“At that time I thought it was interesting,” says Orenstein, who is now a professor at UC Berkeley, and a senior scientist at Lawrence Berkeley National Laboratory, “but I didn’t realize that 30 years later it would still be a completely unexplained mystery that was being related to black holes and information theory.”
The 2013 Science paper and today’s Nature Physics findings show that the slope of the line relating the electron scattering rate to temperature in strange metals is invariably the same: ħ.
In 2004, the Dutch theorist Jan Zaanen gave this curious phenomenon a name: Planckian dissipation. He argued in a Nature News & Views article that electrons in these materials, and in other exotic states of matter sometimes referred to as “quantum soup,” are all reaching a fundamental quantum speed limit on how fast they can dissipate energy.
“If you’re on a freeway and all the cars are going at the same speed, it’s not because their engines are identical; it’s just because there’s a speed limit,” Hartnoll said.
To understand why electrons in strange metals push up against the putative speed limit, theorists want to figure out where it comes from. The best argument traces the speed limit to the uncertainty principle, the famous formula introduced by Werner Heisenberg in 1927 that puts an upper limit on the amount of certainty that you can have about the world—or, equivalently, on the amount of definiteness the world itself possesses. This upper limit is determined by ħ.
Conceived and approximated by Max Planck in 1900 and later put in reduced form by Paul Dirac, ħ shows up all over quantum theory. Its extremely small value, now known with high precision, represents the quantum unit of action, but in addition, as Heisenberg showed, ħ is the quantum unit of uncertainty: an inescapable, base-level fuzziness in nature. The fuzziness appears when you try measuring two things at once: the position and momentum of a particle, for instance, or how much energy it possesses and for how long. In other words, position and momentum can’t both be defined to greater accuracy than ħ; nor can energy and time. The better you know one, the less certain the other.
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The hypothesis is that electrons in strange metals might be “dissipating as quickly as they can consistent with the uncertainty principle,” Hartnoll explained. The electrons possess an amount of energy that’s proportional to the temperature of the strange metal, and dissipation is a process that takes a certain amount of time. Time and energy can’t both be defined to arbitrary precision because of the uncertainty principle, Hartnoll said, so it’s possible that Planckian dissipation arises “when the dissipation time is as fast as it can be.”
It’s only a rough sketch, he admits. He and other theorists want to prove the quantum bound more rigorously, which might help clarify why hordes of electrons in materials like cuprates so naturally reach it.