@pittsburghjoe,
Root 0.
The projection doesn’t change the complex mathematical object. It is just how we view it. QM objects are not is duality, Math is.
Uncertainty gets removed because the anticorrelation between position and momentum is gone. The variables became independent. It can’t be a Cauchy Schwartz inequality anymore.
All quantum behavior is associated with the complex vector. The object being sent to a lower real number dimension kills the behavior.