Reforming the International System of Units

Thanks to considerable progress in quantum technologies, the trend today is to redefine all SI base units from fundamental constants, and we discuss strategies to achieve this goal. We first outline the present situation of each of the seven base units and examine the choice of fundamental constants that can reasonably be fixed. A critical issue is how we should redefine the unit of mass in the context of modern relativistic quantum theory. At the microscopic level, the link of mass with proper time as conjugate variables in the quantum phase S/~ is well established. This link strongly suggests that we should fix the value of Planck’s constant h, thus defining mass through a de Broglie-Compton frequency mc²/h. This frequency can be accurately measured for atomic and molecular species by atom interferometry. The main difficulty is then to bridge the gap with the macroscopic scale for which phases are usually scrambled by decoherence and where all mechanical quantities are built from the classical action S only, without connection to a quantum phase. Two ways are now being explored to make this connection: either the electric kilogram that uses recent progress in quantum electrical metrology, or atom interferometry combined with the Avogadro constant determination using a silicon sphere. Consequences for a new definition of the unit will be explored, as the two methods hopefully converge towards an accurate value of Planck’s constant. Another important choice is the electric charge connecting electrical and mechanical units: we could keep Planck’s charge and vacuum properties μ ₀ and Z ₀, which is the case today, or shift to a fixed electric charge e which seems to be the favourite choice for tomorrow. We recall that temperature and time are linked through Boltzmann’s constant, and there is a general agreement to fix that constant after suitable measurements. Finally, the unit of time is looking for a new, more universal and accurate definition based on Bohr frequencies corresponding to higher and higher frequency clocks. A last challenge is to produce a unified framework for fundamental metrology in which all base quantities and relevant fundamental constants appear naturally and consistently. I suggest a generalized 5D framework in which both gravito-inertial and electromagnetic interactions have a natural geometrical signification, and in which all measurements can be reduced to phase determinations by optical or matter-wave interferometry.