Akinbo,
let's assume for the moment that there are photons (particles) out there and those particles are divisible.
In principle, this view is appealing, because in the MZI (Mach-Zehnder-Interferometer), one can recombine the two partial beams (only one photon is in the interferometer per experimental run) in arbitrarily continous steps and deduce out of it that classical wave mechanics is at work. So, a photon could be split in two parts and reunited again at the second beamsplitter.
Now the energetical picture: Due to QM, a photon has the energy hv. If it is divisible, 'it' can also have hv/2. Now suppose that the original photon is split into two parts with each hv/2 at the first beamsplitter. At the second beamsplitter, these two parts are split again (now having hv/4 each) and interfere with each other such, that two of the remaining beams built constructive interference, the other two built destructive interference. So for the case with the second beamsplitter in the setup, only one and the same detector will indicate - what - well, hv.
For constructive interference you need the two beams that are in phase and lead to the clicks of the photomultiplier, altough these two beams only had 2*hv/4 energy. But anyways, perhaps i have something misunderstood here, it's some years ago i examined the MZI in more detail. But let's continue, besides my question what happened with the energy of the two beams that build destructive interference (the latter means:light light can give darkness, or energy energy can give no energy).
The energy balance of the known energy send out from the source and the energy received at the detectors is known to be always in equilibrium. Even if we make such experiments without the second beamsplitter, what is send out will equal what is detected (statistically). Assuming photons with hv/2 to trigger the detector is in contradiction to Bohrs v=(Em-En)/h. Those photons with hv/2 then would dissappear from our observable world, surley taking with them their energy.
One could probably 'circumvent' the latter restriction by skipping some assumptions built in to v=(Em-En)/h, but as far as i know, nobody ever managed to do so (because he would have to 'flip' major parts of known physics).
But anyways, here is another argument against the hypothesis of photon-divisibility. Consider a tiny photon source that can emitt a photon from time to time toward a random direction. We now can position our detector arbitrarily at some point around this source and see, if a photon is detected. Let's assume that the detector is some distance away from the source. By detecting the photon, one should deduce (under ideal experimental conditions), that other detectors more far away from the source, will not detect this photon anymore. But again, anyways, if one conceptualizes the photon as a wave which spreads form the source symmetrically in all directions, the energy hv of that photon should be distributed over that area until the 'photon' is detected. By detecting this 'photon', it has to instantanously recollect its total amount of energy (if one believes in some 'energy' of a 'photon').
A possibility to circumvent this would be to say, well, all these frayed out photon energies will sooner or later recombine and therefore are again able to be absorbed. But what about thermodynamics with relation to black-body-cavity-radiation? Smuggle in a few photons of hv/2 by placing in a beamsplitter of the kind we discussed, and guess due to what rules the splitted energies could recombine to keep up the thermodynamical equilibrium in that cavity.
Even if you have a model that wants to do exactly the latter, it would have to explain why in the MZI-scenario with the second beamsplitter in the setup, the one detector that is considered to give almost no clicks, does not click more times than has been measured. Due to recombined frayed out parts of hv, it should be possible in principle that around the setup there are myriads of such frayed out photon intensities. The latter because there are multiple surfaces with multiple different reflective properties in our world. These photon intensities then should lead to more clicks also for the other detector. I am sure one can validate this idea mathematically and on the basis of empirical data quantitatively to come to a better conclusion wether such a picture of a 'photon' is plausible or not.
Maybe those lines of reasoning can help you in some ways. I haven't yet read the papers of Franson JD, maybe i will do it the next days. Personally i think that modelling something that wants to achieve a more realistic view of QM via photon divisibility a very hard and ambitious task. I cannot exclude the possibility that the idea behind matches reality, but personally i would be cautious.
Best wishes,
Stefan
