Does the earth have TWO cores?

Conventional cutaway images of the earth depict the continents and oceans atop a thin crust overlying an immense mantle. Beneath that is a biphasic core with an outer molten layer and an inner, presumably iron, center.

Two scientists have recently proposed the interesting theory that the earth has two separate cores. It is generally accepted that our moon was formed when the primordial earth was struck by an object about the size of Mars (video here).

Haluk Cetin and Fugen Ozkirim of Murray State University think the core of the Mars-sized object may have been left behind inside Earth, and that it sank down near the original inner core. There the two may still remain, either separate or as conjoined twins, locked in a tight orbit.

Most scientists think the two cores would have fused by now, but if they haven't, their presence could offer one explanation for plate tectonics:

Based on models of Earth's interior, Cetin thinks the two cores rotate in opposite directions, like the wheels of a pasta maker. Their motion would suck in magma from behind and spit it out in front. If this motion persisted for long enough, it could set up a giant current of circulation that would push plates of crust apart in front, and suck them down into the mantle in back.

(image credit here)