The definitions of several SI base units have evolved significantly since the original writing of this section. To ensure accuracy and alignment with the latest international standards, we have revised this section to reflect the modern definitions based on fundamental physical constants.

We began our discourse from the simplest things. For what can be simpler than measuring distances, time intervals, and mass? Indeed, this was so in the early days of physics, but today the methods used in measuring length, time, and mass are so sophisticated that they require a knowledge of all branches of physics. What we are going to discuss now in more or less detail is studied in the fourth book, Photons and Nuclei. With this in mind, I suggest that if this is your first book in physics, postpone reading this section until later.

The International System of Units, abbreviated SI from the French “Le Système International d’Unités,” was adopted in 1960. It is now the dominant system of units worldwide. While some older units may still be encountered occasionally, particularly in specific fields, the SI system is the standard used in science, technology, and most other areas.

Over time, there has been a deliberate shift in metrology from relying on material, man-made artifacts to defining units based on fundamental natural constants. This transition reflects the scientific community’s desire for measurements that are universally consistent, precise, and independent of physical objects that may change or degrade over time. Natural standards, such as the speed of light or atomic transitions, do not vary with location or time, ensuring that measurements remain stable and reproducible across the world. This evolution marks a significant milestone in the pursuit of accuracy in scientific measurements.

The SI system is based on seven base units: the metre, the kilogram, the second, the mole, the ampere, the kelvin, and the candela.

Let us start with the first four. My purpose is to emphasize a significant tendency of a general nature rather than to expound the details of measuring the corresponding quantities. The tendency is to discard material (i.e., man-made) standards and instead use natural standards, that is, standards whose values do not depend on the measuring devices and do not change with time.

We will begin with the metre. The metre is defined by taking the speed of light in vacuum \(c\) to be \(299{,}792{,}458\) metres per second. This definition links the metre to the second, which is itself defined using an atomic transition (as described below). This definition replaced the previous definition based on the wavelength of a specific spectral line of Krypton-86.

The definition of the second is based on the transition between two hyperfine energy levels of the caesium-133 atom. One second is defined as the duration of \(9{,}192{,}631{,}770\) periods of the radiation corresponding to this transition. This definition is extremely precise and stable.

The kilogram, the unit of mass, is now defined by fixing the Planck constant \(h\) to be \(6.62607015 \times 10^{-34}\ \mathrm{kg{\cdot}m^2{\cdot}s^{-1}}\). This definition links the kilogram to fundamental constants and avoids the reliance on a physical artifact like the international prototype kilogram.

The mole is the unit of amount of substance. One mole contains exactly \(6.02214076 \times 10^{23}\) elementary entities. This number is known as the Avogadro constant, \(N_\mathrm{A}\). The entities can be atoms, molecules, ions, electrons, or any other specified particle. This definition replaced the earlier definition based on the mass of carbon-12.

In contrast to these brilliant achievements, the precision in measuring mass directly, while greatly improved, still presents challenges. The kilogram’s redefinition, however, has shifted the focus from direct mass measurement to the precise determination of the Planck constant.

The Fourteenth General Conference of Weights and Measures (1971) introduced the mole. The introduction of the mole as an independent unit of amount of substance is related to the concept of the Avogadro number. The Avogadro number is the number of entities in one mole.

The introduction of the mole and its redefinition in terms of a fixed number of entities reflects the understanding that mass and amount of substance are distinct concepts, particularly when dealing with elementary particles. While related, they are measured and defined in different ways.

The redefinitions of the kilogram and mole, along with the continuing refinement of measurement techniques, demonstrate the ongoing evolution of the SI system to achieve ever greater accuracy and consistency based on fundamental physical constants.