International System base units

There are seven base units –one for each of the seven base quantities– in the International System of Units (SI) representing, by convention, the following physical quantities: length, mass, time, electric current, temperature, amount of substance, and luminous intensity 1,2.

Names, symbols, and dimensions for SI base units

base quantity	unit name	unit symbol
† this official name for all English-speaking nations is officially misspelled as meter in the United States –see, for instance NIST publications 3– †† also flux or flow
length	metre†	\( \mathrm{m} \)
mass	kilogram	\( \mathrm{kg} \)
time	second	\( \mathrm{s} \)
electric current††	ampere	\( \mathrm{A} \)
thermodynamic temperature	kelvin	\( \mathrm{K} \)
amount of substance	mole	\( \mathrm{mol} \)
luminous intensity	candela	\( \mathrm{cd} \)

The SI introduces a definition for each seven base unit. For instance, the second is defined as:

The second is the duration of \( \scriptstyle 9192631770 \) periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

However, this definition of the second lacks rigour because omits measurement conditions such as environment temperature and dynamical state of the atom. Specially problematic is the definition of the kilogram, which is based in a prototype held in Paris. New definitions of the base units are being examined by the CIPM and may be considered at the 25th meeting of the CGPM, scheduled for 2014.

The reference 3 states that:

The SI is founded on seven SI base units for seven base quantities assumed to be mutually independent

However, the base quantities are not independent at all. The SI definition of the metre reads:

The metre is the length of the path travelled by light in vacuum during a time interval of \( \scriptstyle 1/299 792 458 \) of a second.

which implies a functional dependence upon the unit of time \( \mathrm{m} = (c/299 792 458) \;\mathrm{s} \). Similar functional relationships are found for other base units; e.g., the ampere could be derived using physical laws and the value of the elementary charge.

The role of the mole as SI basic unit has been also subject to some criticism. However, the critics seems to be overlooking some basic aspects behind the concepts of unit mole and of amount of substance 4,5. For a defense of the concept of mole against such critics see 6.

Metre or meter? As noticed in the above table, the SI unit metre is misspelled as meter by the NIST 3. This official misspelling is guided by unacceptable economic and political motives, as Pat Naughtin has denounced.

Effectively, early North Americans as Benjamin Franklin, Thomas Jefferson, and John Quincy Adams all used the spelling metre in accordance with the universal spirit behind science. However, a change in the spelling of several words was first actively promoted by Noah Webster in 1828 with the publication of An American Dictionary of the English Language. Among the political motives that he promoted, we remark the following:

Besides this, a national language is a band of national union. Every engine should be employed to render the people of this country national; to call their attachments home to their own country; and to inspire them with the pride of national character.

As an independent nation, our honour requires us to have a system of our own, in language as well as government. Great Britain, whose children we are, and whose language we speak, should no longer be our standard [...] Numerous local causes, such as a new country, new associations of people, new combinations of ideas in arts and sciences, and some intercourse with tribes wholly unknown in Europe, will introduce new words into the American tongue.

And, among the economic motives 7 that he promoted, we emphasize the next:

But a capital advantage of this reform in these states would be, that it would make a difference between the English orthography and the American. This will startle those who have not attended to the subject; but I am confident that such an event is an object of vast political consequence. For, the alteration, however small, would encourage the publication of books in our own country. It would render it, in some measure, necessary that all books should be printed in America. The English would never copy our orthography for their own use; and consequently the same impressions of books would not answer for both countries. The inhabitants of the present generation would read the English impressions; but posterity, being taught a different spelling, would prefer the American orthography.

As a consequence, Chester H. Page –editor of the (UK) National Physical Laboratory English language translation of Le Système International d'Unités– refused to appear on the American version when the United States Government Printing Office insisted that the American spelling of metre is meter. Fortunately, the debate still continues within the United States, with an increasing number of people calling for an acceptance of the international standards.