Quantum Particles and information
DENNIS DIEKS
Utrecht University (Netherlands)
 
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Classical particles can be counted and labeled. This labeling is done on the basis of qualitative features that make the particles physically distinguishable; indeed, classical particles differ at least by their spatial positions, even if they are of the same kind (“identical particles”, in the parlance of physics). The particle labels in this case represent information contained in the set of qualitative properties of a physical system. In the quantum mechanical theory of “identical particles” the situation is very different. According to the standard account the particle labels here cannot be associated with qualitative differences, since all single particles are in exactly the same state (obtained by partial tracing from the many-particles state). Apparently, then, the labels carry an informational content that cannot be reduced to qualitative physical characteristics.
In this paper we shall propose an alternative to this standard view, according to which particle labels do serve to represent qualitative physical information contained in the quantum state. However, we shall find that such informationally relevant labels do not coincide with the indices labeling the individual Hilbert spaces in the tensor product Hilbert space of the “many-particles system”. For example, in the case of two electrons in spatially widely separated wave packets, we shall associate particle labels with these individual wave packets rather than with the Hilbert space indices.
More generally, we shall investigate the structure of “many-particle states” and the information about particles contained in them. As it turns out, physically meaningful particles labels cannot be introduced under all circumstances. The associated inapplicability of the particle concept has consequences for long-standing interpretational problems of quantum mechanics, for example those relating to non-locality..