  The two-slit experiment with quantum particles provides many insights into
the behaviour of quantum mechanics, including Bohr's complementarity principle.
Here we analyze Einstein's recoiling slit version of the experiment and show
how the inevitable entanglement between the particle and the recoiling slit as
a which-way detector is responsible for complementarity. We derive the
Englert-Greenberger-Yasin duality from this entanglement, which can also be
thought of as a consequence of sum-uncertainty relations between certain
complementary observables of the recoiling slit. Thus, entanglement is an
integral part of the which-way detection process, and so is uncertainty, though
in a completely different way from that envisaged by Bohr and Einstein.
