Why quantum gravity looks timeless—and how clocks fix that

In timeless, generally covariant quantum theories—including quantum gravity—transition amplitudes naturally take the form cos(S/ℏ), combining forward and backward propagating terms, rather than the expected single exponential. This 'cosine problem' has prompted attempts to modify the fundamental dynamics. Working in a simple nonrelativistic closed system as a proxy for full quantum gravity, the authors show that Schrödinger evolution emerges once a clock degree of freedom is placed in a semiclassical 'good-clock state,' which breaks time-reversal symmetry and selects the forward-propagating amplitude—no modification of the underlying dynamics required. The result sharpens the case that quantum gravity is fundamentally timeless, with the arrow of time an emergent property of the clock subsystem.