2 The conceptual basis of the individuality interpretation of quantum theory

According to the assumptions above, an individuality interpretation of a probabilistic theory does not make sense. This means that the boundaries of this simple framework have to be left far behind in order to establish QT as a theory about single particles. There are individuality interpretations which require more than a single universe or the participation of the observer’s brain [3]. We shall not discuss such interpretations here but restrict ourselves to the standard, Copenhagen interpretation (CI). In order to overcome the fundamental conflict between deterministic and probabilistic predictions the CI denies the reality of unobserved properties [21]. The properties ’come into being’ by the act of measurement in a way which is unknown and presents an unsolvable ’measurement problem’. The CI ’solves’ the fundamental conflict in a sophistic sense because it is not the task of a physical theory to make predictions about non-existing things. But it does not answer the question how things come back to reality. The CI’s claim for an individuality interpretation may also be expressed by the statement that QT is a ’complete’ theory as regards the description of individual particles; a more detailed analysis of the term ’complete’ will be given in section 4.

The CI shows several strange features, which have as a common origin the switching forth and back between reality and un-reality of properties as observation begins and ends. This problem becomes more stringent if two conjugate properties (non-commuting observables) have to be measured at the same time. A number of principles or concepts have been introduced, by the founders of the CI, in order to support the individuality interpretation and to explain its strange features. There seem to be essentially three such principles. Let us begin with

This principle will be referred to as individual uncertainty principle (IUP). The IUP presents the most important cornerstone of the CI because it supports, if true, the idea that certain (conjugate) properties of a single microscopic system cannot be simultaneously real. The second concept supporting the CI is

This idea can be considered as a complement to the IUP. In fact, according to the IUP particles have either sharp values of position or of momentum, depending on the experimental conditions. The former case corresponds to the particle picture, the latter to the wave picture. The degree of reality of these two pictures is determined by the measurement arrangement. The third idea supporting the CI is expressed as an assertion about

The relevance of this last point for the individuality interpretation is obvious. If QT really describes individual particles (for nonzero ℏ  ), then it should not change its character - as a theory describing individual particles - if the limit ℏ →  0  is performed. This limit must agree with a classical individualistic theory, namely classical mechanics. Otherwise the CI as an individuality interpretation must be called into doubt.

An important point to note is that no one of these three principles is part of the quantum theoretical formalism. This means each one needs justification from experiment or theory. A second important point is that these principles have been set up in the first half of the last century and that enormous technological progress has been made since then. A re-examination, taking today’s results into account, seems useful.