I collect here info from another thread, to have a more focussed discussion. ''this particular assumption'' refers to the assumption that |psi(x_1,...,x_n|^2 is the probability density of observing simultaneously particle k at position x_k (k=1:N). Please show me a comparison with experiment that does this. Nonrelativistic particles have no different interpretation than relativistic ones. Particle detectors respond to the momentum of a particle, not to its position. Scattering experiments are interpreted in the momentum picture. Nobody is interested in the position of particle tracks, only in their momentum (which tells about masses). It could be this _only_ if you can prepare an experiment that realizes such a P_k. But this is a matter of experimental technique and not one about the interpretation of quantum mechanics. But there are no such operators since the spectrum of position is continuous. No. This unrealistic assumption is needed _only_when one wants to insists on a probability density interpretation of |psi(x)|^2. And for the position representation of an N-particle state, one would need an even more ideal precise measuring device that can measure the simultaneous presence of N particles in N different, arbitrarily small regions covering the size of an uranium atom (N=92), say. This is ridiculous - such measurement devices are impossible! Whereas the form in which I stated the probability interpretation assumes nothing. it makes claims only for those projectors that are actually realizable. it is therefore much more realistic.