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Thermodynamics constrains interpretations of quantum mechanics

16 December 2016

Theories that incorporate hidden variables are consistent with quantum mechanics only if the systems they describe can store unlimited information.

John Stewart Bell’s famous theorem is a statement about the nature of any theory whose predictions are compatible with those of quantum mechanics: If the theory is governed by hidden variables, unknown parameters that determine the results of measurements, it must also admit action at a distance. Now an international collaboration led by Adán Cabello has invoked a fundamental thermodynamics result, the Landauer erasure principle, to show that systems in hidden-variable theories must have an infinite memory to be compatible with quantum mechanics.

In quantum mechanics, measurements made at an experimenter’s whim cause a system to change its state; for a two-state electron system, for example, that change can be from spin up in the z-direction to spin down in the x-direction. Because of those changes, a system with hidden variables has to have a memory so that it knows how to respond to a series of measurements; if that memory is finite, it can serve only for a limited time. As an experimenter keeps making observations, the system must eventually update its memory, and according to the Landauer principle, the erasure of information associated with that update generates heat. (See the article by Eric Lutz and Sergio Ciliberto, Physics Today, September 2015, page 30.) In the electron example, if all spin measurements must be made along the x– or z-axis, each measurement dissipates a minimum amount of heat roughly equal to Boltzmann’s constant times the temperature. Cabello and colleagues show, however, that if an experimenter is free to make spin measurements anywhere in the xz-plane, the heat generated per measurement is unbounded—obviously, an unphysical result.

Heat need not be produced in a hidden-variables theory if a system could store unlimited information. Such is the case, for example, for David Bohm’s version of quantum mechanics, in which a continuous pilot wave serves as the information repository. And in formulations of quantum mechanics without hidden variables, such as in the Copenhagen interpretation, heat is not generated because there is no deterministic register to update. (A. Cabello et al., Phys. Rev. A 94, 052127, 2016.)

Theories that incorporate hidden variables are consistent with quantum mechanics only if the systems they describe can store unlimited information.

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