measure for measure Quantifying the quantum Stephan Schlamminger looks at the origins of the Planck constant and its current role in redefining the kilogram.

child on a swing is an everyday mechanical constant (h) with high precision, measure a approximation of a macroscopic a macroscopic experiment is necessary, force — in A harmonic oscillator. The total energy because the unit of mass, the kilogram, can this case of such a system depends on its amplitude, only be accessed with high precision at the the weight while the frequency of oscillation is, at one-kilogram value through its definition of a mass least for small amplitudes, independent as the mass of the International Prototype m — as of the amplitude. So, it seems that the of the Kilogram (IPK). The IPK is the only the product energy of the system can be adjusted object on Earth whose mass we know for of a current continuously from zero upwards — that is, certain2 — all relative uncertainties increase and a voltage the child can swing at any amplitude. This from thereon. divided by a velocity, is not the case, however, for a microscopic The revised SI, likely to come into mg = UI/v (with g the oscillator, the physics of which is described effect in 2019, is based on fixed numerical Earth’s gravitational by the laws of quantum mechanics. A values, without uncertainties, of seven acceleration). quantum-mechanical swing can change defining constants, three of which are Meanwhile, the its energy only in steps of hν, the product already fixed in the present SI; the four discoveries of the Josephson of the Planck constant and the oscillation additional ones are the elementary and quantum Hall effects frequency — the (energy) quantum of charge and the Planck, led to precise electrical the oscillator. Boltzmann and Avogadro measurements involving In 1901, the idea of energy quantization constants. Any experiment the Planck constant and the was put forward by Max Planck1. The year that can be used in the present elementary charge5. For the product before, Planck had published an article SI to measure the Planck of voltage and current UI, the wherein he predicted the spectral shape constant from known elementary charge cancels out; it only of black-body radiation (the radiation calibration masses can be depends on the Planck constant, two emitted from a perfect absorber). However, operated backwards in microwave frequencies, f1 and f2, used better experimental evidence became the revised SI: it for the Josephson voltage standard, and a available, with which Planck’s initial would measure known numerical factor r, which depends SIMONE BRAUNER theory was discrepant. So he attempted mass based on on the experimental setup. Hence, the mass another calculation and used an ‘audacious a fixed, defined can be expressed as m = hrf1f2/gv. assumption’: energy quantization. A black value of h. Such an Replacing a century-old artefact with a body can be described as a distribution experiment translates set of fundamental constants and recipes to of oscillators, the energy of which Planck between the quantum and the obtain the unit of mass from these constants required to be the product of an integer, macroscopic world3. and the Kibble balance brings the SI closer a new constant h, and the oscillator’s One experiment that connects h to the to a system of units that is “for all time, for frequency. Using elementary combinatorics kilogram involves a balance invented in all people”. ❐ and Boltzmann’s entropy equation, he 1975 by Bryan Kibble4. At the heart of the managed to obtain an equation for the Kibble balance, formerly known as the watt STEPHAN SCHLAMMINGER is at the spectral shape of the black-body radiation balance, is a coil in a magnetic field that can Physical Measurement Laboratory at that matched the experimental observations operate as both a motor and a generator. the National Institute of Standards and perfectly. From the published spectral For the former, a current I is passed through Technology, 100 Bureau Drive, Gaithersburg, data and his theory, Planck estimated a the coil, resulting in a force F. For the latter, Maryland 20899-8171, USA. value of 6.55 × 10–34 J s for h. Today, the the coil is swept with velocity v through the e-mail: [email protected] accepted value for the Planck constant field, producing an induced voltageU at is 6.626070040 × 10–34 J s, with a relative the coil’s terminals. Kibble realized that due References uncertainty of 1.2 × 10–8. to the symmetry in Maxwell’s equations, 1. Planck, M. Ann. D. Phys. 4, 553–563 (1901). 2. SI Brochure: The International System of Units (SI) 8th edn The unit of the Planck constant, J s, can the quotient of force and current, F/I, is (BIPM, 2014); http://www.bipm.org/en/publications/si-brochure/ 2 –1 be written as kg m s . This equivalence identical to the quotient of voltage and coil 3. Haddad, D. et al. Metrologia 53, A83–A85 (2016). hints at an interesting idiosyncrasy in velocity, U/v, if the velocity and force point 4. Kibble, B. P. in Atomic Masses and Fundamental Constants Vol. 5 (eds Sanders, J. H. & Wapstra, A. H.) 545–551 the present version of the International in the same direction. This principle enables (Springer, 1976). System of Units (SI): to measure a quantum one to equate both quotients and hence 5. Piquemal, F. Nat. Phys. 12, 284 (2016).

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