Measuring Temperature of Schrödinger’s Coffee

A new uncertainty relation, linking quantum mechanics and the precision with which temperature can be measured, has been discovered by University of Exeter theoretical physicists Janet Anders and Harry Miller.

How hot is Schrödinger’s coffee? Image credit: Myriams Fotos / Wynn Pointaux / Sci-News.com.

How hot is Schrödinger’s coffee? Image credit: Myriams Fotos / Wynn Pointaux / Sci-News.com.

“If you measure the temperature of your coffee with a standard over-the counter thermometer you may find 90 degrees Celsius give or take 0.5 degrees,” Dr. Anders and Miller said.

“The temperature uncertainty in your reading arises because the mercury level in the thermometer fluctuates a little bit, due to microscopic collisions of the mercury atoms.”

“Things become more interesting when trying to measure the temperature of small objects, such as nanometer devices or single cells.”

“To obtain precise measurements one needs to use nanoscale thermometers made up of just a few atoms.”

The researchers have developed a new theoretical framework that allows the characterization of tiny thermometers and establishes their ultimate achievable accuracy.

It turns out that under certain circumstances the uncertainty in temperature readings are prone to additional fluctuations, which arise because of quantum effects.

Specifically, tiny thermometers can be in a superposition between different temperatures, e.g. 90.5 degrees Celsius and 89.5 degrees Celsius, just like Schrödinger’s cat can be in a superposition between being dead and alive.

“In addition to thermal noise that is present when making a temperature measurement, the possibility of being in a superposition means that quantum fluctuations influence of how we observe temperature at the nanoscale,” Miller said.

The discovery establishes a new connection between quantum uncertainty, arising from such superposition states, and the accuracy of temperature measurements.

In the future this uncertainty relation will be useful for experimentalists to design optimal nanoscale thermometers that take into account the effects of quantum mechanics.

“This finding is an important step for extending thermodynamic concepts and laws to the nanoscale, where our macroscopic assumptions break down,” Dr. Anders said.

The research is published in the journal Nature Communications.

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H.J.D. Miller J. Anders. 2018. Energy-temperature uncertainty relation in quantum thermodynamics. Nature Communications 9 (2203); doi: 10.1038/s41467-018-04536-7

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