There are basically two processes: decoherence and measurement.
Decoherence occurs when a wave function goes from more quantum mechanical behavior to more “classical behavior”.
So, as the wave passes through the double slit, initially it’s wave function is something like (left + right) entangled with (left – right) (it’s been a long time since my college qm class so this may not be technically correct but you get the idea).
Then, as the wave interacts with the detector, noise from the environment interacts with the quantum wave, and you end up with a state that’s more like 50% left and 50% right.
Now at this point, the wave function has decohered, but it hasn’t really “collapsed”. At some point, our universe has to flip a coin and decide whether the particle actually went left or right. This is a measurement.
How this happens no one actually knows. Physicists can guess when this might or might not happen based on experience, but no one can give a precise mathematical description of the measurement process. It remains to this day a major and obvious “there be monsters here” blank spot at the center of physics.
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