We get an interesting paradox if we try to simulate the time evolution according to the schrödinger equation on a classical machine. Consider simulating an observer measuring the z-component of a spin in the state:
a ¦up> + b ¦down>,
where ¦a¦ is not equal to ¦b¦.
The classical computer will end up simulating the states of the observer having measured spin up and spin down. The probability for the observer in any of these states is 1/2 irrespective of a and b.
Therefore from the first person's perspective the laws of quantum mechanics are violated.