A null test of quantum mechanics is proposed. It is based on an arrang
ement in which a source sends two signals to two detectors. At each de
tector one of two different quantities can be measured. If the source
satisfies three conditions, all of which can be verified experimentall
y, then, according to quantum mechanics, a particular outcome is forbi
dden. This result follows only from the way in which quantum mechanics
constructs probabilities, and does not involve any dynamics. Looking
for this outcome is a test of quantum mechanics. It is shown how this
test can be realized using two-photon down-conversion.