Does alternating current (AC) require a complete circuit? This popular question about "whether an AC circuit with one end grounded to Earth and the other end grounded to Mars would work (ignoring resistance/inductance of the wire)" was recently asked on the Electronics SE.

(Picture edited from the one in the above link)
Though I respect the AC/DC experts there, I think (with the exception of the top answer) they are all wrong.

My issue is that they all assume that AC requires a complete circuit in order to function.  However, my understanding is that a complete circuit is necessary for DC, but not AC.  My intuitive understanding is that AC is similar to two gas-filled rooms with a pump between them - the pump couldn't indefinitely pump gas from one room to another without a complete circuit (DC), but it could pump the gas back and forth indefinitely (AC).  In the latter case, not having a complete circuit just offers more resistance to the pump (with smaller rooms causing a larger resistance).
Is my understanding correct - can AC circuits really function without a complete loop?
More importantly, what are the equations that govern this?
If larger isolated conductors really offer less AC-resistance than smaller AC conductors, how is this resistance computed/quantified?  Would its "cause" be considered inductance, or something else?
 A: You are correct and your answers are to be found in the characterization of how antennas support a current in and radiate power out of an "RF circuit", they are "RF closed" but not physically closed - similar to capacitors really.
A: Indeed, AC can flow without a "complete circuit" - that's what happens in LC circuits all the time. An LC circuit is technically not complete - the capacitor of LC circuit contains an insulator between its plates and so electrons are unable to flow through the capacitor (unless it fails). Still the oscillations in the LC circuit happen because of alternating current flows inside the LC circuit charging and discharging the capacitor through the inductor.
The resistance to AC current increases as the inductor inductance increases (inductance is the measure of how much the inductor can affect the current flowing through it and so the more inductance the more resistance) and as the capacitor capacitance decreases.
A: 
Does AC current require a complete circuit?
Can AC circuits really function without a complete loop?

I think that neither AC nor DC theoretically needs a complete loop. (ie, without reusing the electrons/charge carriers that flow in the circuit)
And you don't even need to think about capacitors for that. A capacitor in a DC circuit still has an electric field between the plates (in case of a parallel plate capacitor): the same electric field responsible for current in the circuit, and that, to me constitutes a closed circuit.
Of the top of my head, I think the following illustrations would suffice to back what I am saying:

A: What do you mean by "to work"? If you mean that you can transfer energy, then to where?
If you continuously alternate the potential at one end of a wire, then this creates a wave that propagates to the other end. Say that other end is earth. If the potential is 0 on earth like and ideal ground, this means it cannot sustain a wave passing through. It is like a mirror. The oscillation will reflect back and you obtain a stationnary beating of counter-propagating waves. Just like agitating a string with the other end attached. This does not convey energy. (You can apply the same reasonning on the Mars side).
A: For me, AC is a closed circut all together within the same unique wire
As the + and - are chasing eachother in the same line.  As for DC, the - chase the + around the other end of the loop
