In order to investigate the long-term dimensional stability of matter, we have operated an optical resonator fabricated from crystalline silicon at 1.5 K continuously for over one year and repeatedly compared its resonance frequency fres with the frequency of a GPS-monitored hydrogen maser. After allowing for an initial settling time, over a 163-day interval we found a mean fractional drift magnitude |f −1 res dfres/dt| < 1.4 × 10 −20 /s. The resonator frequency is determined by the physical length and the speed of light, and we measure it with respect to the atomic unit of time. Thus, the bound rules out, to first order, a hypothetical differential effect of the universe's expansion on rulers and atomic clocks. We also constrain a hypothetical violation of the principle of Local Position Invariance for resonator-based clocks and derive bounds for the strength of space-time fluctuations.In this paper we address experimentally the question about the intrinsic time-stability of the length of a macroscopic solid body. This question is related to the question about time-variation of the fundamental constants and effects of the expansion of the universe on local experiments. It may be hypothesized that, in violation of the Einstein Equivalence Principle (EP), the expansion affects the length of a block of solid matter and atomic energies to a different degree. The length, defined by a multiple of an interatomic spacing, can be measured by clocking the propagation time of an electromagnetic wave across it. This procedure effectively implements the Einstein light clock, or, in modern parlance, an electromagnetic resonator. The hypothetical differential effect would show up as a time-drift of the ratio of the frequency f res of an electromagnetic resonator and of an atomic (or molecular) transition (f atomic ). A resonator and an atom are dissimilar in the sense that the former's resonance frequency intrinsically involves the propagation of an electromagnetic wave, while the latter does not. Specifically, the time-drift would violate the principle of Local Position Invariance (LPI) of EP. The natural scale of an effect due to cosmological expansion, here the fractional drift rate The suitable regime in which to investigate the dimensional stability of matter is at cryogenic temperature, when the thermal expansion coefficient and the thermal energy content of matter are minimized. Ideally, during the cooling down and then permanence at cryogenic temperature, a stable energy minimum of the solid is reached. The expected high dimensional stability and the magnitude of H 0 lead to a challenging measurement problem: how to resolve tiny length changes, and how to suppress the influence of extrinsic disturbances. The problem can be addressed by casting the solid matter into an electromagnetic resonator of appropriate shape, by supporting it appropriately, and by measuring its resonance frequency using atomic time-keeping and frequency metrology instruments, which indeed permit ultra-high measurement precision and accur...