What is time?

How to find the fundamental limits of measuring time?

Einstein once joked, “Time is what a clock measures.” Physicists say, “A clock is a flow meter for entropy.” Let’s explore.

From general relativity point of view, time is the fourth coordinate of a smooth manifold called spacetime. In quantum mechanics time doesn’t play the same role as other quantities, like position or momentum, there is no observable for time — no exact, intrinsic time stamps on quantum particles that can be read off by measurements. In fact, time is a smooth parameter, a reference against which to gauge the evolution of other observables. Since we cannot measure time directly, there should be a way of time measurements that is complete and autonomous. One possible thermodynamic answer: autonomous quantum clocks (AQC)
[PRX: 7, 031022 (2017), 11, 011046 (2021)].

‼️: an ideal clock would burn an infinite amount of energy and produce infinite entropy, which is not possible. Thus, the limited.

Why is it important?
(i) for better quantum computers
(ii) for completeness of quantum gravity we have to reconcile these two notions

A clock is a thermal machine, anything that undergoes irreversible changes in which energy spreads out among more particles or into a broader area.

The mechanism of AQC (swipe):
A “hot” atom (1) connects to a heat source (e.g., the photon from the Sun), a “cold” atom (2) couples to the surrounding environment, and a third atom that’s linked to (1) and (2) “ticks” by undergoing excitations and decays. Energy enters the system from the heat source, driving the ticks. Entropy is produced when waste energy gets released into the environment. The ticks become more regular the more entropy the clock produces.

The big question is whether the fundamental limit on the accuracy of clocks reflects a fundamental limit on the smooth flow of time itself — in other words, whether stochastic events like collisions of coffee and air molecules are what time ultimately is.

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