  We revisit the cosmological constant problem using the viewpoint that the
observed value of dark energy density in the universe actually represents a
rather natural value arising as the geometric mean of two vacuum energy
densities, one being extremely large and the other one being extremely small.
The corresponding mean energy scale is the Planck-Einstein scale l_PE = (l_P
l_E)^1/2 = (hbar G/ c^3 Lambda)^1/4 ~ 0.037 mm, a natural scale both for dark
energy and the physics of superconductors. We deal with the statistics of
quantum fluctuations underlying dark energy in superconductors and consider a
scale transformation from the Planck scale to the Planck-Einstein scale which
leaves the quantum physics invariant. Our approach unifies various
experimentally confirmed or conjectured effects in superconductors into a
common framework: Cutoff of vacuum fluctuation spectra, formation of Tao balls,
anomalous gravitomagnetic fields, non-classical inertia, and time uncertainties
in radioactive superconductors. We propose several new experiments which may
further elucidate the role of the Planck-Einstein scale in superconductors.
