The inability to adjust one’s thinking to the new phenomena gave rise to the idea of hidden variables, made popular by Bohm.³ He (and many others) wrote the Schrödinger equation in a form resembling the classical Hamilton–Jacobi equation, concealing the counter-intuitive features of quantum mechanics in a “quantum potential.” That DeBroglie initially regarded the wave function as a pilot wave is understandable, but the fact that he revived it in 1957 only means that he refused to accept the quantum mechanical picture.⁴ Even a nonlinear interaction with our consciousness has been suggested.⁵ Ghirardi–Rimini–Weber⁶ proposed to modify the Schrödinger equation so as to make it agree with their ideas about how reality ought to look.

Take the much discussed case of a beam of electrons passing through two slits in an opaque screen and producing interference stripes on a receiving screen. There is no way to explain this if one thinks of electrons as classical particles even if dressed up with some quantum features (except perhaps a Bohm potential of a very weird kind). Bohr solved the problem by emphasizing that the question, through which slit a particle had passed, is illegitimate as long as one has no way of observing that passage, and any set-up that makes this observation possible destroys the interference. This can be checked by an explicit quantum mechanical treatment of both the observed system and the apparatus.⁷  A perennial bone of contention is the following “measurement problem.” The evolution of a system is given in terms of a complex wave function but one observes only probabilities given by its absolute square. Von Neumann,⁸ being a mathematician, introduced as an axiom that observation reduces the wave function (or “probability amplitude”) to a probability distribution. Others concluded that an observation splits the entire universe into many worlds,⁹ but this picture is not open to verification, nor does it solve the question. The fact that the observed state of a system is not sufficient to compute its future, not even its probable future, was regarded as unacceptable by Einstein.

The solution of the measurement problem is twofold. First, any observation or measurement requires a macroscopic measuring apparatus. A macroscopic object is also governed by quantum mechanics, but has a large number of constituents, so that each macroscopic state is a combination of an enormous number of quantum mechanical eigenstates. As a consequence the quantum mechanical interference terms between two macroscopic states virtually cancel and only probabilities survive. That is the explanation why our familiar macroscopic physics, concerned with billiard balls, deals with probabilities rather than probability amplitudes.¹⁰

Incidentally, this is also the answer to the Schrödinger cat paradox. The Hilbert space of the cat does not consist of two eigenstates for life and death, but of two macroscopic subspaces corresponding to life and death and the interference terms between them cancel. Such a situation is not unusual. We know that air and water consist of molecules, but in everyday life we are dealing with their macroscopic averages: wind and currents.

Second, in order that a macroscopic apparatus can be influenced by the presence of a microscopic event it has to be prepared in a metastable initial state—think of the Wilson camera and the Geiger counter. The microscopic event triggers a macroscopically visible transition into the stable state. Of course this is irreversible and is accompanied by a thermodynamic increase of entropy.

This is the physics as determined by quantum mechanics. The scandal is that there are still many articles, discussions, and textbooks, which advertise various interpretations and philosophical profundities. In the seventeenth century Cartesians refused to accept Newton’s attraction because they could not accept a force that was not transmitted by a medium. Even now many physicists have not yet learned that they should adjust their ideas to the observed reality rather than the other way round.

REFERENCES
1. Hrvoje Nikolić, “Would Bohr be born if Bohm were born before Born?,” Am. J. Phys. https://doi.org/10.1119/1.2805241 76, 143–146 (2008).
2. For ample literature see Nikolić, loc cit. or Quantum Theory and Measurement, edited by J. A.Wheeler and W. H.Zurek (Princeton U.P., Princeton, 1983); V. Laloë, “Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems,” Am. J. Phys. https://doi.org/10.1119/1.1356698 69, 655–701 (2001).
3. D.Bohm , “A suggested interpretation of the quantum theory in terms of “hidden” variables. I,” Phys. Rev. https://doi.org/10.1103/PhysRev.85.166 85, 166–179 (1952); “A suggested interpretation of the quantum theory in terms of “hidden” variables. II,” Phys. Rev. https://doi.org/10.1103/PhysRev.85.180 85, 180–193 (1952).
4. L. de Broglie, La Théorie de la Mesure en Méchanique Ondulatoire (Gauthier-Villars, 1957).
5. E. P. Wigner, Symmetries and Reflections (Indiana U.P., 1967), p. 171.
6. G. C. Ghirardi, A. Rimini, and T. Weber, “Unified dynamics for microscopic and macroscopic systems,” Phys. Rev. D https://doi.org/10.1103/PhysRevD.34.470 34, 470–491 (1986).
7. N. G. van Kampen, “Ten theorems about quantum mechanical measurements,” Physica A https://doi.org/10.1016/0378-4371(88)90105-7 153, 97–113 (1988).
8. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932).
9. The Many-Worlds Interpretation of Quantum Mechanics, edited by B. S. DeWitt and N. Graham (Princeton U.P., Princeton, 1973).
10. N. G. van Kampen, “Quantum statistics of irreversible processes,” Physica (Amsterdam) https://doi.org/10.1016/S0031-8914(54)80074-7 20, 603–622 (1954).