What is the phyics behine a smoke alarm?

LED's. They look at ambient visibility. If the vis goes below a preditermined level, smoke in the room, a switch closes, and you here about it. I've had mine go of whie I was cooking. That's embarrassing...

The method that CaptainRich mentionned is actually just one of the ways that detectors work. There are 2 other ways. I should mention that Infra-Red LED's are used, not visible light. (I'm not sure what you mean by "ambient visibility", Capt.)
Smoke scatters this light, which then causes a decrease in signal.

The detector can also work by putting the sensor to one side, and detecting and INCREASE in the scattered light.

The third way it can work is by using a long-half-life alpha radiation source. The alpha particles are attenuated by the smoke. This causes a decrease in the ionization and so signal goes down.

Hope this helps. If you have any more questions, please feel free to ask :)