Why Do Voltages in Series Add: Explained Physically

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Why do voltages in series add? I would like to have this explained physically. Most answers I get are something like: "Because in a parallel circuit the voltage is constant." I have memorized the concept but want to try and learn why this is so. What physically goes on with the circuit to make the voltages add.


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Okay take the case of two batteries in series each with a voltage V. What this voltage means is that the potential different between the two nodes of the battery is V. So imagine a circuit connecting these two batteries in series and follow the current. Let's s say we're going up in potential as we cross batteries. So first we're at zero volts. Then we hit the - terminal and to get to the + terminal is V volts. so we're at +V volts overall. Now we hit the - terminal of the next battery and again to go to the + terminal on this battery is +V volts. So we see that the total voltage of the circuit is 2V.

Not sure if this is the kind of explanation you were looking for, but there it is.
 
It's called a "potential difference" for a reason. No different than, for example, a ball being at a height h above the floor vs the same ball being at a height 2h. In the latter case, there is double the potential energy with respect to the floor.
 
To add what the above posters have said, think of it in terms of work required to move a unit of charge, say one Coulomb. If you have two voltages in series and you are a charge moving through a circuit, work is done on you to move you across the first PD, then across the second PD, and since work is a scalar you just add it up - the total work done would have been the same as if it were just one PD.

I hope that's clear..