 The upshot of this objection is that having a lower bound on the product of the standard deviations of position and momentum, as the Heisenberg-Kennard uncertainty relation  (9)  gives, does not by itself rule out a state where both the probability densities for position and momentum are extremely concentrated, in the sense of having more than \((1- \epsilon)\) of their probability concentrated in a a region of size smaller than \(\delta\), for any choice of \(\epsilon, \delta &gt;0\). This means, in our view, that relation  (9)  actually fails to express what most physicists would take to be the very core idea of the uncertainty principle.