Table Of ContentDe Gruyter Studies in Mathematical Physics 20
Editors
Michael Efroimsky, Bethesda, USA
Leonard Gamberg, Reading, USA
Dmitry Gitman, São Paulo, Brasil
Alexander Lazarian, Madison, USA
Boris Smirnov, Moscow, Russia
Valery A. Slaev
Anna G. Chunovkina
Leonid A. Mironovsky
Metrology and Theory of
Measurement
De Gruyter
Physics and Astronomy Classification Scheme 2010: 06.20.-f, 06.20.F-, 06.20.fb, 03.65.Ta,
06.30.-k, 07.05.Rm, 07.05.Kf, 85.70.Kh, 85.70.Li
ISBN 978-3-11-028473-7
e-ISBN 978-3-11-028482-9
ISSN 2194-3532
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“To measure is to know.”
Lord Kelvin
“We should measure what is measurable
and make measurable what is not as such.”
Galileo Galilei
“Science begins when they begin to measure . . . ”
“Exact science is inconceivable without a measure.”
D.I. Mendeleyev
“. . . for some subjects adds value only an exact match
to a certain pattern. These include weights and mea-
sures, and if the country has several well-tested stan-
dards of weights and measures it indicates the pres-
ence of laws regulating the business relationship in
accordance with national standards.”
J.K. Maxwell
Preface
During the 125th anniversary of the Metre Convention in 2000, Steve Chu, now Pres-
ident Obama’s Energy Secretary and a one-time metrologist, spoke and included the
now famous quotation: “Accurate measurement is at the heart of physics, and in my
experience new physics begins at the next decimal place”.
Metrology, as the science of measures or measurements traceable to measurement
standards [323], operates with one of the most productive concepts, i.e., with the con-
cept of measurement accuracy, which is used without exception in all natural and tech-
nical sciences, as well as in some fields of social sciences and liberal arts.
Metrology, by its structure, can be considered a “vertically” designed knowledge
system, since at the top level of research it directly adjoins the philosophy of natural
sciences, at the average level it acts as an independent section of the natural (exact)
sciences, and at the bottom level it provides the use of natural science achievements
for finding solutions to particular measurement tasks, i.e. it performs functions of the
technical sciences. In such a combination, it covers a range from the level of a knowl-
edge validity criterion to the criterion of correctness in the process of the exchange of
material assets.
For metrology the key problem is to obtain knowledge of physical reality, which
is considered through a prism of an assemblage of quantity properties describing the
objectively real world. In this connection, one of the fundamental tasks of metrology is
the development of theoretical and methodological aspects of the procedure of getting
accurate knowledge relating to objects and processes of the surrounding world which
are connected with an increase in the measurement accuracy as a whole. Metrology,
as the most universal and concentrated form of an organizing purposeful experience,
allows us to make reliability checks of the most general and abstract models of the
real world (owing to the fact that a measurement is the sole procedure for realizing the
principle of observability).
Metrology solves a number of problems, in common in a definite sense with those
of the natural sciences, when they are connected with a procedure of measurement:
the problem of language, i.e. the formalization and interpretation of measurement
results at a level of uniformity;
the problem of structuring, which defines the kind of data which should be used
depending on the type of measurement problem being solved, and relates to a system
approach to the process of measurements;
viii Preface
the problem of standardization, i.e. determination of the conditions under which the
accuracy and correctness of a measurement result will be assured;
the problem of evaluating the accuracy and reliability of measurement information
in various situations.
At present, due to the development of information technologies and intelligent mea-
surement systems and instruments, as well as the growing use of mathematical meth-
ods in social and biological sciences and in the liberal arts, there were a number of
attempts to expand the interpretation of metrology [451] not only as the science about
measurements of physical quantities, but also as a constituent of “gnoseo-techniques”,
information science, “informology” and so on, the main task of which is "to construct
and transmit generally recognized scales for quantities of any nature", including those
which are not physical. Therefore, it remains still important to determine the place of
metrology in the system of sciences and its application domain more promptly, i.e., its
main directions and divisions [9, 228, 429, 451, 454, 503, 506, and others].
It is possible to analyze the interconnection of metrology and other sciences from
the point of view of their interaction and their mutual usefulness and complemen-
tariness, using as a basis only its theoretical fundamentals and taking into account a
generally accepted classification of sciences in the form of a “triangle” with vertexes
corresponding to the philosophical, natural, and social sciences [257], but paying no
attention to its legislative, applied, and organizational branches.
Among such sciences one can mark out philosophy, mathematics, physics, and tech-
nical sciences, as well as those divisions of the above sciences, the results of which are
actively used in theoretical metrology, and the latter, in its turn, provides them with
materials to be interpreted and given a meaning to.
It is known that in an application domain of the theoretical metrology two main
subdivisions can be singled out: the general theory of measurements and the theory of
measurement assurance and traceability.
The general theory of measurements includes the following directions:
original regulations, concepts, principles, postulates, axiomatic, methodology,
terms, and their definitions;
simulation and investigation of objects, conditions, means, and methods of perform-
ing measurements;
theory of scales, measures, metrics, references, and norms;
theory of measurement transformation and transducers;
theory of recognition, identification, estimation of observations, and data process-
ing;
theory of measurement result uncertainties and errors;
theory of dynamic measurements and signal restoration;
Preface ix
theory of enhancement of the measurement accuracy, sensitivity, and ultimate capa-
bilities taking into account quantum and other limitations;
automation and intellectualization of measurement information technologies, inter-
pretation and use of measurement information in the process of preparing to make
decisions;
theory of the optimal planning for a measurement experiment;
theory of metrology systems;
theory of measurement quality estimation, as well as of technical and social-eco-
nomic efficiency of metrology and measurement activities.
The theory of measurement assurance and traceability consists of the following direc-
tions:
theory of physical quantities units, systems of units, and dimensionality analysis;
theory of measurement standards;
theory of reproducing, maintaining, and transferring a size of quantity units;
theory of estimating normalized metrological characteristics of measuring instru-
ments;
methodology of performing metrology procedures;
theory of metrological reliability and estimation of intercalibration (interverifica-
tion) intervals;
theory of estimating the quality of metrology systems, and the methodology of op-
timizing and forecasting their development.
Let the particular features of measurement procedures be considered in the following
order: interaction of an object with a measuring instrument ! recognition and selec-
tion of a measurement information signal ! transformation ! comparison with a
measure ! representation of measurement results.
Interaction of an object under investigation with a measuring instrument assumes
searching, detecting, and receiving (reception) a quantity under measurement, as well
as, if necessary, some preparatory procedures of the probe-selection or probe prepara-
tion type, or exposure of the object to some outside influence for getting a response
(stimulation), determining an orientation and localization in space and time.
Discrimination or selection assume marking out just that property of an object to
which the quantity under measurement corresponds, including marking out a useful
signal against a noise background and applying methods and means for noise con-
trol.
Transformation includes changes of the physical nature of an information carrier or
of its form (amplification, attenuation, modulation, manipulation, discretization and
quantization, analog-digital and digital-analog conversion, coding and decoding, etc.),
as well as the transmission of measurement information signals over communication
