Two independent lasers shining at perpendicular angles will not create an interference pattern, as they do not interact with each other. The readings on a photon detector will remain unchanged because the second laser does not illuminate the detector. Even if the lasers crossed at right angles, any interference would only occur at the intersection point and would not affect the overall readings. The principle of superposition indicates that the field vectors from the lasers add linearly without interaction. Thus, no interference effects will occur between the two beams.