Interpretation for Probability Wave and Quantum Measured Problem

By using Hamilton-Jacobi-Bellman equation with complex time, we investigate quantum theory in timelike curve. State vectors of a physical system in the two-dimensional timelike curve not only obey Schrödinger equation in the observed timespace but also involve random motion in the traversal timespace. The random motion with hidden variables is successfully to explain why the wave function is a probability wave. Quantum measurement are discussed in present work. The results are in agreement with the conventional interpretation of quantum theory.