We consider the concept of entanglement for pure cases of finite dimensional state spaces. The criterion of unentangled states is related to demanding rank one of an associated eigenvalue problem. In addition to the conventional procedure based on the Schmidt decomposition, we devise a method based on the spectral resolution of unsymmetric matrices. In particular, we consider the case when all eigenvalues are zero, and find that the method still works.

This paper recognizes that quantum theory is not satisfactorily formulated; in spite of its empirical success, we may wish to consider the possibility to find more intuitively acceptable foundations. It is emphasized that the difference between classical physics and quantum theory lies in the fact that the latter depends in an essential way on classical descriptions of the observations from preparation to recording. In addition, only statistical predictions are possible. We discuss the case of entangled quantum systems. Performing an experiment (...) on one subsystem, we move a realized prediction to be a precondition for subsequent observations. The quantum features presented do not fit into a unified interpretation, they are found to be incompletely defined but pragmatically applied. No uniquely well defined interpretation is adequate for all cases. (shrink)

The content of this book is essentially one argument. The aim of this book is to consider the breakdown of a certain world view during the twentieth century. This is mirrored in the treatment of both science and philosophy. As these form the foundation for the human position in the world, a major reorganization of the body of knowledge had to take place. Bohr and Wittgenstein have been chosen as the main actors to represent this revision. Each one had to (...) replace apparent order and certainty by an understanding based on limited concepts in constant flux. The conclusion is that the modern synthesis is far from satisfactory. By leaving the story unfinished in its present state, the book hopes to provoke a renewal of the discussion and the eventual emergence of a reformed clarity and understanding. Reality is to be left as it is, but the human mind is also to be left as it is. The problem is to find a way to effect a harmonious combination of these. (shrink)