Constraints on extra dimensions from precision molecular spectroscopy

TL;DR

This paper uses high-precision molecular spectroscopy to set new constraints on the size of extra dimensions predicted by theories like string theory, by comparing experimental data with quantum calculations.

Contribution

It introduces a novel method of constraining extra dimensions using molecular energy levels and precision measurements, providing bounds within the framework of extra-dimensional theories.

Findings

Limits on the size of seven extra dimensions are set to less than 0.6 micrometers.

Molecular spectroscopy can probe space-time geometry at chemical bond length scales.

The method offers potential for tighter constraints with further technological advances.

Abstract

Accurate investigations of quantum level energies in molecular systems are shown to provide a test ground to constrain the size of compactified extra dimensions. This is made possible by the recent progress in precision metrology with ultrastable lasers on energy levels in neutral molecular hydrogen (H$_2$, HD and D$_2$) and the molecular hydrogen ions (H$_2^+$, HD$^+$ and D$_2^+$). Comparisons between experiment and quantum electrodynamics calculations for these molecular systems can be interpreted in terms of probing large extra dimensions, under which conditions gravity will become much stronger. Molecules are a probe of space-time geometry at typical distances where chemical bonds are effective, i.e. at length scales of an \AA. Constraints on compactification radii for extra dimensions are derived within the Arkani-Hamed-Dimopoulos-Dvali framework, while constraints for curvature or brane separation are derived within the Randall-Sundrum framework. Based on the molecular spectroscopy of D$_2$ molecules and HD$^+$ ions, the compactification size for seven extra dimensions (in connection to M-theory defined in 11 dimensions) of equal size is shown to be limited to $R_7 < 0.6 \mu$m. While limits on compactification sizes of extra dimensions based on other branches of physics are compared, the prospect of further tightening constraints from the molecular method is discussed.