Uncertainty, being perhaps the most basic principle of quantum mechanics, distinguishes the world of quantum phenomena from the realm of classical physics. Quantum entanglement, being perhaps the most surprising consequence of quantum mechanics, on the other hand apparently suggests paradoxes relating to or violations of the quantum mechanical uncertainty principle in some experimental situations. Popper's thought experiment is an example. We wish to report a recent realization of Popper's experiment. The experimental data show that there appears to be a violation of the uncertainty principle. This is, however as we shall argue in this paper, only an illusion provided that we take the teachings of quantum mechanics seriously.
An entangled pair of photons (1 and 2) are emitted to opposite directions. A narrow slit is placed in the path of photon 1 to provide precise knowledge of its position on the
y axis and this also determines the precise
y position of its twin, photon 2, due to quantum entanglement. Is photon 2 going to experience a greater uncertainty in momentum, i.e., a greater
Δpy, due to the precise knowledge of its position
y? The experimental data shows $\Delta y\Delta p_{y}<\hbar $ for photon 2. Can this recent realization of the historical thought experiment of Karl Popper signal a violation of the uncertainty principle?