Quantum time dilation in a gravitational field

Abstract

According to relativity, the reading of an ideal clock is interpreted as the elapsed proper time along its single classical trajectory. In contrast, quantum theory allows the association of many simultaneous paths with a single quantum clock. Here, we investigate how the superposition principle affects the gravitational time dilation observed by a simple clock-a decaying two-level atom. Placing such an atom in a superposition of positions enables us to analyze a quantum contribution to a classical time dilation, manifested in the process of spontaneous emission. In particular, we show that the emission rate of an atom prepared in a coherent superposition of separated wave packets in a gravitational field is different from the transition rate of the atom in a classical mixture of these packets, which gives rise to a nonclassical-gravitational time dilation effect. In addition, we show the effect of spatial coherence on the atom's emission spectrum.

Study Review of the Speed of Light in Space-Time for STEM Student

“…There is a link between proper time and coordinate time, and this link is described by the concept of time dilation (Bravo et al, 2023). Time dilation is a phenomenon that occurs when two clocks are moving relative to each other, or when one clock is in a stronger gravitational field than the other (Paczos et al, 2022). Time dilation predicts that the time interval measured by a clock in a stronger gravitational field or moving at a higher velocity will be shorter than the time interval measured by a clock in a weaker gravitational field or moving at a lower velocity (Roura et al, 2021).…”