Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. In the theory of general relativity time flows at different rates depending on the space–time geometry. Here, a drop in the visibility of a quantum 'clock' interference in a gravitational potential is predicted, which cannot be explained without the general relativistic notion of time.Current attempts to probe general relativistic effects in quantum mechanics focus on precision measurements of phase shifts in matter–wave interferometry. Yet, phase shifts can always be explained as arising because of an Aharonov–Bohm effect, where a particle in a flat space–time is subject to an effective potential. Here we propose a quantum effect that cannot be explained without the general relativistic notion of proper time. We consider interference of a 'clock'—a particle with evolving internal degrees of freedom—that will not only display a phase shift, but also reduce the visibility of the interference pattern. According to general relativity, proper time flows at different rates in different regions of space–time. Therefore, because of quantum complementarity, the visibility will drop to the extent to which the path information becomes available from reading out the proper time from the 'clock'. Such a gravitationally induced decoherence would provide the first test of the genuine general relativistic notion of proper time in quantum mechanics. In the theory of general relativity time flows at different rates depending on the space–time geometry. Here, a drop in the visibility of a quantum 'clock' interference in a gravitational potential is predicted, which cannot be explained without the general relativistic notion of time.

arXiv:1105.4531Nature CommunicationsOct 18, 2011251 citations

Quantum Tunneling Time: Relativistic Extensions

Dai-Yu Xu, Towe Wang, Xun Xue

Foundations of PhysicsSep 13, 20136 citations

Proper Time as a Parameterization of the Phase of the Relativistic Action

Jonatan P. camargo

This short note proposes a structural interpretation of relativistic time dilation in terms of the dynamical phase associated with the action. The starting point is the general relation $\phi=\frac{S}{\hbar},$ and, in the case of a free massive particle, the minimal relativistic action $S=-mc^2\tau.$ It follows immediately that the dynamical phase is proportional to the proper time, $\phi=-\frac{mc^2}{\hbar}\tau=-\omega_C\tau, \qquad \omega_C=\frac{mc^2}{\hbar}.$ Thus, the proper time can be interpreted as a geometric parameterization of the phase of the relativistic action. It is then shown that the time dilation observed in relative reference frames can be read as a modification of the accumulation rate of the dynamical phase when the geometry of the worldline is altered. This work does not intend to fully derive special relativity nor substitute its geometric formulation. Its objective is more restricted: to formally register that the relativistic structure of proper time admits a natural interpretation as the phase dynamics of the action. Finally, it is indicated that the truly new element of the broader program is not only in this reinterpretation, but in the condition $\Delta S=2\pi n\hbar$ as a structural criterion of interferential compatibility between dynamical systems.This short note proposes a structural interpretation of relativistic time dilation in terms of the dynamical phase associated with the action. The starting point is the general relation \[ \phi=\frac{S}{\hbar}, \] and, in the case of a free massive particle, the minimal relativistic action \[ S=-mc^2\tau. \] It follows immediately that the dynamical phase is proportional to the proper time, \[ \phi=-\frac{mc^2}{\hbar}\tau=-\omega_C\tau, \qquad \omega_C=\frac{mc^2}{\hbar}. \] Thus, the proper time can be interpreted as a geometric parameterization of the phase of the relativistic action. It is then shown that the time dilation observed in relative reference frames can be read as a modification of the accumulation rate of the dynamical phase when the geometry of the worldline is altered. This work does not intend to fully derive special relativity nor substitute its geometric formulation. Its objective is more restricted: to formally register that the relativistic structure of proper time admits a natural interpretation as the phase dynamics of the action. Finally, it is indicated that the truly new element of the broader program is not only in this reinterpretation, but in the condition \[ \Delta S=2\pi n\hbar \] as a structural criterion of interferential compatibility between dynamical systems.

Mar 17, 20260 citations

This short note proposes a structural interpretation of relativistic time dilation in terms of the dynamical phase associated with the action. The starting point is the general relation

\phi=\frac{S}{\hbar},

and, in the case of a free massive particle, the minimal relativistic action

S=-mc^2\tau.

It follows immediately that the dynamical phase is proportional to the proper time,

\phi=-\frac{mc^2}{\hbar}\tau=-\omega_C\tau, \qquad \omega_C=\frac{mc^2}{\hbar}.

Thus, the proper time can be interpreted as a geometric parameterization of the phase of the relativistic action. It is then shown that the time dilation observed in relative reference frames can be read as a modification of the accumulation rate of the dynamical phase when the geometry of the worldline is altered. This work does not intend to fully derive special relativity nor substitute its geometric formulation. Its objective is more restricted: to formally register that the relativistic structure of proper time admits a natural interpretation as the phase dynamics of the action. Finally, it is indicated that the truly new element of the broader program is not only in this reinterpretation, but in the condition

\Delta S=2\pi n\hbar

as a structural criterion of interferential compatibility between dynamical systems.