How is the alternating current in your home a complete circuit?
The gap is bridged by the power company driving the current through your wires.

You can think of it as a remote generator pushing the current through your house, but in actuality there are several transformers isolating the current between generation and your house.  So the current itself recirculates at the transformer near your house, and that current is driven by current in the transformer's primary coils.

If all is working properly (and nominally), there is no current to earth.  That connection is there only to guarantee that each loop&mdash;including your house current loop&mdash;never has a potential voltage to ground greater than 120 volts.  If a loop were not grounded, that portion could conceivably float to any voltage through static effects or other processes.