What is the 'law' of a pan control? Is there such a thing as an illegal pan?
In early stereo mixing consoles, the choice of placement of a mono signal in the stereo 'sound stage' was simple - left, center or right. There were no other options. But then some clever person invented the panoramic potentiometer, which today we know as the panpot or pan control. The panpot is a continuously operating device that can position a mono signal anywhere in the stereo sound stage.
But let's look at what happens to the levels as a signal is panned.
Start with the signal panned left. The sound comes only from the left speaker, and nothing comes from the right. Now move the pan towards the center. Since the right speaker is now contributing more and more to the level in the room, the signal sent to the left speaker has to be lowered. In fact, when a signal is panned center, it needs to be 6 dB lower in level than when it is panned hard left or hard right. If the panpot is designed so this happens, then the sum of the levels in the left and right channels will remain constant whether it is panned left, center or right..
In the early days of stereo, when mono compatibility was important, then panpots did indeed have a 6 dB drop in level at the center, which meant that a signal could be panned all the way from left to right, and someone listening in mono would hear no change in level.
But that doesn't account for stereo listening. It should work in theory - sound pressure adds in exactly the same way as voltage. So the pan control with a 6 dB drop in the center ought to work fine. You should be able to pan all the way from left to right, and the signal level should be subjectively the same all the way.
But that doesn't account for the fact that most listeners enjoy their sound from a point in the diffuse field, where the sound has had chance to bounce around the walls of the room many times before reaching the listener's ears. This is totally different to the near-field monitoring technique that is currently popular.
If measurements are taken from a point in the diffuse field, then it will become apparent that it is better to have only a 3 dB drop in the center of the panpot's travel. Many panpots in real world designs compromise on a 4.5 dB center drop.
Added to this is the question about what happens in positions other than hard left, center and hard right. This will be determined by the 'law' of the resistive tracks of the panpot (or the digital algorithm, where the same factors apply), which has a closer relationship to the laws of physics than the legal system. It has been known science since the 1930's that the law should follow the sine and cosine functions for the two channels respectively. However, many analog consoles 'bodge' this instead of using the more expensive component necessary.
To be honest, most of this doesn't matter that much in music production. But where it does matter is in 5.1 post-production for film and home cinema. Designing a 5.1 channel panpot is a far more complex affair than stereo, and similar considerations regarding levels apply. However, a stereo panpot simply has to go from left to right. A 5.1 panpot might have to pan from left to left surround, center to right surround, perhaps even into the low frequency effects channel. And all the channels will have to contribute to the acoustic signal in the correct proportion.
A fascinating field of research, and real heavy-duty sound engineering.