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Title: Measure quantum time dilation of a clock in a momentum superposition
Plain: A moving clock ticks slower by an amount fixed by its speed. If the clock is in a superposition of two speeds, theory predicts an extra effect that no ordinary random mixture of speeds can produce, and no measurement of it has been reported.
Precise: For a clock of rest mass m with internal Hamiltonian $H_{\mathrm{clock}}$ whose center of mass is in a coherent superposition of momenta, the mass-energy coupling $H = \sqrt{p^{2} c^{2} + (m c^{2} + H_{\mathrm{clock}})^{2}}$ gives a proper-time distribution that differs from that of the corresponding classical mixture of momenta by a coherence-dependent term (Smith and Ahmadi, Nature Communications 2020). Determine whether atomic or ion clocks can resolve this quantum contribution, the momentum separation and fractional frequency resolution required, and measure it.
Settled by: A clock comparison in which a momentum-superposed clock and a matched classical mixture show the predicted difference in frequency shift.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: Predicted in 2020 (doi:10.1038/s41467-020-18264-4); no measurement was found in the sources checked.
Posed since: 2020