The half-silvered mirror is linear, but with complex amplitudes, not with probabilities. So you can shoot a positive amplitude and a negative amplitude through and things will cancel.
Still, I agree that the math used was not justified at all, and a treatment with normal quantum mechanics would have backed it up. I suppose it can be forgiven: the justification is a bit tricky. There is an article on the effect here.
The half-silvered mirror is linear, but with complex amplitudes, not with probabilities. So you can shoot a positive amplitude and a negative amplitude through and things will cancel.
Still, I agree that the math used was not justified at all, and a treatment with normal quantum mechanics would have backed it up. I suppose it can be forgiven: the justification is a bit tricky. There is an article on the effect here.