Impedance is a term use in speakers and speakers don’t care how the amp is set because the speakers have a given impedance curve. So notice that you only changing the amp when you bridge it. Speaker’s impedance is not an amp’s function, but the tolerance of the amp to a given impedance depends completely on the way the amp is set. A bridged into a given impedance amp draws twice as much current as it would if it driving two separate channels, each at that impedance. So a four ohm speaker will be a four ohm speaker if it is attach to one channel or a bridged channel amp. But it’s more stressful for the amp to drive any impedance bridged than unbridged.
So what about the impedance halving? It is a simple that is wring but are easy to explain. When an amp is bridged, each channel is seeing half the load given to the amp. Meaning, if you bridge an amp to 4 ohms, each channel sees 2 ohms. So each channel give twice as much power, and the combined output is quadruple a single channel at 4 ohms.
It is still wrong because each channel is not really used as a single channel. Using the part of one channel and an inverted part of another channel to create a totally new bridged channel. And also it is impossible for a channel to see only part of a circuit. If it’s seeing half the speaker, it’s seeing it all.
And also, the impedance is not really, literally changing. If so it should be safe to run a 4 ohm mono stable amp into a 4 ohm speaker, but the impedance halves creating a 2 ohm unusable speaker. That is just wrong and confusing.
