Here is a thought experiment that is supposed to show that standard quantum mechanics and pilot wave theory do not make the same prediction :
Take the double slit experiment, and add a detector in each slit.
In Standard Quantum Mechanics, the wave function will collapse by entering one slit. If the wave function collapse, it can no longer interfere with itself. Therefore, there won't be any interference pattern on the screen.
With pilot wave theory, measurement has no effect on the state of the particle. Interference pattern will still appear on the screen.
I know that both theories should predict the same result, but I can't find what is wrong in this thought experiment.
What is wrong with it?