KAHIBARO
Table of Contents
Understanding SI Base Units
In physics, every measurement must be expressed in units. To compare results and communicate clearly, scientists all over the world have agreed on a common system of units called the International System of Units, abbreviated as SI. At the heart of this system are a small number of basic building blocks: the SI base units.
These base units are defined very precisely, often using fundamental constants of nature. All other units in physics are constructed from them. In this chapter we focus on what these base units are and what physical quantities they correspond to. How they combine to form other units is treated when we discuss derived units.
The Seven SI Base Quantities and Units
The SI system is built on seven base physical quantities. Each base quantity has a name, a symbol for the quantity, a unit name, and a unit symbol. The table below summarizes them.
| Base quantity | Symbol | SI unit name | SI unit symbol |
|---|---|---|---|
| Length | $l$ | metre | m |
| Mass | $m$ | kilogram | kg |
| Time | $t$ | second | s |
| Electric current | $I$ | ampere | A |
| Thermodynamic temperature | $T$ | kelvin | K |
| Amount of substance | $n$ | mole | mol |
| Luminous intensity | $I_v$ | candela | cd |
Each of these base quantities captures a different aspect of the physical world. In practice, many everyday measurements use combinations, for example metres per second for speed, or newtons for force, but conceptually they all trace back to these seven.
The seven SI base units are: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
In the following sections, we look more closely at what each base unit represents and how modern definitions connect them to physical standards.
Metre: The Unit of Length
Length describes how far apart two points are in space. In SI, length is measured in metres, symbol m. Everyday examples include a person’s height in metres, the width of a room in metres, or the thickness of a book in centimetres, which is a fraction of a metre.
Originally, the metre was tied to the Earth, for example a fraction of the distance from the equator to the North Pole. Modern definitions avoid dependence on physical objects or astronomical bodies and instead use constants of nature.
Today, the metre is defined using the speed of light in vacuum, denoted $c$. The speed of light is taken to have an exact value in SI. The definition is phrased so that when you know how fast light travels, you can define a fixed length.
The metre (m) is defined so that the speed of light in vacuum is exactly
$$c = 299\,792\,458 \,\text{m/s}.$$
A metre is the distance light travels in vacuum in $\dfrac{1}{299\,792\,458}$ of a second.
In practice, measuring a metre does not require timing light in a laboratory for beginners. Instead, physical measuring tools like metre rules or tape measures are made and calibrated so that they agree with this standard.
Kilogram: The Unit of Mass
Mass measures how much matter an object has and how strongly it resists changes in motion. In SI, mass is measured in kilograms, symbol kg. Typical examples are your body mass in kilograms, or the mass of a small fruit in grams, which is one thousandth of a kilogram.
Historically, the kilogram was defined by a physical object, a metal cylinder kept in a vault near Paris. Modern SI definitions avoid such artefacts and connect units to fundamental constants. For mass, the key constant is the Planck constant, $h$, a fundamental quantity that appears in quantum physics.
In the current SI, the Planck constant is assigned an exact value, and the kilogram is defined in such a way that this value holds. At an advanced level, this definition connects measurements of electrical quantities to mass through devices such as the Kibble balance. For a beginner, it is enough to know that the kilogram is no longer just "what the metal block weighs", but is linked to a universal constant.
The kilogram (kg) is defined by fixing the value of the Planck constant $h$ to be exactly
$$h = 6.62607015 \times 10^{-34}\,\text{J·s}.$$
This links mass to fundamental physical constants.
In everyday laboratory work, masses are still compared using balances and calibrated weights, but these weights ultimately trace back to the modern SI definition.
Second: The Unit of Time
Time allows us to order events and describe how long processes take. The SI unit of time is the second, symbol s. A second is the base for larger units like minutes and hours.
Older definitions connected the second to the Earth's rotation, for example a fraction of the day. However, the rotation of the Earth is not perfectly regular, so it is not ideal for a precise standard. The modern definition uses the natural oscillations of atoms.
Specifically, the second is defined using the frequency of a particular transition in the caesium-133 atom. Atoms of a given type behave identically, so they provide a very stable "clock".
The second (s) is defined as the duration of
$$9\,192\,631\,770$$
periods of radiation corresponding to a specific transition in the caesium-133 atom.
Highly accurate atomic clocks implement this definition. Ordinary clocks and watches are calibrated to agree with time as maintained by networks of atomic clocks around the world.
