The Twin Paradox in Quantum Field Theory

TL;DR

This work addresses how vacuum fluctuations in quantum fields affect observer-dependent time measurements for microscopic clocks along relativistic trajectories. By modeling clocks as finite-sized quantum systems whose elapsed time is read from vacuum-induced de-excitations, it shows that long-time limits reproduce classical time dilation while short-time, finite-size regimes introduce trajectory- and clock-shape dependent corrections. The approach combines an Unruh-DeWitt–type detector framework with explicit trajectory constructions and Gaussian clock profiles to quantify de-excitation probabilities $P_A$ and $P_B$, revealing QFT-induced deviations from the classical ${T_B}/{T_A}$ ratio, and it discusses implications for atomic clocks and experimental observability. Overall, the paper demonstrates that at the smallest time scales, time is not universal but entwined with both the observer's path and the clock's microscopic structure, highlighting the need to incorporate QFT effects in operational time measurements.

Abstract

Vacuum fluctuations in quantum field theory impose fundamental limitations on our ability to measure time in short scales. To investigate the impact of universal quantum field theory effects on observer-dependent time measurements, we introduce a clock model based on the vacuum decay probability of a finite-sized quantum system. Using this model, we study a microscopic twin paradox scenario and find that, in the smallest scales, time is not only dependent on the trajectory connecting two events, but also on how vacuum fluctuations interact with the microscopic details of the clocks.

Figures (3)

• Figure 1: Density plot of the regions of interaction of Alice (blue) and Bob (purple) for $\sigma = 0.1 T$ and $\sigma = 0.3 T$. The rest surfaces of constant $\tau$ are shown in gray, and the curves of constant $\bm \xi$ are shown in purple.
• Figure 2: Ratio between Bob’s elapsed time and Alice’s elapsed time for different clock sizes (controlled by the parameter $\sigma$), with energy gap $\Omega = 2 T_{0}$, and for trajectories satisfying $aT = 2$ and $aT = 4$.
• Figure 3: Relative deviation $\alpha(T, \Omega, \sigma)$ between our model and an ideal clock in an inertial scenario, for different clock sizes (as controlled by the parameter $\sigma$) and with energy gap $\Omega =2 T_{0}$.