The reason we know the photons are indistinguishable is because quantum mechanics deals with configurations of particles at locations, and these configurations

The reason we know the photons are indistinguishable is because quantum mechanics deals with configurations of particles at locations, and these configurations predict different outcomes depending on whether "photon A here and photon B there" is a different configuration than "photon B here and photon A there". If A and B are distinguishable, the configurations aren't the same, and you'll notice real quick when your experimental results don't line up with expectations based on them being the same. Mathematically it's as simple as the fact that x^2 + y^2 != (x+y)^2 for all x,y. To read a longer discourse on this, you can check out http://lesswrong.com/lw/ph/can_you_prove_two_particles_are_identical/ http://lesswrong.com/lw/ph/can_you_prove_two_particles_are_i... (and the sequence in general... which can help you with the 'change direction' bits)