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There are several published studies that do demonstrate low level positive drug urine and blood drug tests after passive exposure to HIGH levels of marijuana smoke. This is one of those studies:
In this case, individuals who spent time in a small unventilated room in which 16 joints were smoked were found to have low levels of marijuana for short periods of time.
I believe this addresses the issue of how much exposure might be needed.
HOWEVER, this type of exposure is not really realistic to the claim that someone was accidentally exposed without their knowledge (since you would essentially have to be essentially in a complete cloud of smoke). Multiple studies have been conducted with more realistic levels of exposure and they have NOT found positives with a more typical "passive" exposure above the threshold used in your test. This is the most recent of those studies.
You should also know that the home tests can give false positives because of the technology used. To get a valid test, any positive specimen would need to be sent for GC/MS technology.
The other important point, a negative test does NOT mean that your son is not using marijuana or some other illegal drug. With casual use, the drug tests will only identify the drug metabolites for about 3 days. Even with use 3-4 times per day, the test would likely be negative within 5-7 days. Synthetic cannabinoids ("Spice", "K2" or JWH-018) have similar effects to marijuana however they will not be identified by current drug test that are designed to identify THC.