The Delayed-Choice Quantum Eraser experiment is commonly interpreted as
implying that in quantum mechanics a choice made at one time can influence an
earlier event. We here suggest an extension of the experiment that results in a
paradox when interpreted using a local realist interpretation combined with
backward causation ("retrocausality"). We argue that resolving the paradox
requires giving up the idea that, in quantum mechanics, a choice can influence
the past, and that it instead requires a violation of Statistical Independence
without retrocausality. We speculate what the outcome of the experiment would
be.Comment: 8 pages, 6 figures. v2: minor fixes, references adde
