Local Information Density and the Space-Time Limit: A Physical Framework Grounded in Attosecond Scanning Tunnelling Microscopy

Perspective. The concept of local information density (I_d) has remained largely formal because no experimental technique could resolve the relevant spatio-temporal scales in a well-defined quantum environment. The recent demonstration of attosecond-resolution scanning tunnelling microscopy by Maier et al. (Nature Photonics, 2026, doi:10.1038/s41566-026-01932-0) changes this. By sculpting and tracing single-electron wavefunctions with sub-femtosecond temporal and atomic-scale spatial resolution during barrier crossing, Maier et al. provide the first experimental calibration of a tunable space-time volume for a quantum state. We introduce the dimensional proxy I_d^proxy ~ 1/(dx dy dz dt), show that the intermediate light-matter regime (Keldysh parameter ~ 1) observed in tunnelling junctions is formally analogous to the stochastic-coherent coexistence hypothesized to govern chromatin information maintenance, and propose a tiered experimental ladder connecting attosecond surface science to accessible assays of information density in macromolecular assemblies. Explicit scaling cautions and falsification criteria are stated.