How selecting quantum outcomes could make a clock appear to run ahead

A traveling clock accumulates less time than a stationary one in the familiar relativistic twin paradox. Youka Kaku, Akira Matsumura and Tomohiro Fujita ask what happens when the clock’s motion is quantum mechanical—and researchers retain only a particular measurement outcome.

Their answer is an effective time advance: the selected clock signal can appear ahead of the stationary reference, even though none of its individual motion components runs ahead. Their November 9 arXiv preprint presents theoretical calculations, not an experimental observation.

A clock with two quantum roles

The model separates a clock into its motion through space and its internal ticking. An atom provides a useful example. Its internal state can be a quantum superposition of two energy levels, whose changing relative phase supplies a clock signal. Separately, the atom’s motion can contain different momentum components.

Relativity connects these two roles. Because internal energy contributes to mass, motion and internal ticking become coupled. They can become entangled: the internal state and motion can no longer be described independently.

The researchers calculate how to read this clock using Ramsey interferometry. A first pulse prepares the two internal energy levels in a superposition. After an interval of evolution, a second pulse recombines them. Repeated measurements of the internal state reveal an interference signal whose phase encodes elapsed time.

Without any additional selection, their model reproduces ordinary time dilation. A moving quantum clock falls behind the stationary reference, to the order of approximation considered.

Selecting an interference outcome

The crucial change is postselection. Before the final clock-reading pulse, the researchers mathematically project the clock’s motion onto a chosen quantum state. Only trials producing that outcome contribute to the conditional clock signal.

This is not simply sorting classical particles by speed. The selected state can coherently combine different motion components, allowing their probability amplitudes to interfere.

In one example, the initial motion combines a component near zero momentum with another near a nonzero momentum. The selected final state combines those components with an opposite relative sign. For suitable initial weights, destructive interference produces an internal clock phase ahead of the stationary reference.

The authors describe this using an anomalous weak value. An ordinary average of squared momentum cannot be negative. But a weak value, which depends on both the initial state and the selected final state, can have a negative real part. In the approximate clock-reading formula, that reverses the sign of the usual slowing correction.

No individual component acquires negative squared momentum. The unusual result belongs to the conditional interference signal. It should not be read as a demonstration that a traveling person could literally age faster by choosing a measurement outcome.

Beyond a two-component example

The study extends the calculation to a weak gravitational field, where both motion and gravitational potential influence the internal clock. Appropriate postselection can again yield an effective advance.

The authors also examine initially smooth, Gaussian wavepackets, called coherent states, rather than specially separated pairs of motion components. They solve the evolution analytically within an approximate gravitational model and find that selecting another coherent state can produce an advance.

In their illustrated case, the advance occurs at early times; later, the selected signal instead shows a delay. They identify the early-time contribution from motion as more promising for observation than the gravitational contribution in this setup, which would require a highly unlikely selection outcome.

A hydrogen-like atom supplies a further physical illustration. A superposition of two electronic orbitals produces an oscillating charge distribution and electric dipole moment. The calculated postselected state shows a phase advance in that dipole oscillation, making the effect more concrete than an abstract clock formula.

What remains to be tested

The analytical solutions are exact only within the chosen approximate Hamiltonian—the mathematical description of the system’s energy and dynamics. The treatment retains leading relativistic corrections, and the coherent-state gravitational calculation expands the potential only to quadratic order in position.

An experiment would also need enough successful selections while preserving sufficient interference contrast to resolve the phase shift. Higher-order corrections and experimental imperfections remain to be assessed. The result is therefore a prediction about conditional quantum clock readings, not an observed reversal of relativistic aging.