Wraiths,
Before we get into the possible quantum physics involved, did you check the current on the neutral after you turned either bank of lights off?
my suggestion would be to look at this the same way you would trouble-shoot a tripping breaker.
Turn each bank off one at a time, taking readings on the neutral after each time.
Is the neutral current only apparent with one of those circuits or is it additive between both?
Are the lights on both circuits the same make, model, amperage, etc?
