Entanglement of quantum clocks through gravity

TL;DR

This paper demonstrates that quantum clocks interacting gravitationally become entangled through time dilation, challenging the classical notion of a well-defined single clock time, and showing how classical time emerges in the limit.

Contribution

It introduces a quantum-gravitational model showing entanglement of clocks via gravity, revealing fundamental limits on defining a single classical time.

Findings

Quantum clocks become entangled through gravity-induced time dilation.

Entanglement causes loss of coherence in individual clocks.

Classical time emerges in the limit of large, classical clocks.

Abstract

In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of clocks along nearby worldlines. However, if time is defined operationally, as a pointer position of a physical clock that obeys the principles of general relativity and quantum mechanics, such a picture is at most a convenient fiction. Specifically, we show that the general relativistic mass-energy equivalence implies gravitational interaction between the clocks, while the quantum mechanical superposition of energy eigenstates leads to a non-fixed metric background. Based only on the assumption that both principles hold in this situation, we show that the clocks necessarily get entangled through time dilation effect, which eventually leads to a loss of coherence of a single clock. Hence, the time as measured by a single clock is not well-defined. However, the general relativistic notion of time is recovered in the classical limit of clocks.