In general relativity, the picture of space–time assigns an ideal clock to each world line. 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 world lines. 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, whereas the quantum mechanical superposition of energy eigenstates leads to a nonfixed 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.

作 者：Esteban Castro Ruiz, Flaminia Giacomini, Caslav Brukner 期刊名称： Proceedings of the National Academy of Sciences 期卷页： March 7, 2017 第卷 第期 页 学科领域：数理科学 » 物理学 » 基础物理学 添加人是否为作者: 否 原文链接：www.pnas.org/cgi/doi/10.1073/pnas.1616427114 DOI： 10.1073/pnas.1616427114 ISBN： 关键词： quantum clocks， entanglement gravity， classical limit 全文地址：下载 备 注： When measuring time, we normally assume that clocks do not affect space and time, and that time can be measured with infinite accuracy at nearby points in space. However, combining quantum mechanics and Einstein's theory of general relativity theoretical physicists from the University of Vienna and the Austrian Academy of Sciences have demonstrated a fundamental limitation for our ability to measure time. The more precise a given clock is, the more it "blurs" the flow of time measured by neighbouring clocks. As a consequence, the time shown by the clocks is no longer well defined. The findings are published in the Proceedings of the National Academy of Sciences of the United States of America (PNAS).