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..