  A form of "remote synchronization" was recently described wherein amplitude
fluctuations across a ring of non-identical, non-linear electronic oscillators
become entrained into spatially-structured patterns. According to linear models
and mutual information, synchronization and causality dip at a certain
distance, then recover before eventually fading. Here, the underlying mechanism
is finally elucidated through novel experiments and simulations. The system
non-linearity is found to have a dual role: it supports chaotic dynamics, and
it enables energy exchange between the lower and higher sidebands of a
predominant frequency. This frequency acts as carrier signal in an arrangement
resembling standard amplitude modulation, wherein the lower sideband and the
demodulated baseband signals spectrally overlap. Due to a spatially-dependent
phase relationship, at a certain distance near-complete destructive
interference occurs between them, causing the observed dip. Methods suitable
for detecting non-trivial entrainment, such as transfer entropy and the
auxiliary system approach, nevertheless reveal that synchronization and
causality actually decrease with distance monotonically. Remoteness is,
therefore, arguably only apparent, as also reflected in the propagation of
external perturbations. These results demonstrate a complex mechanism of
dynamical interdependence, and exemplify how it can lead to incorrectly
inferring synchronization and causality.
