## Abstract

Over the past 40 years, a number of discoveries in quantum physics have completely transformed our vision of fundamental metrology. This revolution starts with the frequency stabilization of lasers using saturation spectroscopy and the redefinition of the metre by fixing the velocity of light *c*. Today, the trend is to redefine all SI base units from fundamental constants and we discuss strategies to achieve this goal. We first consider a kinematical frame, in which fundamental constants with a dimension, such as the speed of light *c*, the Planck constant *h*, the Boltzmann constant *k*_{B} or the electron mass *m*_{e} can be used to connect and redefine base units. The various interaction forces of nature are then introduced in a dynamical frame, where they are completely characterized by dimensionless coupling constants such as the fine structure constant *α* or its gravitational analogue *α*_{G}. This point is discussed by rewriting the Maxwell and Dirac equations with new force fields and these coupling constants. We describe and stress the importance of various quantum effects leading to the advent of this new quantum metrology. In the second part of the paper, we present the status of the seven base units and the prospects of their possible redefinitions from fundamental constants in an experimental perspective. The two parts can be read independently and they point to these same conclusions concerning the redefinitions of base units. The concept of rest mass is directly related to the Compton frequency of a body, which is precisely what is measured by the watt balance. The conversion factor between mass and frequency is the Planck constant, which could therefore be fixed in a realistic and consistent new definition of the kilogram based on its Compton frequency. We discuss also how the Boltzmann constant could be better determined and fixed to replace the present definition of the kelvin.

## Footnotes

One contribution of 14 to a Discussion Meeting ‘The fundamental constants of physics, precision measurements and the base units of the SI’.

↵In this respect we should carefully distinguish two different meanings of time: on the one hand, time and position mix as coordinates and this refers to the concept of time coordinate for an event in space-time, which is only one component of a four-vector; on the other hand, time is the evolution parameter of a composite system and this refers to the proper time of this system and it is a Lorentz scalar (see below).

↵Planck time comes to mind first, but there is no known way to use it for any practical clock and we shall see when we consider interactions that it is natural to introduce it in a dimensionless constant.

↵More generally one could introduce also a polarization tensor

^{λμ}:(2.14)The other Maxwell equations are simply obtained from the dual tensor as:(2.15)↵One can also extend equation (2.8) by introducing the d'Alembertian in curved space-time as in recent theories of atomic clocks and atom interferometry(Bordé 2004

*b*). For an overview of metrology and general relativity see Guinot (1997, 2004).↵The gravitation potentials

*h*_{μν}satisfy Einstein's linearized field equations for the metric written in the harmonic gauge as:(2.20)where_{μν}is the energy–momentum tensor of the source and where . So that, in the Dirac equation, the interaction term can be written as a dimensionless gravitational charge*p*_{α}/*m*_{e}*c*multiplied by a field having the dimension of a linear momentum.↵One should avoid the introduction of massless photons in this definition to make the connection between energy and frequency. We have sufficiently emphasized that there is a direct connection between mass and frequency in quantum mechanics. Furthermore, mass and the Compton frequency are relativistically invariant quantities (Lorentz scalars) unlike an energy or a de Broglie frequency (or wavelength). A definition based on the de Broglie wavelength has been proposed by Wignall (1992) without any connection to the watt balance.

↵The other choice would be to fix the value of the electron charge

*e*to a nominal value to turn the volt into a unit derived from the joule (and hence from the second, once*h*fixed). This requires to let*μ*_{0}be determined by the value of*α*fixed by nature. This situation would be opposite to the present one, in which*μ*_{0}is fixed and*e*has to be measured.↵The Avogadro number

_{A}is defined here as the number of atoms, isolated, at rest and in their ground state, contained in 0.012 kg of carbon 12. It is therefore, up to a numerical factor 0.012, the dimensionless ratio of the mass of the kilogram standard to the mass of the carbon atom. The Avogadro constant*N*_{A}stands usually for the same number per mole and it is expressed in mol^{−1}. This number and this constant are just a way to express the mass of the carbon atom or its 12th, which is the unified atomic unit of mass*m*_{u}. One should note that, if the kilogram is characterized by its Compton frequency , the Avogadro number is related to the Rydberg constant byand thus that, if this frequency is fixed, the Avogadro number will be implicitly linked to the atomic time.- © 2005 The Royal Society

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