Ampere: The Unit of Electric Current
Electric current describes how much electric charge passes through a surface per unit time. In SI, electric current is measured in amperes, symbol A. You may encounter values like a few amperes in household circuits, or milliamperes in small electronic devices.
In earlier definitions, the ampere was tied to the force between two long parallel wires carrying current. Today, like other base units, it is defined through a fundamental constant: the elementary charge $e$, the charge of a single proton (or the negative of an electron's charge).
The elementary charge is given an exact value in SI. Since electric current is the rate of flow of charge, fixing $e$ allows us to define an exact link between the number of elementary charges that pass per second and one ampere.
The ampere (A) is defined by fixing the elementary charge $e$ to be exactly
$$e = 1.602176634 \times 10^{-19}\,\text{C}.$$
One coulomb (C) is the charge of exactly $1/e$ elementary charges, and an ampere is one coulomb per second.
In practice, current is often measured with ammeters and electronics that are calibrated and, at the highest level, traceable back to this constant-based definition.
Kelvin: The Unit of Thermodynamic Temperature
Temperature describes how hot or cold something is in a thermodynamic sense. The SI base unit of thermodynamic temperature is the kelvin, symbol K. Unlike degrees Celsius (°C), the kelvin scale starts at absolute zero, the theoretical lowest possible temperature.
The Celsius and kelvin scales are related by a simple shift. If $t$ is temperature in degrees Celsius and $T$ is temperature in kelvin, then
$$T = t + 273.15.$$
Modern SI ties the kelvin to the Boltzmann constant $k_B$, which connects temperature to energy at the atomic level. This constant is given an exact value in the definition.
The kelvin (K) is defined by fixing the Boltzmann constant $k_B$ to be exactly
$$k_B = 1.380649 \times 10^{-23}\,\text{J/K}.$$
This definition anchors temperature to energy per particle. In laboratories and everyday life, thermometers are calibrated through practical fixed points, such as the freezing and boiling points of water, and these calibrations are ultimately linked back to the kelvin definition.
Mole: The Unit of Amount of Substance
Amount of substance tells you how many elementary entities, such as atoms, molecules, or ions, are present in a sample. It is not a count of individual particles directly, but a way to express very large numbers of them in a manageable way.
The SI unit of amount of substance is the mole, symbol mol. One mole is associated with a fixed number of specified entities. That fixed number is called the Avogadro constant, $N_A$.
Modern SI defines the mole by assigning an exact value to the Avogadro constant. This makes the mole a counting unit, in the same way that a dozen is always twelve items.
The mole (mol) is defined so that the Avogadro constant $N_A$ is exactly
$$N_A = 6.02214076 \times 10^{23}\,\text{mol}^{-1}.$$
One mole contains exactly $6.02214076 \times 10^{23}$ specified entities.
For example, one mole of water molecules contains that many water molecules. The mass of one mole of a substance, in grams, is given by its molar mass, a quantity you will meet when studying thermal physics and chemistry related topics.
Candela: The Unit of Luminous Intensity
Luminous intensity describes how bright a light source appears in a particular direction, as perceived by the human eye. The SI unit of luminous intensity is the candela, symbol cd.
Unlike physical quantities such as mass or time, luminous intensity involves human vision. The human eye is not equally sensitive to all wavelengths of visible light. It is most sensitive to green light around a wavelength of 555 nanometres.
The modern definition of the candela uses the power emitted by a light source at a given frequency, weighted by the standardised response of the human eye.
The candela (cd) is defined so that a source emitting monochromatic radiation of frequency
$$540 \times 10^{12}\,\text{Hz}$$
with a radiant intensity of
$$\frac{1}{683}\,\text{W/sr}$$
has a luminous intensity of 1 cd.
Here W is the watt, the unit of power, and sr stands for steradian, the unit of solid angle. The details of these derived units are treated when discussing derived quantities and photometry, but for now it is enough to know that the candela connects physical power of light to perceived brightness.
Why Base Units Matter
Base units serve as the foundation on which the entire structure of measurement in physics is built. Once the base units are defined, all other units can be constructed as combinations of them. For instance, velocity uses metre and second, force uses kilogram, metre, and second, and electric resistance uses kilogram, metre, second, and ampere.
Because the definitions of base units are tied to constants of nature, they are stable in time and space. This ensures that measurements conducted in different laboratories, by different people, and at different times, can be compared consistently.
In further chapters, you will see how these seven base units combine to form derived units and how to convert between different units efficiently. For now, it is important to recognize the names and symbols of these base units and understand which type of physical quantity each one describes.