I am working with the Hanbury-Brown and Twiss experiment, and I noticed a property of this experiment, similar to tunnelling.
Consider a pair of particles, A and B, the particle A passing through the slit A - see figure - and the particle B passing through the slit B.
Assume that the probability of getting a joint detection at the points P'1 and P'2, Prob(P'1, P'2), is null, or very small.
The quantum mechanics, however, permits that the probability of a joint detection in the detectors D1 and D2 be very big, Prob(P'1, P2) = Max, which may be 1000times greater than Prob(P'1, P'2).
That means that in the experiment described here, from all the trials in which one particle is detected at the point P'1, the number of trials in which the other particle is detected at the point P2, is 1000 times greater than the number of trials in which the other particle would have been detected at P'1 if a detector were placed at P'2.
How is this possible? The quantum mechanics shows that the detectors can be reached in two ways, picked with equal probability:
1) directs paths, i.e. from the slit A to D1 and from the slit B to D2,
2) crossed paths, i.e. from the slit A to D2 and from the slit B to D1.
But this is impossible: the direct paths are not allowed, QM says that if the particle A reaches the detector D1, the particle B doesn't reach the point P'2. As to the crossed paths, QM says that if the particles would follow only the crossed paths, the probability of joint detection in D1 and D2, would be much less than the value Max.
So, do we have tunnelling here? Do particles tunnel through the point P'2?
In my opinion the only way to get consistent answers in QM in terms of paths is via Feynman's formalism: consider all possible paths, and sum up the corresponding amplitudes. Once your detectors are in given positions, you sum up the amplitudes of getting to these detectors, and square that sum. The fact, for example, that two particles cannot simultaneously reach P1' and P2' is related to the fact that the paths carrying both particles there interfere destructively. This, however, has nothing to do with the total amplitude of reaching detectors D1 and D2, since there is no reason for the particle to go through P2'.
Of course, I realise you know all this. My point is that it is probably difficult, most likely impossible, to obtain a ``reasonable'' picture of QM in classical terms, where trajectories are well-defined and satisfy logical requirements.
In fact, I believe there are Bell type inequalities involving momentum and position whenever the Wigner function of the corresponding state has negative values.
I believe your insistence on a classical picture is understandable, but I reiterate my doubts: I do not believe such a picture can be made to fit the facts.
Dear François,
Yes, this is the situation, as you say.
When dealing with particles, they have to follow continuous trajectories. A particle cannot disappear from one region of the universe and instantly appear in another region, non connected to the former, otherwise, a moving frame of coordinates can be found by which, the particle is present for a while in both regions.
Rays endowed with amplitudes, as in Feynman's path integral, produce interference. Two waves can pass through one another, undergo destructive interference, and then separate and regain full intensity. But a particle cannot disappear by destructive interference, it has to have a continuous path.
Hopeless, as long as you believe in corpuscles.
Two centuries ago, the interferences proved that light is undulatory. This proof is still valid.
So any "which way" false problem is doomed to remain silly.
The concept you are looking for is found in the category of beam splitting experiments. Your two slit experiment is just one decision gate in a system of quantum events. Data is robust, but interpretations are divided into camps of strong arguments, both of which are probably wrong.
One camp says the particles don't really exist except as probabilities and that all decisions are delayed until a final measurement is made. The other camp allows a time reversal event to account for the data.
I prefer to look at the results from the reference frame of action for the moving particles. In this representation all the decisions are made at the same time and in the same place. The oddity occurs as an illusion when the results are transformed into the laboratory frame.