 Another observation is that Ozawa’s conclusion that there is no lower bound for his error-disturbance product for is not at all surprising. That is, even without probing the system by a measurement apparatus, one can show that such a lower bound does not exist. If the initial state of a system is prepared at time \(t=0\) as a Gaussian quasi-monochromatic wave packet with \(\expval{\bQ_0}_\psi =0\) and  evolves freely, we can use a time-of-flight measurement to learn about its later position. Ehrenfest’s theorem tells us: \(\expval{\bQ_t}_\psi = \frac{t}{m} \expval{\bP}_\psi\).