157
quantity characteristic of a class of objects guarantees both its stability and accessibility. And if the identified constant were too far from the anthropometric scale to
be suitable, the reference quantity could be defined as an appropriate multiple or
submultiple of the constant, so as to maintain a principle of continuity, such that
different definitions could subsequently be adopted while ensuring that the defined
reference quantity remains the same. For example, in 1960 the 11th General
Conference of Weights and Measures redefined the metre as “the length equal to 1
650 763.73 wavelengths in vacuum of the radiation corresponding to the transition
between the levels 2p 10 and 5d 5 of the krypton 86 atom” (BIPM, 2019: Appendix 1).
The critical point of this definition is the assumption that the chosen radiation has a
constant wavelength, whereas the numerical value, 1 650 763.73, was only chosen
precisely for the purpose of guaranteeing that the metre remained the same length
despite the change of its definition.
17
By exploiting the functional relations that are known to hold among quantities, a
more sophisticated version of this strategy allows for the definition of a reference
quantity as a function of constants of different kinds, and possibly of previously
defined reference quantities. For example, according to Einstein’s theory of relativity the speed of light in vacuum is constant, and so the class of all light beams in
vacuum is such that the length of their path in a given time interval is also constant.
By exploiting the relation
length speed time duration
=
·
among general quantities, the definition is then
l ref := R
S
T
[ ]∆
where S[R] is the speed of light in vacuum (R then being intended as the class of all
light beams in vacuum) and ΔT is the chosen time interval. This is in fact how in
1983 the 17th General Conference of Weights and Measures defined the metre: “the
length of the path travelled by light in vacuum during a time interval of 1/299 792
458 of a second” (BIPM, 2019: Appendix 1). Once again, the appropriate choice of
the numerical value, 1/299 792 458, was the condition of validity of the principle of
continuity.
With the aim of emphasizing the role of the defining constant quantity S[R], this
definition can be rephrased as
the reference length is such that R
ref
r ef
l
l
S
T
[ ]=
−
∆
1
17 This is one more case in which the distinction between sense and reference (see Sect. 5.3.2) is
relevant. The assumption of validity of the principle of continuity can be written as
metre 1889 = metre 1960 , in which the fact that the metre was defined in different ways in 1889 and in
1960 makes the senses of the two expressions (“the metre as defined in 1889” and “the metre as
defined in 1960”) different, while their referents are the same.
6.3 Constructing values of quantities
quantity characteristic of a class of objects guarantees both its stability and accessibility. And if the identified constant were too far from the anthropometric scale to
be suitable, the reference quantity could be defined as an appropriate multiple or
submultiple of the constant, so as to maintain a principle of continuity, such that
different definitions could subsequently be adopted while ensuring that the defined
reference quantity remains the same. For example, in 1960 the 11th General
Conference of Weights and Measures redefined the metre as “the length equal to 1
650 763.73 wavelengths in vacuum of the radiation corresponding to the transition
between the levels 2p 10 and 5d 5 of the krypton 86 atom” (BIPM, 2019: Appendix 1).
The critical point of this definition is the assumption that the chosen radiation has a
constant wavelength, whereas the numerical value, 1 650 763.73, was only chosen
precisely for the purpose of guaranteeing that the metre remained the same length
despite the change of its definition.
17
By exploiting the functional relations that are known to hold among quantities, a
more sophisticated version of this strategy allows for the definition of a reference
quantity as a function of constants of different kinds, and possibly of previously
defined reference quantities. For example, according to Einstein’s theory of relativity the speed of light in vacuum is constant, and so the class of all light beams in
vacuum is such that the length of their path in a given time interval is also constant.
By exploiting the relation
length speed time duration
=
·
among general quantities, the definition is then
l ref := R
S
T
[ ]∆
where S[R] is the speed of light in vacuum (R then being intended as the class of all
light beams in vacuum) and ΔT is the chosen time interval. This is in fact how in
1983 the 17th General Conference of Weights and Measures defined the metre: “the
length of the path travelled by light in vacuum during a time interval of 1/299 792
458 of a second” (BIPM, 2019: Appendix 1). Once again, the appropriate choice of
the numerical value, 1/299 792 458, was the condition of validity of the principle of
continuity.
With the aim of emphasizing the role of the defining constant quantity S[R], this
definition can be rephrased as
the reference length is such that R
ref
r ef
l
l
S
T
[ ]=
−
∆
1
17 This is one more case in which the distinction between sense and reference (see Sect. 5.3.2) is
relevant. The assumption of validity of the principle of continuity can be written as
metre 1889 = metre 1960 , in which the fact that the metre was defined in different ways in 1889 and in
1960 makes the senses of the two expressions (“the metre as defined in 1889” and “the metre as
defined in 1960”) different, while their referents are the same.
6.3 Constructing values of quantities