Evil Bunny said:
This may be true. In fact, I ventured into a physics forum and everyone here is waaaay smarter than me and you certainly sound like you know what you're talking about, so I will concede that it is in fact true. I was wrong.
I'd prefer it if you understood it, rather than just conceding the point, which tells me, "I wasn't convinced by your argument, so I'll just let it go." It would be a shame if you did that, because what you're saying is not impossible because of some hard-to-understand physics that I know and you do not. What you are saying is simply a mathematical or logical impossibility. You know arithmetic, therefore, you should be able to understand my argument. It stems from this:
If x = y
and,
y = z
then it must be true that:
x = z
Do you agree? Otherwise we have a logical contradiction. The same contradiction occurs in your scenario. You state that:
potential of pole A = potential of ground (because you measure no difference between them) [1]
And also potential of pole B = potential of ground [2]
From this it MUST follow that:
potential of pole A = potential of pole B.
Since A and B clearly do not equal each other (it was GIVEN that they differ by 120 V in our example), statement [1] and statement [2] cannot BOTH be true. In particular, if one of the poles has the same potential as ground, then the other one MUST differ from ground by 120 V, since the other pole differs from the first pole by 120 V.
Evil Bunny said:
But I think this difference is extremely small and probably hard to measure with common instruments. Let's say that your volt meter doesn't have a decimal point and it is accurate to only the nearest volt. I bet the display on your meter reads 120 Volts between the poles and 0 Volts between either one of the poles and the earth. Do you disagree with that?
Yes, I disagree, because, physics aside, it is a
logical contradiction. (see above)
Evil Bunny said:
If we can't agree on that, let's change the example to something we can test easily ourselves. Let's get a battery and a volt meter and take some measurements. A car battery would be best, but we can use a little 9V battery for simplicity. If you measured voltage across the (+) and (-) terminals of the battery you would get the battery voltage (assuming it was charged of course). I bet we all agree on that.
Now for the meat of it... I contend that you will get 0V if you measure between either one of the battery terminals and the Earth (lets make sure the battery is isolated from the earth. If you can't levitate it, then I guess you could put it on a piece of wood or a wooden table or something to make sure there is no connection being made from the Earth to either terminal

). Stick one lead on the positive terminal and the other lead into the earth. What does your meter display? Now move the lead from the positive terminal to the negative terminal of the battery, (leaving the other lead stuck in the earth) what does your meter display?
I contend your meter will display 0 Volts. Try it and let me know please...
I don't need to try it. Once again, we've started with the premise that the potentials of the + terminal and the - terminal differ by +9 V. Therefore, whatever you measure as the difference between the potentials of the - terminal and ground, the difference between the + terminal and ground HAS TO be 9 V
higher than that. Otherwise, it would contradict our premise that the + terminal is 9 V higher than the - terminal.
So, if you measure the difference between the - terminal and ground, and you happen to get 0.00512 V (5.12 millivolts), then the voltage between the + terminal and ground MUST be 9.00512 V (otherwise the difference between the terminals would not be 9 V). I really hope that you see that this must be true.
Evil Bunny said:
I would try this myself, but the Earth around me is frozen solid with 3 feet of snow on top of it.

However, I did try it in my house with my meter and a AA battery. My results were 1.6V between the terminals and 0V from either terminal to my tile floor. That's the best I could do.
Yeah, but that's because your tile floor is an insulator, and so the probe of the meter is not at the same potential as the floor. If you don't believe me, then let me ask you this: what does your meter read when neither of the probes is touching anything (or each other)? In other words, the voltage between the probes is "floating" (because the probes are not electrically connected and each one's potential could change independently by small amounts). I bet it displays 0 V as a default value. That's what my cheapo multimeter displays when the voltage between the probes is floating.
EDIT: Or it could be that any initial imbalance in potential between the two probes is equalized by the flow of charge from one probe to another. Since the second probe is not connected to anything that can sink charge, those charges have nowhere to go and "pile up", balancing out any initial differences in potential.
When we talk about "Earth", we mean something that acts like an ideal conductor (something that can be the source of or the sink for an arbitrary amount of charge without changing its electric potential). You'd have to dig a probe into the ground to get behaviour anything like that. Or you could just try measuring the voltage at each end of your battery relative to some conductor.
EDIT 2: No, that probably won't work for any finite conductor, because of what I said in my first EDIT. Charges can flow freely between the two conductors until their potentials have equalized. But it will work in theory for any point that has a definite and constant potential and is not free to "float" up to some higher potential through the transfer of charge..