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From the viewpoint of gauge gravitational theories, the path dependentgravitational phase factors define the Lorentz transformations between thelocal inertial coordinate systems of different positions. With this point weshow that the spectral shifts in the curved spacetime, such as thegravitational and cosmological redshifts, can be understood as Doppler shifts.All these shifts are interpreted in a unified way as being originated from therelative motion of the free falling observers instantaneously static with thewave source and the receiver respectively. The gravitational phase factor ofquantum systems in the curved spacetime is also discussed.

Understanding the gravitational and cosmological redshifts as Doppler shifts by gravitational phase factors