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We actually use a feeler gauge that one uses to set the gaps on struts on a car. That being said, we do that more to test our capability vs. the manufacturer's specs. The number is less important than the actual result.
So, that being said, the real point it to lower the action to a point where it takes minimum effort to get the string down and firmly against the fret wire. At the same time, the goal is to be able to have that minimum effort on every string, every fret, without being so low as to cause any rattle. (For instance, it's common to set it too low and then hear the string hitting another fret down the neck when pressing the string at fret 12.)
In theory, it does make bending notes a little easier, because the absolute string tension is a little lower at pitch when the string is as straight a line between the nut and the bridge. (If the strings are high, they're higher at the bridge. The nut height is more or less fixed. So, just like Pythagoras said, if you change the angle, the string is effectively longer. To get equal pitch, it has to be tighter.) However, i haven't really noticed a huge difference.
Lowering the action makes it EASIER to push the string down, because it hits the fret wire while building less spring tension. (Think of the string as a spring.) Raising the action makes it harder.
Some guys like the action up because they have a heavy handed style, (lots of finger pressure) and a really low action can cause them to move the string laterally after it's down. This pulls things slightly out of pitch. So, some guys like it higher. Guys like me who play fast and use lots of fan picking and hammer-ons like it low.
Last Answer: The closer the strings to the pickup, the louder the signal. The pickup is a magnet that throws off a field, in which the metal string vibrates. Since magnetic fields decay exponentially, the change in distance makes a large change in the amount of electrical signal that's produced. If the pickups get too hot when you lower the strings, you need to bring the pickups down. If the pickups get too close to the pickup, also, you might have so much magnetic strength that when you fret, the string gets pulled down a little extra toward the pickup. This causes detuning. So, you might have to adjust the pickups down, or put the strings back up a bit to avoid that.
See! You wanted to ask questions, and i said ok. You said "be careful what you ask for"! Right back at ya! How happy are you now, that you got me started? The Professor
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