Spacetime discreteness via consistent microscopic measurement

Abstract

The physical origin of spacetime discreteness remains a central open problem in quantum gravity, with most existing approaches relying on specific microscopic structures or model-dependent assumptions. In this letter, spacetime discreteness can arise instead as a consequence of consistent microscopic measurement. By treating infinitesimal spacetime intervals as scale-dependent measurement outcomes rather than predefined geometric entities, we formulate a Micro-Measurement Principle in which spacetime quantum fluctuations are encoded directly in the scaling structure. An equivalent dual representation of microscopic lengths leads to discrete, equidistant measurement outcomes, with the corresponding scaling-deformed uncertainty relation thereby reducing to the standard Heisenberg form. The microscopic lengths are further governed by a geometric renormalization-group flow admitting finite-length fixed points. This construction preserves Lorentz invariance and general covariance without ad hoc cutoffs or symmetry breaking. Our results show that the classical continuous-spacetime description corresponds to an unstable limiting regime, whereas a finite microscopic length and a discrete spacetime structure arise naturally from the fundamental requirements of micro-measurement consistency.

8 pages, no figure

References in corpus (7)

• Exact evolution equation for the effective potential
• Background Independent Quantum Gravity: A Status Report
• Lorentz invariance with an invariant energy scale
• Quantum fields, non-locality and quantum group symmetries
• The minimal length: a cut-off in disguise?
• Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity
• Scaling-Based Quantization of Spacetime Microstructure