Assumed data streams from a delayed choice gedanken experiment must satisfy
a Bell's identity independently of locality assumptions. The violation of
Bell's inequality by assumed correlations of identical form among these dat
a streams implies that they cannot all result from statistically equivalent
variables of a homogeneous process. This is consistent with both the requi
rements of arithmetic and distinctions between commuting and noncommuting o
bservables in quantum mechanics. Neglect of these distinctions implies a lo
gical loophole in the conventional interpretation of Bell's inequalities. P
ublished by Elsevier Science B.V.