How much "earth" does it take to create an "earth ground" for measuring voltage? I was contemplating the idea of a multi-meter that had a "built in" Earth ground to it, and if it did have this ability how much earth/dirt would it take to register as a true Earth ground to register voltage of 120v when touching a standard household outlet. I imagine it'd be either a) a massive resistor or b) a ton of 'earth/dirt'. If it was a ton of dirt, how much exactly would create a ground such that you read 120v from a typical 120v hot wire and the earth. I've attached a picture to show that there is indeed a specific (unknown?) amount of earth to create an earth ground if you begin to consider it incrementally in terms of the amount of earth needed to be a ground. 

 A: The ground/earth works because all the electricity suppliers agree to use the electrical potential of the earth as a reference point of zero voltage. Since the Earth is a conductor, if not a terribly good one, all electrical installations are in principle connected together to establish a uniform zero potential.
If you take your meter and connect one terminal to a large bucket of soil you aren't achieving anything useful because that bucket of soil isn't connected to the rest of the Earth. In effect you've just connected a rather small capacitance to one terminal of your meter.
Increasing the size of the bucket of soil would increase the capacitance, but it still wouldn't be very useful until you electrically connect it to the rest of the Earth.
A: This is a quite subtle issue! I think to really answer it, you'd need to specify the details of how the power plant works and how charges build up in the Earth, so there's no one-sentence theoretical answer.
Jon Custer's right that if the same piece of Earth contained both the power plant and the voltmeter, then it should work correctly, because you'd have a complete circuit through the Earth. But what if they're on opposite pieces of the Earth that are completely electrically insulated from each other?
My intuition is that if the power plant and the voltmeter were connected to separate "grounds" that were large enough (like half the size of the Earth each), and at similar distances from the Sun that they receive similar levels of charged particles from the solar wind, then they'd be at similar potentials. (That's assuming the two halves are the same size - if they're different sizes, then they'd have different capacitances and so could be at different potentials. The size difference between the two pieces of Earth might well be more important than their absolute sizes. It would also depend on the details of how you split the Earth in two.) So if the power plant were providing AC voltage, then everything would be fine. But I have no idea what the quantitative answer to your question is.
If the power plant were providing DC voltage though, and you couldn't complete a circuit, then a charge buildup would eventually neutralize whatever process the power plant was using to create the voltage difference. The bigger the piece of Earth your voltmeter were connected to, the longer you'd have before this happens, but I have no idea what actual numbers look like.
A: You don't need any "Earth" to "ground". Ground is simply whatever you're using as a reference for 0V. It usually has to be something with enough material that it's impedance prevents local effects from affecting its global behavior.
