Why does connecting a battery's positive terminal to the negative terminal of another battery not create a short circuit? This is a question regarding the physics behind the observation.
I have guessed the answer to the question, but I may be wrong, so I want to wait for the responses before posting it.
Some major considerations:


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*A battery's positive terminal does have a positive potential. ie, a test positive charge will repel it and a test negative charge will attract it. Vice versa for negative terminal.
From the paper below (Section 1.2.1), it seems abundantly clear that the battery will have positive and negative potential on respective terminals.

*Given 'point 1', above, connecting the positive terminal of battery A to negative terminal of battery B will lead to current flow in the conductor.

*If the potential difference only comes into effect when the circuit is closed using the terminals of the same battery (due to cell chemistry), then does that mean that 'point 1' will not be valid after this experiment (connecting positive terminal of A to negative terminal of B)?

*If it is only a tiny quantity of current that flows, then will it ever stop? And what determines this quantity? (Equation would be nice)
Related paper: http://www.astrophysik.uni-kiel.de/~hhaertel/Circuit/electric_circuit.pdf
 A: Suppose that we do as you suggest and connect the positive terminal of one battery to the negative terminal of another. Initially, I agree with your assessment that there is a potential difference between the two ends of the wire and so current will flow. However, charge is flowing from one side of the wire to the other and there is no way for that charge to flow back to the original battery, so there must be a buildup of charge either at the edges of the wire or in the battery's terminals. If we were just using one battery this charge would move through the chemical cells and out through the other terminal, but since we are using 2 it has nowhere to go. I don't think the cell chemistry is particularly important. Even if the charge makes it from the entering terminal of the battery to the unconnected terminal, it still has no place further to go and there will be a buildup.
This buildup of charge will start to equalize the potential difference across the wire. At some point, enough charge will have accumulated that current will stop flowing. 
I can't say exactly how much charge will have to move before current stops flowing, but I believe that it will be a small amount. In a normal circuit, there is a surface charge that accumulates near/on places where the wire bends such that the electric field always points in the direction of current flow (this is the microscopic Ohm's Law). This surface charge is usually quite small, on the order of a few electrons worth of charge. I imagine that to calculate the current flow for some specific case would be quite difficult. You would need to know the potential difference and the geometry/configuration of the wire, I imagine.
A: Simply it is because the circuit is not complete. There is no way for the electrons to flow back and without a valid pathway they will not flow.
A: I think this picture answers the question:

The battery's terminals are not charged. It's just a chemical reaction that starts the charge.
There's a $\text{Zn}$ and a $\text{CuSO}_4$.  When they meet each other via a cable, the $\text{Zn}$ gives 2 electrons to $\text{CuSO}_4$ and becomes $\text{Zn}^{2+}$.
$\text{Cu}^{2+}$ of $\text{CuSO}_4$ becomes $\text{Cu}$ and becomes electrostatically neutral, and separates from $\text{SO}_4^{2-}$.
Then we have $\text{SO}_4$ with -2 charge and $\text{Zn}$ with +2 charge. So, $\text{SO}_4^{2-}$ moves to $\text{Zn}^{2+}$ to get bound to each other.
In the end, we have $\text{ZnSO}_4$ and $\text{Cu}$.
With two different batteries, it's not possible. The $\text{SO}_4^{2-}$ has nowhere to go and make new connections. Thus the chemical and electrical process doesn't start.
A: You need to realize that the terms positive and negative are relative. The positive side of a battery is only "positive" in relation to the "negative" terminal of the same battery. When you hook a wire from the positive terminal of the first battery to the negative terminal of the second, a very small amount of current will flow until the potential difference reaches zero. 
Let's take an example with 2 nine volt batteries. If I hook the negative terminal of battery 1 to ground (which we will arbitrarily define as zero volts), and hook the negative of battery 2 to the positive of battery 1, then the negative of battery 2 will come quickly to equilibrium at 9V relative to ground. The positive of battery 2 is now at 18V relative to ground because it is always 9V above its own negative terminal at equilibrium. 
As for a short circuit, in order to get a short circuit, I have to provide a complete circular path for current to flow through. I can do this by adding another wire between any two terminals. 
