“Well, don't worry too much” (Michel).How would you show that Born is not right?
What to do if Born is wrong?
Consider single electron/photon set up. According to the Born’s statistical interpretation, after beam splitter one obtains the statistical distribution which represents the potential reality carried by the single particle due to interaction with itself. Alternatively, you may treat it as the same particle propagating in the different waveform after interaction with the beam splitter. The difference is that according to the laws of the statistical mechanics, it is impossible to assemble back the initial wave packet. According to deterministic “interpretation” it is enough to include into the measurement assembly a device that will perform the inverse transformation in order to obtain the initial wave packet. If it is correct, then it is clear that the Mach-Zehnder interferometer will do a job. We (I and my son) discussed that as a proposal and turned to the literature to see what A.Tonomura et al. (in particular) are doing last time. We were not surprised to find that they are doing something very similar (“Double-biprism electron interferometry”, App. Phys. Lett., 84(17), 3229 (2004); “Triple-biprism electron interferometry”, JAP, 99, 113502 (2006)). Moreover, it seems that the presented results confirm our expectation. We still do not understand all necessary details of the experiment to be sure that that it (Triple-biprism is expected to present the pattern obtained after the first biprism as in the original 1989 experiment).
From the theoretical side, it was pointed out by Y. Aharonov and L.Vaidman, Phys.Rev.A, 41,11,(1990) that in case of two component wave packet the expansion coefficients are the eigenvalues of two self-adjoint mutually commuting operators (observables) which provide the necessary information about the system and have nothing to do with statistics. Now I work to extend that statement for the n-component case. In principle, I have no problems, but the description is not elegant enough so far and also I would like to see how it works when I consider n-level system. We intend to submit the paper with the detailed discussion for publication when it will be cooked enough.
What to do if Born is wrong? Nothing. You may continue if you wish to consider the deterministic evolution of the probability amplitudes (which describe the potential reality) and the interference effects between them. It is just English or psychology and we both agree that the physics is not there.
To be more serious, I expect to obtain the criterions how the “reading” devices should be constructed in order to extract the information stored in the quantum system without spoiling it (indeed using the collapse phenomenon which Michel consider useless).
With all my sincere respect, Dany.