(Δs)2 = 0

        It is wrong to then equate this to some sort of proper time Δτ, find that

    Δτ = 0

    for a photon, and thus conclude that photons always "experience" zero proper time. No. Remember that Δτ is defined as the 
    time difference between two events as measured by an observer (i.e., an inertial frame) that actually travels between the events. Photons 
    have no reference frames! So the definition of Δτ doesn't apply to null paths.