W
weller2
Guest
You are confusing two things here.
First off, the interference pattern will only emerge on the detector after many photons are fired at it. Each one will hit a particular pixel on the detector. If you connect your detector to the screen, so that brightness of each pixel on the screen corresponds to the amount of photons which hit each detector pixel, ONLY THEN you will see the interference pattern. This is because the wave function describes probability that the photon will hit pixel (x,y), but when it actually hits the detector, it will hit a particular pixel.
The Copenhagen interpretation says that the wave function collapses when the photon hits the detector – it is in all possible places when in motion, but only one place is chosen randomly when it hits the detector.
Another interpretation of QM (de Broglie - Bohm interpretation) says that photons are actually point particles, and the wave function just describes how they move through space in statistical terms. So when under Copenhagen, each photon is everywhere, under Bohm, each photon has perfectly defined position all the time, you just can’t tell where it is until it hits the detector.
Now, if you put detectors at the slits, the intereference pattern disappears. This is actually quite simple: in order to be detected, the photon must interact with the detector, and this interaction changes (collapses) the wave function at the slit. Since the wave function is already collapsed, it will remain collapsed when it hits the screen. In mathematical terms, the new wave function is a convolution of the photon’s wave function and detector’s wave function – and this resulting function, for a correctly working detector, is fully deterministic (left slit / right slit). Consequently, if your detector is malfunctioning (i.e. only works half of the time), you will get a combination of the interference pattern and slit image – because half of photons will have collapsed wavefunction, and the other half will have original, uncollapsed wave function.
Now the fun part: it turns out that it if you destroy the “which-path” information, you will get the interference pattern back (i.e. un-collapse the wave function). If you want to learn something mind blowing, look up “quantum eraser”, “delayed choice experiment” and “delayed choice quantum eraser”.