Myths and Some Key Open Issues
• Discovering the Discrete Universe

Cited by in corpus (4)

• Ten questions on Group Field Theory (and their tentative answers)
• Emergent Models for Gravity: an Overview of Microscopic Models
• A quantum theory of distance along a curve
• On a digital quantum description of physical space versus the continuum description