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There is no battery involved in the system. Just the charge, a power source, and the wire.
There is no 'short' as the current is all in the one wire. The resistance of the wire causes it to get red hot.This is how glass pipes for glass plumbing systems was cut back when. It worked perfectly The principle is exactly the same as for the filament in an incandescent light bulb. The styrofoam 'hot wire' cutter works on exactly the same principle. And, NO, there are no sparks.
Very clearly, I am talking about DC, as this is what automobile batteries provide. Flow is from Positive (+) pole to the Negative (-); at least according to both the chemistry and physics courses I have had. Thus, there are two (2) poles! Kapisch? If this is not so, then why are the battery terminals (=2 poles) labeled (+) and (-)? I agree flow is along the path of least resistance.
No, there will be no short. To get a short, you have to have two different polarities involved. There is only one polarity in the system.
A nichrome, or SS, piece of wire, an auto battery charger and a pitcher of ice water is all that is needed to make such a cut. Make a single turn of the wire around the bottle at the desired point. Measure location of wire from a common point (up from bottom, etc.) on the bottle to make sure you will get a concentric cut. Attack the battery charger clips to the ends of the wire, and turn the charger ON. In very short order, the wire should begin to glow red (red hot). Give it 10-15 seconds to heat the glass through and through. Pour the ice water over the red hot wire. You should get a very nice clean break.