When is coherence is gained in interference effects? The primary rule concerning indistinguishability is based upon the indistinguishability of the description of the source of the system and the path of the system, rather than the indistinguishability of the path of the source of the system only. It could be argued that in the case of interference, coherence is not only contingent upon indistinguishability of path but also indistinguishability of the description of the sources also. It is commonly argued that the interfering sources must be identical in description. When analyzing that which is fundamental to interference effects, I consider this argument to be incorrect. In interference effects, there is only an additional contingency upon the identical nature of the sources because the detection systems being used are capable of discriminating between the distinct states of the interfering system. It is always the case in interference experiments that the measurement system (for example an absorbing electron) is one which could in principle be measured itself to indicate the state of the system, which would in turn also infer the path of origin of the system. Due to the unitary nature of the measurement transition, it is always possible in principle to measure the final state of the absorbing system to infer the state of the system absorbed which would infer the absorbed system’s path of origin. If one wishes to get interference between distinguishable states, then one must use a detection system which measures (absorbs) the exact state which is the superposition of distinguishable states which are the possible sources of the system. For instance, in the case of a 45degree polarized wave, if we split this with a polarizing beam splitter (PBS) and then recombined it with another PBS at identical path lengths then we would have the original 45degree polarized wave (which could be tested with a 45degree polarizer and detector). But if we modulated one path length of the recombination we would only find a sweep out of the intensity (the intensity of 45degree polarization) as a function of the coherence length, we would not find interference in the intensity with a modulation of path length. However, if we don’t use a 45degree polarizer with a normal detector and we rather use a detector which absorbs only 45degree polarized light (which could be constructed with a 45degree absorber placed in front of a normal detector), then this detector would not be capable of discriminating between the paths of origin of the system by virtue of the distinguishability of the final state of the absorbing system. This type of non-discriminatory detection would allow for the display of interference in the detected intensity with optical path difference of the two sources, regardless of the fact that the two sources are distinguishable by polarization. Of course, this type of experiment has yet to be realized due to the fact that it has never been attempted. It is argued that in interference effects, much like in recombination effects (for example spin recombination), there is no contingency upon indistinguishability of the description of the sources of the system, the inteference is only contingent upon the indistinguishability of the path of origin of the system. Only indistinguishability of path of origin is fundamental to interference effects.
Correction, where I state, Is incorrect. In order to construct a detector which is indiscriminatory concerning H and V polarization, we would need a medium which detects/absorbs only 45degree polarized light. You would need the medium to regester its photon counts like a normal detector would. This is in principle possible, but to my knowledge this type of detection system does not exist. The idea is that any distinguishable sources can be used for interference, if and only if you can construct a detector which only absorbs particles that are in the superposition of the two distinguishable states. Is this feasible?
