This article is from the Car Audio FAQ, by Ian D. Bjorhovde (email@example.com) with numerous contributions by others.
Impedance is a characteristic of the speakers. The speakers don't give
a flip how the amp is configured: they have a given impedance curve,
and that's that. It should be clear that when you bridge an amp, you
are changing *the amp*. The speaker's impedance is *not* a function of
the amp, but the amp's tolerance to a given impedance depends
completely on the way the amp is configured. If you'll remember from
section 4, an amp bridged into a given impedance draws twice as much
current as it would if it were driving two separate channels, each at
that impedance. So, a four ohm speaker stays a four ohm speaker, if
it's hooked to one channel, a bridged channel, a toaster, or the wall
socket. But, it is more stressful for the amp to drive any impedance
bridged than unbridged.
So, why do people talk about the impedance halving? Well, it's a
simple model that isn't correct but is easy to explain to people who
don't know what's really going on. It goes like this: When you bridge
the amp, each channel is "seeing" half the load presented to the amp.
So, if you bridge an amp to 4 ohms, each channel "sees" 2 ohms.
Therefore, each channel puts out twice as much power, and the combined
output is quadruple a single channel at 4 ohms.
Why is that still wrong? Because each channel isn't really used as a
single channel. You've used part of one channel, and an inverted part
of another channel to create a totally new channel, the bridged
channel. Also, there's no way for a channel to "see" only part of a
circuit. If it's "seeing" half the speaker, it's "seeing" it all.
Second, it makes it awkward if people believe that the impedance is
really, literally, changing. If you use that model, is it safe to run
a 4 ohm mono stable amp into a 4 ohm speaker? It should be, but we
just said the impedance halves, so that's now a 2 ohm speaker, and you
can't use it. That's wrong, and confusing, and it makes people think
they can't do things they really can.