GiuseppeP said:
But on the other hand the part of this problem is model we are creating trying to describe the phenomena and we hope to make prediction from it
You've hit the quantum nail on its rather uncertain head here.
There simply aren't any 'classical' pictures that work here - by a classical picture I mean something that is built up from our usual everyday ideas about how things work - so trying to think in terms of particles or waves, for examples.
I find the beamsplitter version of this experiment a bit cleaner in terms of pointing out the conceptual difficulties. Imagine we had a source that produced a single photon every second. We can test that we have a single photon by doing a single-photon detection (OK that's not a foolproof test because we can explain single-photon detection without ever requiring photons!). But let's not worry too much what the photon is - it would seem to be a particle, or possibly some localized wavepacket that kind of looks like a particle - so let's run with that.
Let's now see what happens at a 50:50 beamsplitter - which is just a device for, erm, splitting beams so that if we had a nice classical beam of light we'd get half the light going into one output arm (call this arm 1) and half the light going into the other output arm (call this arm 2).
What happens with our single-photon source if we point that at the beamsplitter? Well we find that if we put detectors in the output arms 1 and 2 we see that only one detector clicks, never both (we would say there is a zero coincidence count). And we've assumed we have perfect ideal detectors - which is usually far from the case. So it looks like this photon, which we imagine to be a particle, or wavepacket, or some blob of energy either goes one way or the other. Furthermore, which of the detectors fires seems to be entirely random.
That's cool, because it explains how a 'classical' beam can be thought of as containing zillions of these blobs so that roughly half of the blobs go one way and half go the other way - which gives us our half/half picture for a classical beam.
So we have a source that's producing blobs of energy and we can't split these blobs so that we get half a blob going one way and half the other way. All of the incident energy, per timeslot or second, appears at either detector 1 OR detector 2. These detectors might conceivably be many kilometres apart.
At this stage we're now entirely justified in thinking of indivisible blobs of energy going one way or another - it's hard to think of any other picture that would explain the observations (zero coincidence count, all the energy at either detector 1 or detector 2). If we tried to say that this blob is split or that a 'wave' goes along both arms then it's hard to see how all of the energy could suddenly appear at one detector at random. I don't know of any way of explaining this with just standard classical fields and quantum detectors.
OK that's experiment 1. Now we take the output arms from this beamsplitter (BS1) and we use them as the input arms to another 50:50 beamsplitter (BS2). We'd have to use mirrors to steer everything towards this second beamsplitter. Now we put detectors in the output arms of this second beamsplitter (let's call them arms 3 and 4). We call this new experiment, experiment 2.
What do we predict? Well based on experiment 1 we think that there's a blob of energy that 'makes' a random choice of which output arm (1 or 2) to go on. So that means when we run experiment 2 what we have is one of the blobs in either output arm 1 (which becomes input 1 to the second beamsplitter) or output arm 2 (which becomes input 2 to the second beamsplitter).
But based on experiment 1 if we have a single blob incident on our second beasmplitter BS2 then it has to emerge in one of the output arms 3 or 4 at random. So our 'blob' picture tells us that we should see the detectors in arm 3 and 4 fire randomly as before.
That's not what happens. If we adjust the path lengths correctly then what we see is that the detector in arm 3 fires, but the detector in arm 4 never fires. If we really had just a single blob going one way or the other this could not happen - it's inconsistent with our explanation for experiment 1. So, we conclude, something must actually be going on both output arms and when we bring the output arms from BS1 together as the inputs to BS2 we get an interference which is responsible for making detector 3 (and only detector 3) fire.
But if 'something' is going on both output arms of BS1 how do we now account for the properties of experiment 1? It's as if all of the energy goes one way or the other but some 'influence' which carries zero energy proceeds along both arms.
Furthermore, one might ask how the incident thing to BS1 (blob or wave or whatever it is) 'knows' it's going to be subject to experiment 1 or experiment 2 - in one case it has a 'natural' explanation in terms of blobs (expt 1) and in the other a 'natural' explanation in terms of waves (expt 2); but neither of these 'natural' explanations works for both experiments.
I can't see any 'natural' way of explaining this - other than recourse to the axioms of QM - and different people have different ideas about how 'natural' they are. The failure here is one of conceptualization. It's impossible to create a consistent classical picture (blobs or waves, for example) that will work for both experiment 1 and experiment 2.
So if by 'clear' explanation, you mean "without recourse to the notions of QM", then you won't find one. At some point we just have to accept that QM is the way the world works, however batshit insane it appears to us (and again, different people ascribe different levels of insanity to QM).
