ash,
You and newey are both correct, although it will appear that I am "calling you out" in the following discussion. It's your intent that is correct, and I hope you'll see where I'm coming from, as you read through this. (Hopefully on your third or fourth shot! ;D)
It's really a matter of terminology, and each of you has hit on an important aspect. Even EE's sometimes get bogged down in denoting the exact meaning of these terms when engaged in a heavy design session.
To my mind, a pickup is
not an AC generator, it's a transducer, faithfully tranducing one form of energy (magnetic) into another form (electrical). The magnetic field changes in accordance with the disturbance caused by the strings vibrations, and that string is, of course, vibrating at many harmonic frequencies as well as the fundamental. In audio terms, the relationships thus engendered are denoted as "phase". For a single vibrating string, it's not only possible for some of the harmonics to be "out of phase", it's guaranteed that some them will be, at any given time. But remember, at the initial outset, each harmonic did indeed swing in the same direction as the fundamental. The differences come about as a result of both physics and mathematics. Fortunately for us, we can ignore that level of detail for the remainder of this discussion, but take note, this is the first definition of the word "phase".
Now, as to polarity. If we introduce two transducers into the equation, we can't physically mount them in the same place - one must be located elsewhere along the string, yes? Then the string's set of "phase relationships" (that vary over time, remember?) are different, at that second transducer's location.
Now we can talk about "in phase" or "out of phase", and we'd be correct. As newey noted, we need to have two more sources for comparison of phases, and so we've just proven. This is the second, and more common, definition of the word "phase".
Motorboat, you say! (But, but, but, but.....) What happens when we reverse the polarity of one of those transducers? Ah, that's a good question.
Regarding how a magnet is used to generate a current within a coil, we see that it must (repeat: must) first swing the current from zero towards one direction or the other, positive or negative. (These terms are used for lack of anything better. They refer to how a meter registers the action of the current being generated - no current = zero, and from there, the needle must swing either left or right, which we've long grown used to calling positive or negative. From an engineering standpoint, it makes no difference that we didn't invent new names for this action, and in fact, there are cross-correlations to other fields that support this seeming "doubling up" of the cognomen.)
OK, so we have a magnet inducing a current in the coil's wire. For the sake of having a starting point, let's say it went positive. But wait, there's more than one frequency here, we just said so. Yes, and all of the frequencies that excited the magnet all forced it to go positive. The important thing to remember right now is, they went the same direction, but at different strengths. Remember that.
Now, let us introduce the second transducer. Assume that it's identical to the first one in all respects. What happens next is obvious to us guitar/bass players, but I'll state it anyways, just so there are no missed assumptions down the line. If we position this second transducer anywhere else along the string, we get a different set of harmonic relationships, don't we? Meaning, the strength of each harmonic as related to the fundament is different from what we see at the first transducder's location
at any given instant in time. That time part is important, it always is, and we shouldn't forget it.
So, we have two transducers that are now working together to send separate signals to one output. Each of them shows the signal to have swung from zero to the positive direction when the string was first set to vibrating. Fine so far. But what happens when connect one transducer's leads backwards (reverse the polarity, if you will)? Easy - the magnet has now induced the current to swing (at the outset) from zero to the negative side. And that causes a whole new set of relationships between the two signals, doesn't it?
Consider: if we look only at the fundamental, and we look first at only one transducer's output, we see nice "peaks and valleys". The same view occurs when looking at only the second transducer. But each of those views is occuring in real time - we need to see what happened at the exact moment of the starting vibration. OK, that's simple, we need only apply some algebra and perhaps a touch of calculus, and we can find the precise moment in time when things starting rolling. But the point here is, when comparing one transducer to the other, the fundamental's initial swing away from zero did
not occur at the same moment in time.
So, again, what happens if we reverse the polarity of one of the transducers?
Well, since the string's vibration didn't "move the magnetic fields" at the same time, then it stands to reason that the two signals won't entirely cancel each other out - there will remain a slight residual signal, comprised of lower levels of peaks and valleys, but at the same frequency nonetheless.
And from that, it's obvious (I hope!) that the same remains true for all the harmonics, and all of their relationships. It's very complex to model, but the end results are, we can hear a big difference in the final output, the tonality, as it were. We say "it's out of phase", and in the literal sense of audio, that's true - some of the harmonics have been diminished, and some of them have been reinforced, thanks to the fact that the string vibrates with different strengths of harmonics at differnt points, for any give instant in time. In phase or out of phase, it's up to the listener to decide which way sounds best.
But the hookup of the reversed transducer, that's definitely a polarity change, in the electrical sense. We call the switch a "phase reversal" because of what happens in the audio sense, but it is indeed a polarity reversal, when viewed in strictly electrical terms.
<rant>
It doesn't help our cause (and I mean the whole playing community, not just us Nutz) that the mixing of ideas and terminology is perpetuated via the Innerwebs each and every time that someone uses Google. Like ChrisK's rant about the Trem-o-Leo
®, it's worse than fighing City Hall. At least politicians get outted when their skeletons are finally disclosed, or they die of old age, but educating beginners in what the classically trained, true Engineers in every sense of the word, wish they'd learn from the start......... fuggedaboudit.
Too many EE-wannabe's on the 'tardwebs, only too glad to spread the bad word.
</rant>
OK, now that I've just exposited 1250 words to embellish what newey said in less than 600, it's high time I go find my meds!
HTH
sumgai