  A newly developed observable for correlations between symmetry planes, which
characterize the direction of the anisotropic emission of produced particles,
is measured in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV with ALICE.
This so-called Gaussian Estimator allows for the first time the study of these
quantities without the influence of correlations between different flow
amplitudes. The centrality dependence of various correlations between two,
three and four symmetry planes is presented. The ordering of magnitude between
these symmetry plane correlations is discussed and the results of the Gaussian
Estimator are compared with measurements of previously used estimators. The
results utilizing the new estimator lead to significantly smaller correlations
than reported by studies using the Scalar Product method. Furthermore, the
obtained symmetry plane correlations are compared to state-of-the-art
hydrodynamic model calculations for the evolution of heavy-ion collisions.
While the model predictions provide a qualitative description of the data,
quantitative agreement is not always observed, particularly for correlators
with significant non-linear response of the medium to initial state
anisotropies of the collision system. As these results provide unique and
independent information, their usage in future Bayesian analysis can further
constrain our knowledge on the properties of the QCD matter produced in
ultrarelativistic heavy-ion collisions.
