  Quantum walks are powerful tools not only to construct the quantum speedup
algorithms but also to describe specific models in physical processes.
Furthermore, the discrete time quantum walk has been experimentally realized in
various setups. We apply the concept of the quantum walk to the problems in
quantum foundations. We show that randomness and the arrow of time in the
quantum walk gradually emerge by periodic projective measurements from the
mathematically obtained limit distribution under the time scale transformation.
