Mara- Your ground and neutral lines meet at the same place in the junction box. There should be no voltage difference measured across the two sockets. It is possible that either some piece of gear (could be some house appliance) is connected to the same circuit, and has enough leakage current to provide the voltage difference in combination with poor wire junctions or loosened wire-nuts. The best solution would be to have a dedicated a/c circuit installed with no splices.
This is not a good situation as the ground line is supposed to provide a low impedance safety path to ground. You can try to track down and unplug all devices plugged into this circuit (not always easy considering the ridiculous way in which most houses are wired), actually all outlets using the same ground conductor (even more difficult to determine)and then remeasure the voltage difference. Then, plug in one device at a time and remeasure the voltage difference. It may just be the cumulative effect of many small leakage currents through a poor wire connection that is invariably buried within a wall. You might get lucky and find the culprit at the back of a duplex outlet ground connection or at the junction box, but it's usually a crappy wire-nut. If you're unfamiliar with working around a/c, then get an electrician or electronics tech to help you with these steps. Don't get the nickname of SPARKY!!
After much needed sleep, I must add that my previous comments were given with the assumption that the ground line was 6 volts positive with respect to the neutral line. However, if the opposite is true, then the voltage differential could simply be due to the IR drop from the current flowing in the neutral leg and the series resistance of the neutral wire and all of the connections back to the junction box. If the current flowing through that circuit is rather substantial, then 6 volts may not be an indicator of any serious problem. It all depends on the amount of current from which one can then derive the total resistance in the line back to ground.
However, I would still suggest that at least for improved sonics from your system, that you invest in at least one, preferrably two, dedicated a/c circuits for your system.