  Invariably, time-reversal symmetry (TRS) violation in a state of matter is
identified with static magnetism in it. Here, a directional scalar spin chiral
order (DSSCO) phase is introduced that disobeys this basic principle: it breaks
TRS but has no density of static moments. It can be obtained by melting the
spin moments in a magnetically ordered phase but retaining residual broken TRS.
Orbital moments are then precluded by the spatial symmetries of the spin
rotation symmetric state. It can exist in one, two and three dimensions under
different conditions of temperature and disorder. Recently, polar Kerr effect
experiments in the mysterious pseudogap phase of the underdoped cuprates hinted
at a strange form of broken TRS below a temperature $T_{K}$, that exhibits a
hysteretic "memory effect" above $T_{K}$ and begs reconciliation with nuclear
magnetic resonance (which sees no moments), X-ray diffraction (which finds
charge ordering tendencies) and the Nernst effect (which detects nematicity).
Remarkably, the DSSCO provides a phenomenological route for reconciling all
these observations, and it is conceivable that it onsets at the pseudogap
temperature $\sim T^{*}$. A testable prediction of the existence of the DSSCO
in the cuprates is a Kerr signal above $T_{K}$ triggered and trainable by a
current driven along one of the in-plane axes, but not by a current along the
other.
