Fig. 2: Magnitude of quantum time dilation.
From: Quantum clocks observe classical and quantum time dilation
The strength of the quantum time dilation effect \({\gamma }_{{\rm{Q}}}^{-1}\) is plotted in a as a function of the momenta difference \((\bar{p}_{{\mathrm{A}}}^{\prime} -{\bar{p}}_{{\mathrm{A}}})/mc\), where \({\bar{{\bf{p}}}}_{{\mathrm{A}}}=({\bar{p}}_{{\mathrm{A}}},0,0)\) and \(\bar{{\bf{p}}}_{{\mathrm{A}}}^{\prime} =(\bar{p}_{{\mathrm{A}}}^{\prime} ,0,0)\) denote the average momentum of the wave packets comprising the superposition state in Eq. (22) for θ = π/8, and in b as a function of superposition weight θ for \((\bar{p}_{{\mathrm{A}}}^{\prime} -{\bar{p}}_{{\mathrm{A}}})/mc=0.17\). Different values of the average total momentum \((\bar{p}_{{\mathrm{A}}}^{\prime} +{\bar{p}}_{{\mathrm{A}}})/mc\) are shown and ΔA/mc = 0.01 in all cases. The thin black line in plot a traces the trajectory of the optimal momentum difference \({\bar{p}}_{{\rm{opt}}}\) for different total momentum \(\left(\bar{p}_{{\mathrm{A}}}^{\prime} +{\bar{p}}_{{\mathrm{A}}}\right)/mc\).
