6 months ago, I moved to apartment with quartz countertops. Today I realized that at the bottom of the all kitchen shelves beneath the countertops is a fine white powdery dust. It seems dust is falling and accumulating inside the cabinetry below the shelves; my pots, food, plates, cutlery, kitchen towels.
Is this normal? Did the renovating company not wipe dust from the install or there a defect in the countertops? Should I try to complain? And is this dust harmful for inhalation or ingestion? Is silica dust safely cleaned by wiping with damp cloth or washing in washing machines? 
Best Answer
Pretty common practice for most trades not to clean after themselves. Even the trades that do clean after themselves I have a hard time imagining cleaning the underside of the slab.
My experience is the same as yours. If you touch the underside of the slab you are likely to come away with dust - unless you personally cleaned it.
I wouldn't worry about it.
Silica or silicon dioxide is regulated by the FDA to be no more than 2% by weight of any food sold. It is unlikely whatever did drop into your plates was more than 2% by weight of your food.
The danger with silica is inhalation but the concern is really around industrial exposure where you are working with concrete cutting/grinding or mixing and there are visible clouds of it in the air and you are breathing these clouds on a semi-regular basis.
I find it hard to imagine that you could ever expose yourself to enough of the dust left under the counter for it to have an affect on you. You probably get more exposure from buildings being demolished, city workers doing work on sidewalks/roadways, renovators mixing mortar or concrete or thinset in your neighborhood, etc.
FDA regulation