Prof Buxton, let me please explain what I mean by 5000mile away ground. What I mean is not that any point 5000 mile away can be used to ground the neutral. What I meant is whether AFTER grounding the neutral at a point on the earth, if you can use Any Other points on the earth whatever (by sticking one of your multimeter ends deep into pure Soil), (disregarding astray currents and voltages), to measure voltages along your circuit. You explained to me previously that this can be done because the earth is just like a big metal piece..... Is this correct ? This is really my most important question and the big issue that I've had all along...Paulo, please note carefully that at the point where your supply comes from(usually a big transformer on a pole or substation) one side of the supply is connected to very solidly connected to earth. This forms the reference point. Now two wires are run to you house(or domicile).
one wire is called the "neutral" because it is connected to side connected to earth. That makes the other wire "hot" or "live" with respect to the "neutral" or any earth point. Note I refer to our distribution system on Down Under.
Regarding measuring the volts 5000km away I would suspect that there would be so much stray currents from a lot of sources the result would be meaningless unless you could switch off all other supplies and control any self generated currents in the soil.