  It is generally believed that dispersive polarimetric detection of collective
angular momentum in large atomic spin systems gives rise to: squeezing in the
measured observable, anti-squeezing in a conjugate observable, and collective
spin eigenstates in the long-time limit (provided that decoherence is suitably
controlled). We show that such behavior only holds when the particles in the
ensemble cannot be spatially distinguished-- even in principle-- regardless of
whether the measurement is only sensitive to collective observables. While
measuring a cloud of spatially-distinguishable spin-1/2 particles does reduce
the uncertainty in the measured spin component, it generates neither squeezing
nor anti-squeezing. The steady state of the measurement is highly mixed, albeit
with a well-defined value of the measured collective angular momentum
observable.
