  Continuous time crystals (CTCs) - media with broken continuous time
translation symmetry - are an eagerly sought state of matter that spontaneously
transition from a time-independent state to one of periodic motion in response
to a small perturbation. The state has been realized recently in an array of
nanowires decorated with plasmonic metamolecules illuminated with light. Here
we show that this as-yet-unexplained CTC state can be understood as arising
from a nonreciprocal phase transition induced by nonconservative radiation
pressure forces among plasmonic metamolecules: above a certain intensity
threshold, light drives the inhomogeneously broadened array of thermally-driven
noisy nanowire oscillators to a synchronized coherent space-time crystal state
and ergodicity of the system is broken. At the onset of synchronization, this
mechanism does not require nonlinearity in the oscillators but depends instead
on nonreciprocal forces. As such it is fundamentally different from the regimes
of synchronization that depend on nonlinearity.
