As far as I know, unpolarized light is defined as light which has no clear axis of polarization, but electric field vectors in all directions. However, I also know that electric fields can be superpositioned. So this leads me to the conclusion that if unpolarized light has equal $\vec E$ vectors in all directions, they should cancel.
Obviously, though, this is wrong (we've got light!). What's the explanation?
Answer
One way of thinking about it is to consider light as made up of lots and lots of photons. You're not going to see destructive interference unless the polarizations of all of these photons are lined up and they all undergo destructive interference at the same time. If they're random, some of them will interfere destructively, some of them will interfere constructively, and on average the interference will cancel out and we'll see the average intensity of the light stay the same.
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