  We show an example of benign non-separability in an apparently separable
system consisting of $n$ free non-correlated quantum particles, solitonic
solutions to the nonlinear phase modification of the Schr\"{o}dinger equation
proposed recently. The non-separability manifests itself in the wave function
of a single particle being influenced by the very presence of other particles.
In the simplest case of identical particles, it is the number of particles that
affects the wave function of each particle and, in particular, the width of its
Gaussian probability density. As a result, this width, a local property, is
directly linked to the mass of the entire Universe in a very Machian manner. In
the realistic limit of large $n$ if the width in question is to be microscopic,
the coupling constant must be very small resulting in an ``almost linear''
theory. This provides a model explanation of why the linearity of quantum
mechanics can be accepted with such a high degree of certainty even if the more
fundamental underlying theory could be nonlinear. We also demonstrate that when
such non-correlated solitons are coupled to harmonic oscilators they lead to a
faster-than-light nonlocal telegraph since changing the frequency of one
oscillator affects instantaneously the probability density of particles
associated with other oscillators. This effect can be alleviated by fine-tuning
the parameters of the solution. Exclusion rules of a novel kind that we term
supersuperselection rules also emerge from these solutions. They are similar to
the mass and the univalence superselection rules in linear quantum mechanics.
The effects in question and the exclusion rules do not appear if a weakly
separable extension to $n$-particles is employed.
