Quantum Steampunk by Nicole Yunger Halpern

Author:Nicole Yunger Halpern
Language: eng
Format: epub
Publisher: Johns Hopkins University Press
Published: 2022-04-15T00:00:00+00:00

These quantum clocks enable us to measure time accurately, but they aren’t autonomous: someone—an external controller—measures the atoms and adjusts the laser. What sort of a system could serve as an autonomous quantum clock?

Wolfgang Pauli pondered this question during the 1920s.4−6 Pauli’s exclusion principle explained why a two-fermion Szilard engine can’t perform as much work as a classical engine or a bosonic engine (under certain assumptions). Pauli was an Austrian-American physicist whose interests extended from quantum physics to psychology and philosophy. He homed in on simple, yet fundamental concepts—and what is time, if not fundamental?

Pauli theorized about autonomous quantum clocks (I’ll drop the autonomous from now on). The ideal quantum clock, he wrote, has a time observable. Observable is the physics name for a measurable property of a quantum system. We’ve discussed several observables—energy, position, momentum, and spin components—although I haven’t called them observables till now. An ideal quantum clock could occupy a quantum state in which the time observable has a well-defined value.

In such a state, the energy wouldn’t have a well-defined value, thanks to quantum uncertainty. According to the uncertainty principle, an electron with a well-defined position is in a superposition of all possible momenta. The more well-defined the electron’s position, the less well-defined the momentum. Energy and time participate in a similar trade-off. So, a quantum system with a well-defined time would be in a superposition of all possible energies. This superposition would have an important property: Imagine preparing a system in this superposition and then measuring the energy. Your probability of obtaining one possible outcome equals your probability of obtaining any other possible outcome. That is, a system with a well-defined time is in a superposition spread evenly across all possible energies.

This fact reveals a trade-off between timekeeping and work extraction. Suppose that you have one quantum system, from which you want to extract work or which will keep time. A system performs work reliably if you can predict roughly how much work it’ll provide. You can predict accurately if you know how much energy the system has—if the system has a well-defined energy. So, a well-defined energy often facilitates work extraction, while a poorly defined energy facilitates timekeeping. The ability to tell time trades off with the ability to provide work in quantum thermodynamics.

Pauli proved that no quantum system can have a time observable. If a system did, it could have an infinitely negative amount of energy. Having an infinitely negative amount of energy is impossible in our world. So, our world doesn’t accommodate time observables—or ideal quantum clocks.

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