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How to weigh everything from atoms to apples using the revised SI



Jon R. Pratt


The fact that the unit of mass might soon be derived from the Planck constant, rather than from an artifact standard, can seem daunting and downright baffling when viewed from the vantage point of our day to day perception of mass. After all, at measurement levels that register with our human senses, the connection between the quantum mechanics of Planck (atoms) and the engineering mechanics of Newton (apples) is less than obvious. However, as the physicist Richard Feynman famously observed, “there is plenty of room at the bottom”, and our need to quantify the mass of objects isn’t always limited to the familiar quantities we encounter in the produce section of our grocery store. Here, I explore the connection between mass and the Planck constant and suggest that a benefit of deriving the unit of mass from a fundamental constant is that it is inherently more scalable than the present artifact. For example, scientists and engineers working at the forefront of measurement science are increasingly pushing the boundary on what we consider a measurement of mass. In fact, a group now claims to have measured the mass of a cesium atom to within well below a yoctogram, which is below the mass of a single proton. This unit of mass is a submultiple of our present artifact kilogram so small that it requires twenty seven zeros after the decimal point before it even registers as a significant digit! How are such things possible? Why would you try? Can we even conceive of a traceable yoctogram? To begin grappling with these questions, I will attempt to guide you through the physics of Newton and Planck and hopefully shed some light on how we can weigh everything from atoms to apples in a revised SI based on fundamental constants.
Measure: The Journal of Measurement Science


mass, force, kilogram, watt balance, Avogadro's number, International System of Measurement


Pratt, J. (2014), How to weigh everything from atoms to apples using the revised SI, Measure: The Journal of Measurement Science, [online], (Accessed July 13, 2024)


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Created March 3, 2014, Updated February 19, 2017