Time Dilation in Quantum Thermodynamics.

Magdalena Zych

Magdalena Zych

Nikolaj Weber

Pikovski et al. showed that gravitational time dilation couples the internal energy of a composite quantum system to its center-of-mass position, producing dephasing without modifying quantum mechanics. The resulting decoherence rate depends on the energy variance of internal degrees of freedom and yields a Gaussian temporal profile. Building on the thermodynamic identity Var(H)=k_B T^2 C_V, we evaluate this effect for macroscopic objects modeled as Debye solids in Earth's gravitational field. We demonstrate that the decoherence rate scales as a universal T^{5/2} power law at cryogenic temperatures, providing a unique phenomenological signature distinguishing it from spontaneous collapse models (e.g., CSL) which predict temperature-independent rates. Furthermore, we expand the Pikovski mechanism to structurally disordered materials (fractons) and analytically show that the scaling modifies to T^{(d_s/2)+1}, acting as highly sensitive gravitational noise receptors.

Alto Osada, Rekishu Yamazaki, Atsushi Noguchi

Takeshi Chiba, Shunichiro Kinoshita

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.