In 1774, by order of King Charles Emmanuel III, Father Giovanni Battista Beccaria, Italian physicist and mathematician of the Religious Institute of the Piarists, published the essay entitled Gradus Taurinensis in Turin, attributing the length of 112.06 km to the portion of the terrestrial meridian (the length adopted today is 111.137 km).
In order to determine this length, he used geometric-trigonometric methods similar to those formulated by Eratosthenes of Cyrene (circa 276 BC – circa 194 BC), and it is recalling the figure of Father Beccaria, who based this work on references to physical elements and objects, that will help us gain a better understanding of the meaning of the new SI.
The importance of the new International System, in force since 20 May 2019, is truly great, and could even be considered momentous.
As noted by the then president of INRIM (the Italian National Institute of Metrology) Prof. Diederik Sybolt Wiersma: “It is a revolution that will not involve any big shake-up: we will not have to recalibrate our scales and all the other measuring instruments,” today it is no longer physical reference points that establish the new rules of measurement but rather mathematical laws such as the constants of the universe.
Although they will have no effect on our daily life, the revolutionary scope of these new introductions reduces the uncertainties associated defining the units (while retaining the limits produced by the experiment with which the measurement itself is performed).
But, ultimately, what has changed? Why is this new system of units of measurement important?
Let’s try to think about this now:
- the kilogram is defined by setting the value of Planck’s constant (in practice, the kilogram is achieved by comparing the weight force generated by the mass with an electromagnetic force by means of the Kibble balance)
- the mole is defined through Avogadro’s number
- the kelvin is defined by the Boltzmann constant (in practice, special thermometers are used that can measure the parameters of a gas through the speed of sound)
- the ampere is defined by the charge of the electron e (for very small currents, it is in fact possible to define the ampere by counting the electrons that pass through a conductor in a second, one by one).
As for the other three basic units of measurement (metre, second and candela), these were already linked to constants and their definitions, from 20 May 2019, have changed only in form but not in substance. Let’s see how:
| BASE
QUANTITY |
UNIT OF MEASUREMENT | SYMBOL | NEW DEFINITIONS IN FORCE FROM 20/05/2019 |
| time | second | s | The second is defined by taking the fixed numerical value of the caesium frequency ΔνCs (the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom) to be 9 192 631 770 when expressed in the unit Hz (which is equivalent to s−1). |
| length | metre | m | The metre is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458, when expressed in the unit ms−1. |
| mass | kilogram | kg | The kilogram is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10−34, when expressed in the unit Js (which is equal to kg m2 s−1). |
| electric current intensity | ampere | A | The ampere is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10−19, when expressed in the unit C (which is equal to A s). |
| temperature | kelvin | K | The kelvin by taking the numerical value of the Boltzmann constant k, to be 1.380 649 × 10−23 J K−1 (which is equal to kg m2 s−2 K−1). |
| amount of substance | mole | mol | One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number corresponds to the fixed numerical value of the Avogadro constant NA, expressed in mol-1, and is called Avogadro’s number. |
| light intensity | candela | cd | The candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz Kcd, to be 683, when expressed in the unit lm W−1, or in cd sr W−1 (which is equal to cd sr kg−1 m−2 s3). |
The units of measurement of quantities are also coordinated by the International System: just think that in October 1991, four new prefixes were introduced to represent the extremely small [Zetto (10-21) and Yotto (10-24)] and the extremely large [Zetta (10+21) and Yotta (10+24)] requirements of atomic physics and astronomy respectively.
| PREFIX | SYMBOL | ETYMOLOGY | CONVERSION FACTOR | SCALE | DECIMAL |
| YOTTA | Y | from the Greek
ὀκτώ, okto, “eight”, since 1024= 10008 |
1024 | Septillion | 1 000 000 000 000 000 000 000 000 |
| ZETTA | Z | from the Greek letter ζzeta
(from the Greek ζῆτα “seven”, as in Greek numbering, the letter Z was worth 7 even though it was the sixth letter of the alphabet), since 1021= 10007 |
1021 | Sextillion | 1 000 000 000 000 000 000 000 |
| EXA | E | from the Greek ἕξ, hex,
“six” (omitting the h) since 1018 = 10006 |
1018 | Quintillion | 1 000 000 000 000 000 000 |
| PETA | P | from the Greek πέντε,
pente, “five” (omitting the n) since 1015 = 10005 |
1015 | Quadrillion | 1 000 000 000 000 000 |
| TERA | T | from the Greek τέρας,teras, “monster”, or τετρά,
tetra, “quatrain” (omitting the t) since 1012 = 10004 |
1012 | Trillion | 1 000 000 000 000 |
| GIGA | G | from the Greek γίγας, gigas,
“giant” |
109 | Billion | 1 000 000 000 |
| MEGA | M | from the Greek μέγας, megas,
“great” |
106 | Million | 1 000 000 |
| KILO | k | from the Greek χίλιοι, chilioi,
“thousand” |
103 | Thousand | 1 000 |
| HECTO | h | from the Greek ἑκατόν, hekaton,
“hundred” |
102 | Hundred | 100 |
| DECA | da | from the Greek δέκα deka,
“ten” |
101 | Ten | 10 |
| 100 | One | 1 | |||
| DECI | d | from the Latin decimus,
“tenth” |
10−1 | Tenth | 0.1 |
| CENTI | c | from the Latin centus,
“hundred” |
10−2 | Hundredth | 0.01 |
| MILLI | m | from the Latin mille,
“thousand” |
10−3 | Thousandth | 0.001 |
| MICRO | µ | from the Greek μικρός, mikros,
“small” |
10−6 | Millionth | 0.000 001 |
| NANO | n | from the Greek νᾶνος, nanos,
“dwarf” |
10−9 | Billionth | 0.000 000 001 |
| PICO | p | from the Italian piccolo,
“small” |
10−12 | Trillionth | 0.000 000 000 001 |
| FEMTO | f | from the Danish femten, “fifteen”,
since 10−15 |
10−15 | Quadrillionth | 0.000 000 000 000 001 |
| ATTO | a | from the Danish atten, ”eighteen”,
since 10−18 |
10−18 | Quintillionth | 0.000 000 000 000 000 001 |
| ZEPTO | z | from the Latin septem, “seven”, and by deformation since 10−21= 1000−7 | 10−21 | Sextillionth | 0.000 000 000 000 000 000 001 |
| YOCTO | y | from the Greek ὀκτώ, okto, “eight”, and by deformation since 10−24= 1000−8 | 10−24 | Septillionth | 0.000 000 000 000 000 000 000 001 |
Ultimately, redefining the SI units of measurement based on laws of physics that are valid in every part of the universe enables us to give our measurements a stable foundation in space-time. So can we imagine the measurements we make today having the same value even millions of years from now? And will this redefinition really be the last?
