Extra force in charged resonant capacitors: a new macroscopic effect of vacuum fluctuations ?

TL;DR

The article reports a robust, unaccounted attractive force in charged resonant capacitors with micron‑scale gaps, where the observed tuning of the fundamental mode far exceeds predictions from standard electrostatic models. The authors systematically rule out conventional mechanisms (gap shrinkage, spring softening, fringe and Casimir effects, and environmental factors) and propose a novel edge‑enhanced dielectric mechanism in vacuum, potentially involving vacuum fluctuations forming polarizable virtual dipole clusters near the electrode edge; this is modeled by a diverging effective permittivity as the local field approaches a critical value $E_c$ (approximately $2.2\times10^8$ V/m) with an edge extent $\Delta r$ of a few micrometers. The resulting extra stiffness $K_{un}$ can account for the large, non‑quadratic tuning observed across datasets, and the fit yields consistent $E_c$ and edge parameters, suggesting a possible macroscopic manifestation of vacuum polarization effects in nanoscale gaps. If confirmed, this finding would open new avenues in vacuum physics and macroscopic quantum‑field phenomena, motivating targeted experiments to test the vacuum‑based dielectric hypothesis and its implications for precision electromechanical systems.

Abstract

We report on measurements of the mechanical vibrations of the fundamental mode of resonant capacitive transducers, consisting of parallel plates at different gaps (10 - 26 $μ$m). Resonant frequency data were taken vs the electric field at constant charge, at various temperatures and different configurations. All measurements exhibited unexpectedly large tuning, caused by an additional, unpredicted attractive force. Such force has a divergent behaviour characterized by a critical electrical field and start to diverge long before the critical point. Many known physical mechanisms have been considered to explain this force, but all of them had to be discarded. Thus, we turn to non-conventional physical mechanisms and suggest that vacuum fluctuations inside the gap could be a possible cause of this anomalous force.

Figures (9)

• Figure 1: Tuning curve for the four experimental set considered. Red crosses: measured values; Blue line: behaviour predicted by eq.\ref{['eq:tune']}. Departure from quadratic behaviour is particularly evident in datasets 3 and 4.
• Figure 2: Images of the resonator plate, of the electrode plate and of the assembled transducer
• Figure 3: Schematics (side view) and equivalent circuit of the apparatus. The bias resistors varied in the range $10^3 - 10^7$ Ohm. The d.c. voltage source was then disconnected during measurements.
• Figure 4:
• Figure 5: Tuning of the push-pull transducer. The plot shows the frequency vs voltage behaviour both in the case of d.c. bias in one gap (red dots) and in both gaps (blue diamonds). The expected tuning, based on eq.\ref{['eq:tune']} are also shown (full lines of respective color) for both experiments.