Double slit experiment with polarizers as detectors What is the physical background for the statement that placing polarizers as detectors gives the 'which path information' so the interference pattern disapears? Is it that photons with polarization axes in the same direction can possibly add up or cancel out, whereas two photons with the polarization axes at 90 degrees angles cannot cancel out because the pythagorean law gives a sum of sqares that can only be positive, and therefore can only add up, giving a pattern that cannot show interference?
 A: Scientists say we can not or can never tell which way the photons goes because the photon must go thru both slits because even single photons interfere!  But this is more of a classical interpretation where they photon itself is the only disturbance in the EM field.
Many experimenters tried to determine which slit, and may thought experiments also attempted to understand the phenomenon.  Polarizers were a common method for photons, many of these experiments were also done as part of the quantum eraser experiment.
There are other theories that help to explain the slit experiment itself and also the effects of polarizers, examples are the photon wave function or path integrals (Feynman).  These explanations say that photons have more probable paths and others paths not so probable, these theories are based on the wave nature of possibilities in the EM field and where they have the highest magnitude. The photons goes where the EM field allows it to go.
So it is not based on photons with different axes not being able to cancel out, all photons will tend to follow similar paths where they are allowed. Polarizers can make certain paths very probable and others not. When one slit is effectively blocked by a combination of polarizers the interference dissappears, the allowed pathways have been permanently changed.
