3 Critical discussion of the conceptual basis of the individuality interpretation

The philosophical idea that unobserved things cannot be ascribed reality goes back to Aristotle and has Descartes and Berkeley as prominent advocates. It is in disagreement with the common sense philosophy of physicists but this does, of course, not mean that it can be rejected right from the start. Starting our analysis with the

we should mention at the very beginning that Kennard’s inequality [14], which is commonly written in exactly the same form as the IUP, has a very different meaning. It is a statistical relation which has nothing to do with the simultaneous measurement of position and momentum but expresses the relationship of the statistical fluctuations of independently measured quantities. Its mathematical derivation from the framework of QT is still sometimes erroneously considered as a confirmation of the IUP. The second point to note is that Heisenberg’s famous Gedanken experiment connects the error in position to the disturbance in momentum, and not to the error in momentum (the momentum is assumed to be accurately known at the time of position measurement); see e.g. Margenau and Park [20]. Therefore it seems that the universal acceptance of the IUP is based on two historically-grown misunderstandings, namely the failures to distinguish individual from statistical measurements and measurements from preparations.

Considerable efforts have been undertaken to derive Heisenberg-like relations from QT. This requires, however, additional assumptions, forcing individuality concepts into the statistical formalism of QT. The most important of these is the ’projection postulate’, the assumption that the state vector jumps after a measurement into an eigenspace of the corresponding operator. The details of this process, which is sometimes referred to as ’non-unitary time evolution’, are unknown. This beautiful expression is used to hide the fundamental difference between individual and statistical predictions. The projection postulate was suggested by the ingenious mathematician von Neumann and seems very convincing from the point of view of mathematical simplicity. But it may be a simple error. In this context it must be mentioned that von Neumann’s proof of the non-existence of hidden variables contains a simple error. It was quoted many times, as an argument in favor of ’completeness’ of QT, during a period of more than thirty years (!), until the ’silly error’ in its derivation became widely known [21]. All attempts to derive Heisenberg-like relations from QT use this projection postulate, as well as other assumptions formulated in the abstract language of Hilbert space [13]. Depending on the chosen assumptions some authors derive relations similar to Heisenberg’s inequality [6] while others obtain different expressions [22]. Several experimental violations of Heisenberg’s inequality have been reported, the most recent one by Erhart et al. [10].

Most relevant for the CI’s claim of un-reality of unobserved properties is the IUP, i.e. Heisenberg’s inequality interpreted as a relation between measurement errors of conjugate properties. Astonishingly, the practical basis for the IUP seems to be still Heisenberg’s famous light-microscope Gedanken experiment - despite the fact that it says nothing about the simultaneous measurement of position and momentum. Thus, let us first ask if other ”Gedanken experimente” have been designed which show a violation of the IUP. This is indeed the case. Such idealized measurement arrangements have been proposed by Prugovecki [27], Park and Margenau [24], Ballentine [1], Popper [26] and others. We may, secondly, ask, as a question of primary importance, if the IUP has ever be confirmed experimentally. Not a single experimental confirmation has been reported [6] since Heisenberg’s creation of the IUP in 1927. On the other hand, data showing violations of the IUP have been published. We mention, in particular, the realization of Poppers thought experiment [26] by Kim and Shih [15].

Summing up, we find no experimental or theoretical facts supporting the IUP. This principle does not seem to be an element of science, but rather a historically-grown habit or an object of quasi-religious admiration.

Recent experiments by Tonomura [31] and others have shown that single particles are always particles and never waves. A video on the Hitachi website [30] shows the development of a double-slit interference pattern as a consequence of an increasing number of electrons arriving at the screen. As pointed out by Silverman in his discussion of the Tonomura experiment [29]: ”The manifestations of wave-like behavior are statistical in nature and always emerge from the collective outcome of many electron events” Thus, no mysterious transformation between particles and waves is required. The origin of the miraculous ’particle-wave duality’ is poor resolution of early experimental data.

The idea that classical mechanics must emerge as the classical limit of QT was advocated by Bohr, Dirac and others. But this idea led to a large number of open questions and contradictions. The problem becomes much simpler if one admits the possibility that the classical limit of QT differs from classical mechanics. It has been mentioned before that a straightforward application of the limit ℏ → 0  to Schrödinger’s equation leads to a classical probabilistic theory and not to classical mechanics [21816] A recent, more complete treatment [17] leads to the same conclusion.

To summarize, closer examination shows that neither the IUP, nor the wave-particle duality, nor the claim that classical mechanics emerges as the classical limit of QT present physically well-defined concepts. No support is provided for the philosophical idea that unobserved properties are not real and for the related idea that an individuality interpretation of QT exists. On top of that, this also implies that a fundamental and very successful methodical principle of physics, namely the principle of reductionism, can not be universally valid. This principle is not compatible with the statistical interpretation of QT. As is well-known, the scientific community decided to keep the philosophical dogma of reductionism along with the individuality interpretation of QT. From a psychological point of view this is understandable, since we expect science to yield predictions with certainty, but the question is how much weight should be given to psychological expectations.