Considering a system of particles in a gravitational field for example, in classical mechanics, there is naturally a one-to-one correspondence between the motion observed by an freely falling observer and the motion observed by a distant observer. However, in quantum mechanics, a “good wave packet” whose position and velocity are relatively well determined for one observer is not necessarily a “good wave packet” for another observer, which means the above one-to-one correspondence no longer exists. We will argue that such deviations can be significantly large when non-renormalizable interactions, or interactions that becomes strong at the Planck scale, such as gravity, are taken into account.