2.2 Physical-metrological fundamentals of constructing the RUTS systemsthe RUTS systems
2.2.5 System of reproduction of physical quantity units
2.2.5.2 The choice of base quantities and base units
Issues of constructing unit systems (SI) in metrological theory and practice have thor- oughly discussed for a long time (for example, in [323, 432, 439]). The concept “sys- tem of physical quantities” (SPQ) can be found in the literature on metrology far more seldomly. Some authors deny the usefulness of introducing and considering such a system. Here, in connection with the problems of constructing a RUTS system and analysing properties of the unit reproduction system, only the separate general issues concerning the interrelation of these systems (quantities and units) will be considered.
1) Although physical quantities and their units can be introducedprincipally at will and a system of physical quantities (as well as a system of units, corresponding to it) can also be constructed principally at will, this is true only for the unlikely sit- uation where someone decides to describe the material world and our surroundings completely disregarding all previous knowledge which mankind has accumulated. In reality, the physical world view (natural science ideology) being the reflection of ob-
jective reality properties has chosen for itself and approved for centuries anentirely definitesystem of ideas concerning this reality. These ideas are based on concepts and quantities reflecting general and stable properties of the environment.
The most general idea consists of the following: a substance exists in time and space, the form of its existence is movement. The base quantities must reflect these funda- mental attributes of this substance. The fundamental laws of conservation (of energy, pulse, linear momentum) are connected with the properties of time and space. Quan- tities such astime,length, andangleare introduced as characteristics of the material objects placed in the space–time continuum.
As to length and time, no one has doubted or doubts that they should be considered as base quantities of SPQ. This also applies for their units.
Unfortunately, up to now there is no any consensus of opinion with regard to the angle and its unit. This is reflected in the International system SI, where not so long ago a specific (and poor-understandable) category of additional units was introduced for angular units. As to the unit of a plane angle, an absurd situation has arisen. On the one hand, it is a dimensionless unit, and on the other hand it has its name, i.e., it reveals properties of a denominate number. The majority of authors continue to consider the plane angle to be a derivative quantity.
However, even from the physical point of view all possible space relations cannot be described only in length. One cannot imagine a real rather than formal combination of linear quantities replacing the angle. Rotational movements are not reduced to forward ones, etc. A detailed review of the angle status and its unit is given in [147]. The results of an analysis contained in this review, as a whole, also testify to the usefulness of recognizing it as a base unit of the SPQ. Let us consider that the space–time properties of the material world required the introduction of three base (independent) quantities:
L– length,T – time,ˆ– angle (plane).
2) The next, not less general attribute of substance is movement. It is comprehen- sible for our perception through an interaction, the measure of which is theenergyE which is one of the basic general concepts of the physical world view.
It would be possible to consider only the set of quantities (L,T,ˆ,E) as the main (initial) concepts for describing external objects, if there were not a variety of forms in which energy demonstrates itself (mechanical, electromagnetic, thermal, nuclear, etc. Although all these forms of energy are related toone genericconcept, they are so specific that frequently it is very difficult to connect them. The inaccuracy of corre- sponding equivalents causes a specific quantity, characterizing a corresponding type of interactions and a sphere of events connected with energy to be introduced into each specific field where energy is revealed.
In mechanics where gravitationalinteraction is the determinant factor, it is body (object) mass (m). Here, we will not dwell on all the minute details of the difference
Section 2.2 Physical-metrological fundamentals of constructing the RUTS systems 151 between gravitational and inertial mass, the more so as the general theory of relativity shows (postulates) their equivalents.
In electrodynamics the main type of interaction iselectromagneticinteraction. The main source of an electromagnetic field is an electriccharge,q, and as the base quantity either a charge or a speed of its changing with time, i.e.,electric current(I), should be chosen.
In thermodynamics the characteristic features are the interactions of a statistic nature connected with an energy exchange between macrosystems. The extent of macrosys- tem energy variation in the processes of heat exchange is characterized bytemperature (‚) that is also chosen as the base quantity.
Optical phenomena are a variety of electromagnetic interactions. Therefore, to in- troduce into the SI a unit of light (candela) as a base unit is caused not so much by any objective necessity connected with the specificity of the phenomena in optics, as by the need to measure some light characteristics (visible region of the optical spectrum) connected with a subjective perception of light fields by the eye. They are, as a matter of fact, off-system quantities and units.
The interactions which at present are the most complicated and difficult to under- stand are in the field of nuclear phenomena (weak and strong), particularly, strong interactions, which are difficult to characterize using physical quantities. For weak in- teractions it is possible in the capacity of the base characteristic to choose theactivity of radionuclides which characterize the speed of a radioactive decay (a result of weak interaction).
In the fields of physics and chemistry a quantity of substance is considered as the base one; its unit is the mole. However their role in the system of physical quantities is uncertain and debatable to an extent that a great number of specialists are disposed to remove them from the category of base quantities.
Let us note that the mole, according its present definition, is simply a scale coeffi- cient linking the macromass unit (kilogram) with the unit of atomic (micro) mass.
Thus, in the light of today’s physical world view, as the base quantities of the system of physical quantities it is possible to accept the following: L (length), ˆ (angle), T (time),M (mass),I (electrical current),‚(temperature),A(radionuclide activity).
3) It is possible to show that the concept of dimension is related both to the units and quantities. Dimension serves as it were as a qualitative characteristic of a physical quantity, determining its gender. In this connection two aspects are important.
Firstly, the removal of base quantities (or the ungrounded decrease of their num- bers) from the system can lead to the situation of heterogeneous quantities having similar dimensions. This is not permissable in an exact science. This is exactly what happens, when the plane angle is excluded from the category of base quantities, which is evidence of its base quantity and unit status.
Secondly, since the quantity and its unit are homogeneous concepts and must be expressed in terms of the denominate number of one type, an ambiguous link between the physical quantity and its unit in the system of the SPQ $ SU type cannot be
permittted. At the same time, such is indeed the case of many speed (rotation, flow) and counting quantities, where quantities of a quite different physical nature are expressed in terms of similar units. This was noted more than once, for example in [190].
4) The practice of implementing the measurement standards of base unit reproduc- tion shows that frequently as the base unit adopted by convention for the system of units, a completely different unit is reproduced. This can be accepted, as a rule, with the following explanation. The base units are chosen on the basis of expediency, sim- plicity, and commonness of the material world description, while the base units are adopted due to practical considerations, primarily when achieving the highest accu- racy is necessary, i.e., on the basis of somewhat different criteria. At the same time, transfers from the reproduction of the base units adopted by convention to the most accurate ones of the other type are always realized on the basis of their tight intercon- nection through fundamental physical constants (FPC) (comp.: Ampere, Volt, Ohm and; length, frequency andc0).
At the same time, thenumber of base units(the base ones in a given field)remains unchanged. Therefore, it is useful to formulate the following rule:the number of base units must be equal to the number of base quantities of a system; the number of base units adopted by convention has to be equal to the number of units reproduced in the real RUTS system.